Cordership Discussion Thread

[wwei47]

Here is a period 192 sideways rake which I think is smaller than previous ones.

This one isn't smaller, but it demonstrates that the 4-in-a-row cordership can also be used to make P192 rakes.

Code: Select all

x = 110, y = 108, rule = B3/S23
38b5o7bo$36b2o5b2o4bobo$36bo7bo4bo$36b2o7bo3bo2bo$38b2o6bo3b3o$41bo$
41bo4bo13b2o$42b2obo14b2o3$29b2obo$28b3obo6bobo$27bo4bobo4bo$28b2o6bob
o3bo$29bo3bo2bo2b2o16bo3bo6b2o$32bob2o3bo15bo2bob3o5b2o$31bobo24bobobo
$31bobo12bobo7bo$40b2o4b3obob2ob2o$40b2o6bo2b2o3bobo3bo$56bobo4$82bo$
49b2o31bo$36bo9bob4o30bob3o$12bo18bo3b5o5b2obo3b2o30b3o$11bobo16bob3o
5b2o4bo2b2ob2o31bo13b3o$10b2ob2o17bo5bob2o5b6o32b2o$10b2o16bo5bo5b2o6b
o37bo$16b2o9bo7b5o46b2o13bo$10b3o2bo12b2o7b3o60b2o$14bob2o10bo42bo11b
2ob2o11b3o6b2o$12bo2bo12bobo38b2ob2o10b3o12bo8b2o$15bo11bo3bo52bo12bo$
b3o9b2o11b2o3bo18b3o19b2o23bo3b2o$bobo23bo3b2o40bo27b2o$o3bo8bo13bobob
2o10b2o3bo5bo12bo3bo15b2o9bo$o3bo6b2ob2o11bo3b2o9bo2bo2bo5bo16bo3bo11b
2o10bo2bo$o13bo3b2o8b3o12b2o3bo5bo44b3o$o4b2o4bo6b2o8b3o$o6bo5bo25bo
10b3o16bo$bo5bo30bobo29b3o$b2o35bobo$3bo3bo19bo11bo48bo$4bobo10b2o7b3o
41b3o13bobo$18bo10bo40b3o13bobo$17b3o6b2ob2o7b3o29b2ob2o12bo$b3o21b2ob
2o44bo12b2o$o3bo13bo6b2ob2o6bo5bo29b3o14bo$bo2bo14bo6bo2bo6bo5bo44b2o$
3b2o13b2o7b3o6bo5bo43bobo$18bo8b2o57bobo$38b3o47bo$15bo2bo65bobo$17b4o
63bo$14bo68bobo$15b2o2b2o54b2o6b2o$75b2o5bo$6b2o7b2o66b2o$6b2o6b2o33bo
14b2o18bo$15b2o2bo29bo14b2o$49bo$53bo12bo$49b3o2bo10b2o$48bo4bo11bo17b
2o$48bo3bo30b2o$14b2o33b3o$14b2o19bo30b3o$35bo7bo20b2ob3o$35bo5b3o4bob
o13b2o2bo$34b2o3bobo6bobo13b2ob2o4b2o$40bo2bo4bobo14bobo5b2o$39bo2b2o
4bobo15bo$49b2o3$46b2o$37b2o7b2o$37b2o25bo$63bobo$63bobo$27bo35bobo$
27bo36b3o$27bo39b3o$31bo35b2o$27b3o2bo$26bo4bo$26bo3bo$27b3o10bo$39bob
2o$39bob3o$26bobo11bo3bo$26bobo12b3o$26bobo13bo$26bobo11bo$27b2o10bobo
$39bob2o2$45bo3b2o$41b2ob3o2b2o$39bo6bo$39b2o5bo$44bo2$31b2o$31b2o!

This does however make me wonder if there are any other corderships like it; glider feedback loops aren't exactly baked into any of the corderships that are being used to shuttle around gliders, and high-period puffers can be cleaned up with enough corderships and corderrakes. Meanwhile, the 4-in-a-row cordership seems to "just be P192"; its period-doubler is baked into the cordership itself, without any assistance "from outside".

[dbell]

The edge-sparks from the new Cordership can turn other gliders besides the sideways ones.

In particular it can turn backward gliders into either forward or sideways gliders.

Code: Select all

#C A Cordership turning a backward glider into a sideways glider.
x = 95, y = 77
64boobo$63b3obo6bobo$62bo4bobo4bo$63boo6bobo3bo$64bo3bobbobboo$67boboo
3bo$66bobo16boo$66bobo16boo7$93boo$84boo7boo$71bo9bob4o$66bo3b5o5boobo
3boo$65bobo7boo4bobbooboo$65bo7boboo5b6o$66bo8boo6bo$67bo3b4o$72b3o$
56bobo9boo$56bobobo6bobo$55bobboobo4boo$56boo3boboboobo$56boo3boob5o$
60boboo3boo$59bobo3$o$boo$oo4$65bo$50bo14boo$50bo15boo$50bo15boo$53boo
10bo$53boo10bo$48bo3b3o$49b3o$50bo22boo$49boo22boo$40bo8b3o$32b3o3b4o
9bo$32bobo3booboo6bo$32b3obbo13bo$37boo3bo6b3o$38b4o$39b3o$$73boobboo$
73b6o$73boobboo5$45b3o$44bobbo$35bo4boboo4bo$34bobobobb3o3boobo$36bobo
bobbo3bo3bo12bo$35boobo5boob4o13bobo$37b3o7boo15boo$46boo5$56boo$56boo
!

Code: Select all

#C A Cordership turning a backward glider into a forward glider.
#C The return lane is shifted by one half-diagonal, similar to a
#C kickback reaction.
x = 101, y = 77
70boobo$69b3obo6bobo$68bo4bobo4bo$69boo6bobo3bo$70bo3bobbobboo$73boboo
3bo$72bobo16boo$72bobo16boo7$99boo$90boo7boo$77bo9bob4o$72bo3b5o5boobo
3boo$71bobo7boo4bobbooboo$71bo7boboo5b6o$72bo8boo6bo$73bo3b4o$78b3o$
62bobo9boo$62bobobo6bobo$61bobboobo4boo$62boo3boboboobo$62boo3boob5o$
66boboo3boo$o64bobo$boo$oo7$71bo$56bo14boo$56bo15boo$56bo15boo$59boo
10bo$59boo10bo$54bo3b3o$55b3o$56bo22boo$55boo22boo$46bo8b3o$38b3o3b4o
9bo$38bobo3booboo6bo$38b3obbo13bo$43boo3bo6b3o$44b4o$45b3o$$79boobboo$
79b6o$79boobboo5$51b3o$50bobbo$41bo4boboo4bo$40bobobobb3o3boobo$42bobo
bobbo3bo3bo12bo$41boobo5boob4o13bobo$43b3o7boo15boo$52boo5$62boo$62boo
!

The forward one allows this interesting spaceship to be made.

Code: Select all

#C Two Corderships playing ping-pong with a glider.
#C The back Cordership uses an edge-spark to turn a backward
#C glider into a forward glider.  The front Cordership uses a
#C tub-deletion-to-release-a-glider reaction to turn a forward
#C glider into a backward glider.  Combining these results in a
#C spaceship where a glider travels back and forth between the
#C two Corderships.  This particular spaceship has period 768 but
#C other periods should be possible by adjusting the Corderships.
#C David I. Bell, 27 May 2025
x = 190, y = 135
53bo$52b3o$51boobbo$50boobboo$51boo$52b5o$56boo$54bobbo$55boo12boo$69b
oo4$53b3o$53bobo$53bo$53bobbo20boo$54bobo20boo$55b3o$57boo$51b3o4boo$
57boo$$45b3o$44bobbo$43bo4bo$43bobb3o$43bo5bo$44b7o$50bo$50bo$48boo10$
28bo$27boboo$31bo$25bo3bobbo$23bo9bo5bo$23bo4boobboo4bobo$32boo5bo$5bo
19bo5bo$4bobo19bo4b3o$4bobboo18bo4boo$bb7o14bo5b4o$bobbo3bo14bo$3obb7o
11bo$bb3obbo8bo$3booboo8bo147bo$4b3obobbo151b3o$5b3oboo13boo136booboo$
8bo13boobo135boobobo$21bo3bo134b3obb3o$21bobboo135bo6bo$22b3o137b5obo$
23bo139b4oboo$168bo$167bo12boo$180boo3$165bo$11boo150boobo$11boo$166bo
$163bobbo21boo$164bo23boo$$169boo$162b3o5boo$19boo148boo$19boo135b3o
10bo$155bo3bo$154bo4bo$153bo3bo$153bobbob3o$153bo7bo$155bo3bobo$155bo
3boboo$157b3oboo5$157boo$157boo$158bo$159boo$159bobo$159b3o$158bobo$
156boo$157bo$158b5o$159b4o$160boo$143b3o8bo$142bo3bo6boo13boo$143boo8b
obbo5boo4boo$145booboo4bob3o3boo$131bo15boo7b5oboo$130bobo25b5o$129boo
boo26boo$129booboo$128b3o$128b3o3bo41boo$128b3o4bo40boo$129boo5bo10bo
22boo$113bo15b3o15bo22boboo$114bo15boo15bo25bo$112b3o16boo38bobo$166bo
bobboo$166boo$131bo13bo21bo$130b3o11b3o$129bo3bo9boo$133boo7b3o$132boo
8b3o9$151boo$151boo!

I haven't yet figured out how to make the adjustments to change the period. It is complicated by the fact that the tub deletion reaction is not always safe.

I looked for a simple glider reflection using the two-engine Cordership, but none of the reflections had both the right lane and phase. So I resorted to the tub deletion reaction whose phase is adjustable.

If I'm not mistaken, this is the lowest population adjustable high period Cordership, having about 363 cells.

EDIT:

I have determined one way to adjust the spacing (and thus the period).

Here is another in the series of ping-pong spaceships describing how.

Code: Select all

#C Two Corderships playing ping-pong with a glider.
#C The back Cordership uses an edge-spark to turn a backward
#C glider into a forward glider.  The front Cordership uses a
#C tub-deletion-to-release-a-glider reaction to turn a forward
#C glider into a backward glider.  Combining these results in a
#C spaceship where a glider travels back and forth between the
#C two Corderships.  This particular spaceship has period 1632.
#C Shifting the topmost Cordership by 32 cells will change the
#C period by 288 generations.  The spaceship is also shown at its
#C minimum population of 350 cells.
#C David I. Bell, 27 May 2025
x = 281, y = 227
48b3o$49bo$49bobbo$49bobbo$50bobo$65boo$65boo3$49bo$48bobo$49bo$66bo$
65bo7boo$47b4o22boo$47boo3bo10bo$48bo4bo9bobo$50boboo10bo$51bo3$59bobo
boo$42bo16bobo$41b3o17bobbo$60bo3bo$41b3o16b4obboo$42booboo14bo5boo$
44bo21bo13$25bo$24b3o$23booboo7bo$22boo3bo6bobo$23bobobobo5bo$24boobo
bbo$27boobo$bbo25boo12bobo$bobo39boo$o3bo13b3o22bo$o3bo8bo$obob3o4boob
3o$boobobbo5boboo$5bobo8bo$5boo11bobbo$18b3o11$7boo$7boo7$15boo$15boo
74$254b3o$253bo3bo$252bo3boo$253bo$254b4o$256boboo$256bobbo$257boo12b
oo$271boo3$256bo$256bo$255bobo$256bo$256boo21boo$256b3o20boo$$254bo4b
oo$254bo5bo$254bo5bo$259bo$248bo$247b3o$246boobbo$245boobboo$246boo$
247b5o$251boo$249bobbo$250boo5$248b3o$248bobo$248bo$248bobbo$249bobo$
248boobbo$250bobo$246bobboobbo$247bobbobbo$251bobo$$235bo$235b4o5boob
oo3bo6boo$235bo3bo5boboobboo6boo$246booboobbo$237b3o10bobo$251boo$221b
3o$221bobbo$224bo$221boo44boo$220bobo44boo$221bobb3o34boo$222boobbo10b
3o21boo$222bo3bo33bobbo$223bobo31bobboboo$225bo30bobbo$222bobbo10bo20b
obo$222bo9boo3bo$237bo$221boobbo4bo3bobboo$222b3o4bo5bo$230bo4bo$235bo
$233bo7$242boo$242boo!

The adjustment change of 288 generations is three times the base 96 period of the Corderships. I don't know if there is any more complicated adjustment to get the missing periods.

The minimum population of 350 does beat the other known high period spaceship series. Here is my effort of producing the minimum population spaceship for that.

Code: Select all

#C A high period Cordership based on turning a forward glider into a
#C boat and then back again.  This is shown at its minimum population
#C of 432 cells.  This is an optimized version of a previous spaceship.
#C This spaceship has a period of 3840.  Shifting the topmost Cordership
#C by 16 cells changes the period by 288 generations.
#C David I. Bell, 27 May 2025
x = 322, y = 319
12bo$12bo5b3o$11bobo3boobbo$12bo3bo5bo$12bo3bo$17bobboo$18boo11boo$31b
oo7$b3o35boo$b3o21bo13boo$bbo12boo9boo$3boo9bob3o8boo$4bo9bo3bo10bo$3b
o11boobo5b5o$16bo10bo3$boo$boo$bbo$bbo$bobo$o$bobboo$bbo3bo$4boo$4bo7$
6boo$6boo$19bo$19b3o$20boo$20bo$$18boobo$18b4o$20boo61$301bo$287boo7b
oobbobo$287b3o6b4o3bo$287boobobo7bo$290boo10boboo$302bobo$303bo8boo$
312boo4$275bo$273booboo$275bo$290boo$289bobbo$276boo11booboo$275bobbo
11bo$274boo3bo10b3o26boo$274bo4bo34boo3boo$274bo3bo36b3obboo$275bobbo
36boobb3o$276bo$$254boo36bo$255bobbo4bo24bo3bo$252bobb3obobbobo24bobbo
$252bobbo4b4o25booboo$252bobbo34bobo$255bo6bo28bo$254boobo$262bo11boo
3boo$260boo12boo3boo5$245bo$244bobo$244bobo35boo3boo$244bobbo34boo3boo
$245bobo23bo$248bo22bobo$247boo6bobbo12b3o$247bo8b3ob3o10bo$256boobobo
$258b3o$259boo$245bo$244bobo$246bo$246bo$246bo$$247bo42bo$243boob3o39b
oo$245b3oboo38boo$248bo7$249boo$249boo$264bo$262boobo$261bo4bo$260bo4b
o$260bo5bo$261boo3bo$262boobbo$264bo13$274bo$272boo$273boo21$248boo$
247boo$249bo7$258bo$256boo$257boo41$235bo$235bo5b3o$234bobo3boobbo$
235bo3bo5bo$235bo3bo$240bobboo$241boo11boo$254boo7$224b3o35boo$224b3o
21bo13boo$225bo12boo9boo$226boo9bob3o8boo$227bo9bo3bo10bo$226bo11boobo
5b5o$239bo10bo3$224boo$224boo$225bo$225bo$224bobo$223bo$224bobboo$225b
o3bo$227boo$227bo7$229boo$229boo$242bo$242b3o$243boo$243bo$$241boobo$
241b4o$243boo!

If another small Cordership could be found with the appropriate forward to backward glider reflection reaction, then it might beat the population 350 one shown here. I haven't examined the three-engine Cordership, for example.

EDIT 2:

There is a third high period spaceship series known which I had forgotten about until now.

Here is my optimization of that one, whose lowest population lies between the two shown above.

Code: Select all

#C A high period Cordership based on turning a forward glider
#C into a loaf then back again.  This is shown at its minimum
#C population of 409 cells.  This is an optimized version of a
#C previous spaceship.  This spaceship has a period of 2304.
#C Advancing the topmost Cordership by 64 generations changes
#C the period by 96 generations.  Only every third advancement
#C produces the lowest population, however.
#C David I. Bell, 28 May 2025
x = 214, y = 206
14bo$13bobo5bo$19booboo$13b3obbo3boo$19booboo$19b4o$33boo$33boo7$4bo
36boo$bbooboo34boo$26b3o$5boo9b4o4b4oboo$6bo9boboboo4boobbo$o3bo12boo
9b3o$4bo3bo10bo3bobo3$bbo$3b3o3$3b3o$3b3o$3booboo$7bo$5b3o8$8boo$8boo
$$20b3o$22boo$$21bo$21bo$21b4o$19bo10$149bo$135boo7boobbobo$135b3o6b4o
3bo$135boobobo7bo$138boo10boboo$150bobo$151bo8boo$160boo4$123bo$121boo
boo$123bo$138boo$137bobbo$124boo11booboo$123bobbo11bo$122boo3bo10b3o
26boo$122bo4bo34boo3boo$122bo3bo36b3obboo$123bobbo36boobb3o$124bo$$
140bo$136bo3bo$137bobbo$137booboo$138bobo$139bo$$127boo$127boo7$135boo
$135boo$$188bo$174boo7boobbobo$174b3o6b4o3bo$174boobobo7bo$177boo10bob
oo$189bobo$190bo8boo$199boo4$162bo$160booboo$162bo$177boo$176bobbo$
163boo11booboo$162bobbo11bo$161boo3bo10b3o26boo$161bo4bo34boo3boo$161b
o3bo36b3obboo$162bobbo36boobb3o$163bo$$179bo$175bo3bo$176bobbo$176boob
oo$177bobo$178bo$$166boo$166boo7$174boo$174boo5$172b3o$172bo$173bo10$
185bo$185bo5b3o$184bobo3boobbo$185bo3bo5bo$185bo3bo$190bobboo$191boo
11boo$204boo7$174b3o35boo$174b3o21bo13boo$175bo12boo9boo$176boo9bob3o
8boo$177bo9bo3bo10bo$176bo11boobo5b5o$189bo10bo3$174boo$174boo$175bo$
175bo$174bobo$173bo$174bobboo$175bo3bo$177boo$177bo7$179boo$179boo$
192bo$192b3o$193boo$193bo$$191boobo$191b4o$193boo!

The bottom Cordership is only present to delete extraneous blocks. If it is removed then we get a high period block puffer.

Code: Select all

#C A high period Cordership block puffer based on turning a forward
#C glider into a loaf and back again.  This is shown at its minimum
#C population of 311 (ignoring any produced blocks).  This is an
#C optimized version of a previous puffer.  This puffer has a period
#C of 2304.  Advancing the topmost Cordership by 64 generations
#C changes the period by 96 generations.  Only every third advancement
#C preserves the lowest population, however.
#C David I. Bell, 28 May 2025
x = 209, y = 141
14bo$13bobo5bo$19booboo$13b3obbo3boo$19booboo$19b4o$33boo$33boo7$4bo
36boo$bbooboo34boo$26b3o$5boo9b4o4b4oboo$6bo9boboboo4boobbo$o3bo12boo
9b3o$4bo3bo10bo3bobo3$bbo$3b3o3$3b3o$3b3o$3booboo$7bo$5b3o8$8boo$8boo
$$20b3o$22boo$$21bo$21bo$21b4o$19bo10$149bo$135boo7boobbobo$135b3o6b4o
3bo$135boobobo7bo$138boo10boboo$150bobo$151bo8boo$160boo4$123bo$121boo
boo$123bo$138boo$137bobbo$124boo11booboo$123bobbo11bo$122boo3bo10b3o
26boo$122bo4bo34boo3boo$122bo3bo36b3obboo$123bobbo36boobb3o$124bo$$
140bo$136bo3bo$137bobbo$117boo18booboo$116bobbo18bobo$116bobo20bo$117b
o$127boo$127boo7$135boo$135boo$$188bo$174boo7boobbobo$174b3o6b4o3bo$
174boobobo7bo$177boo10boboo$189bobo$190bo8boo$199boo4$162bo$160booboo$
162bo$177boo$176bobbo$163boo11booboo$162bobbo11bo$161boo3bo10b3o26boo$
161bo4bo34boo3boo$161bo3bo36b3obboo$162bobbo36boobb3o$163bo$$179bo$
175bo3bo$176bobbo$176booboo$177bobo$178bo$$166boo$166boo7$174boo$174b
oo!

I think this is the lowest population high period adjustable period puffer known. It is also notable in that it contains no rakes.

BCNU,
-dbell

[dbell]

Here is a (possibly new?) period 192 puffer.

Code: Select all

#C A four-engine diagonal c/12 period 192 blinker puffer.
#C This uses a two-engine Cordership and a two-engine wing component
#C whose interaction results in a period doubling to produce blinkers.
#C This is shown at its minimum population of 182 cells, excluding
#C any output blinkers.
#C David I. Bell, 29 May 2025
x = 87, y = 67
57bo$57bo$59bo5bo$58bo6bobo$57bo3bobbo$58bobboboboo$63boboo$77boo$77b
oo5$14boo$$13bo3bo67boo$18bo66boo$11bo7bo46boo3bo$10bo4bo48b3o4boo$11b
obobo4bo38b3obo8boo$11bo8bo42bobobb5o$12bo4boobo43bo3b3o$13boboob3o$
14b3oboo$31boo18bo$31boo18bo7bo$51bo5b3o$50boo3bobo$56bobbo$55bobboo3$
39boo$39boo$bbo18boo31bo$bbo11bo5bobboo28bobo$bobo10bo4b3obbo29bo$bboo
bbo7bo4bo4bo$bo5bo11b5o$bo5bo12boo$bo4bo$5bo$bb3o3$ooboo$5bo$oo$bb3o9$
6boo14bobo$6boo14bobbo$22bobbo$$19b3o$18bo$18bo$18bo3bo$14boobbo3bo$
14boo4bobo!

Here is a nice reaction using the puffer.

Code: Select all

#C The phase of a diagonal c/12 period 192 rake can be changed.
#C This can be done by using a forward glider to delete a temporary
#C tub which is produced by the puffer.
x = 99, y = 81
62bo$62bo$62bo$66bo12bo$62b3obbo10boo$61bo4bo11bo$61bo3bo$62b3o$79b3o$
77boob3o$61bobo13boobbo$61bobo13booboo4boo$61bobo14bobo5boo$61bobo15bo
$62boo4$15b3o60bo$77b3o15boo$13bo5bo56b4o$13b7o12bo42boo21bo$15bo17boo
33bobo5bo4boo9bo3b3o$15bo3bo13boo37bo10bo12boo$14bo17boobo18b3o9boo3b
oo10bo8boo$15bo18b3o29bobb3obo9bo$16bo4bo11boboo18bo10b3o3b3obobbo3bo$
16bo4bo11boo20boob3o11b6o4bo$15boobobo12bo6boo12bob4o15bo$14bobo23boo
12bob3o18bobbo$15bo39b3o20bo$56bo3$53booboo$53booboo$b3o50boboo$o3bo
25b3o15bo6boo$boo29bo10boboboboo$3booboo23bobbo8bob3oboo$5boo25booboo
6bo5boo$33bo11b4o$36bo9boo$36bo$32bo3bo$36bo$32bo3boo16bo$28boo3boobo
17bo$27bobboo3bo18bo$26boo3bo$26boobobo$24b3obboo$23b3o$7boo13boo$7boo
9boobboo$$18boobbo$20b3o$85b3o$85bo$86bo$15boo$15boo53bo$70bo$70bo14$
86bo$86bo$86bo!

Another Cordership can be added to the puffer to delete the blinkers to make a six-engine period 192 Cordership.

Alternatively, a period 192 sideways rake can be made by deleting the blinkers with a sideways period 96 rake. There are simpler period 192 rakes, but this one can change its phase by using the above reaction.

BCNU,
-dbell

[dbell]

My previous ping-pong post was getting a bit long so I started another one.

By adjusting the rightmost switch engines I found a smaller version of the edge-spark spaceship.

Code: Select all

#C A diagonal c/12 period 96 edge-sparking Cordership.
#C This uses four switch engines to produce a two-bit spark on its
#C edge which can be used to turn a sideways glider into either a
#C forward glider or a backward glider, and can turn a backward
#C glider into either a sideways or forward glider. The spaceship is
#C shown at its minimum population 172 cells.  This is an improvement
#C on previous ships having these sparks.
#C David I. Bell, 30 May 2025
x = 69, y = 59
47bo$$43bo7bo$43bo8bobb3o$42bo4boo3bobb3o$43bobo6bobboobbo$43boboo10bo
bo$57b3o$32bo15bo18boo$32bo34boo$32bo$29bob3obo$29bob5o$33bobo$30boo8b
oo$30boo8boo$31bo29boo$31boo31bo$32bo3boo22bobbo$32bo24b5o$30boboo24b
3o$31bo27bo5$25bo$25bo5b3o$24bobo3boobbo8boo$25bo3bo5bo7boo$25bo3bo$
30bobboo$31boo3$4boo$4b3o44boo$4boobo43boo$8bo13bo$o3boo3bo12bo$10bo
11bo$7bobo28bo$7bo31boo$bbo4bobo13bo16boo$21bobbo5bo11bo$6b4o11bo3bo4b
oo5b5o$6boo12bo4bo14bo$20bo4bo$24bo$21b3o8$26boo$26boo!

Here is a new ping-pong spaceship with a reduced population.

Code: Select all

#C Two Corderships playing ping-pong with a glider.
#C The back Cordership uses an edge-spark to turn a backward
#C glider into a forward glider.  The front Cordership uses a
#C tub-deletion-to-release-a-glider reaction to turn a forward
#C glider into a backward glider.  Combining these results in a
#C spaceship where a glider travels back and forth between the
#C two Corderships.  This particular spaceship has period 864.
#C Shifting the topmost Cordership by 32 cells will change the
#C period by 288 generations, among other possible adjustments.
#C The spaceship is shown at its minimum population of 326 cells.
#C This is an improved version of similar spaceships.
#C David I. Bell, 30 May 2025
x = 195, y = 137
48b3o$49bo$49bobbo$49bobbo$50bobo$65boo$65boo3$49bo$48bobo$49bo$66bo$
65bo7boo$47b4o22boo$47boo3bo10bo$48bo4bo9bobo$50boboo10bo$51bo3$59bobo
boo$42bo16bobo$41b3o17bobbo$60bo3bo$41b3o16b4obboo$42booboo14bo5boo$
44bo21bo13$25bo$24b3o$23booboo7bo$22boo3bo6bobo$23bobobobo5bo$24boobo
bbo$27boobo$bbo25boo12bobo$bobo39boo$o3bo13b3o22bo$o3bo8bo$obob3o4boob
3o$boobobbo5boboo$5bobo8bo$5boo11bobbo$18b3o11$7boo$7boo7$15boo$15boo
5$182bo$168boo7boobbobo$168b3o6b4o3bo$168boobobo7bo$171boo10boboo$183b
obo$184bo8boo$157b3o33boo$$161bo$157bo3boo$159bobo$156b3o7boo$158bo7b
oo$$157boo28b3o$158boo24boboo$158bo24bo3bo$158boo23bo3bo$157boo25b3o5$
158bo$150b3o3b4o$150bobo3booboo8boo$150b3obbo13boo$155boo3bo$156b4o$
157b3o3$130bobo$129bo47boo$130bobbo43boo$132bobo$135bo11b3o$134b3o$
134bo30bo$132boo31b3o$134bo30b3o$132bobbo12bobo5boo6bo3bo$132bobo11boo
bboo4boo6b4o$132bo13boobb3o11boboo$150boo$147b4o$148boo$148bo7$152boo$
152boo!

BCNU,
-dbell

[dbell]

I searched for nice forward glider reactions to the three-engine Cordership, and found one which other Corderships I have examined before didn't have.

The new reaction is a forward glider to sideways loaf, placed such that it can be turned directly into a new forward glider on the correct lane.

This means that my recent record high period puffer and spaceship are obsolete, since they required an intermediate Cordership to turn a backward facing loaf into a sideways loaf.

Here are the new record holders using the new reaction.

Code: Select all

#C A high period Cordership block puffer based on turning a forward
#C glider into a loaf and back again.  This is shown at its minimum
#C population of 249 (ignoring any produced blocks).  This puffer has a
#C period of 1248.  Advancing the topmost Cordership by 64 generations
#C changes the period by 96 generations.  Only every third advancement
#C preserves the lowest population, however.
#C David I. Bell, 1 June 2025
x = 158, y = 92
23b3o$$27bo$23bo3boo12bo$25bobo13boo$22b3o16bobo$9bo14bo$9bo30boo$9bo
8bo4boo16boo$16bobo5boo14bobbo$10b3obbo3bo4bo15b3o5boo$11bob5o6boo22b
oo$17bo5boo$12boo3$21boo$12boo7boo$12boo25boo$39boo$39bobbo$40bobo$b3o
36bo$42boo$5bo34bobbo$bo3boo34boo$3bobo$3o$bbo18boo$14boo$boo12bobo$bb
oo12boo$bbo14bo$bboo$boo$$14b3o$13bobb3o$16boboo4boo$13boo4boo3boo$15b
3obbo$16bo3bo$17bobo$$6boo129bo$6boo115boo7boobbobo$123b3o6b4o3bo$123b
oobobo7bo$126boo10boboo$138bobo$139bo8boo$148boo4$111bo$109booboo$111b
o$126boo$125bobbo$112boo11booboo$111bobbo11bo$110boo3bo10b3o26boo$110b
o4bo34boo3boo$110bo3bo36b3obboo$111bobbo36boobb3o$112bo$$128bo$124bo3b
o$125bobbo$125booboo$126bobo$127bo$$115boo$115boo7$123boo$123boo5$121b
3o$121bo$122bo!

Code: Select all

#C A high period Cordership based on turning a forward glider
#C into a loaf then back again.  This is shown at its minimum
#C population of 349 cells.  This spaceship has a period of 1344.
#C Advancing the topmost Cordership by 64 generations changes
#C the period by 96 generations.  Only every third advancement
#C produces the lowest population, however.
#C David I. Bell, 28 May 2025
x = 163, y = 150
23b3o$$27bo$23bo3boo12bo$25bobo13boo$22b3o16bobo$9bo14bo$9bo30boo$9bo
8bo4boo16boo$16bobo5boo14bobbo$10b3obbo3bo4bo15b3o5boo$11bob5o6boo22b
oo$17bo5boo$12boo3$21boo$12boo7boo$12boo25boo$39boo$39bobbo$40bobo$b3o
36bo$42boo$5bo34bobbo$bo3boo34boo$3bobo$3o$bbo18boo$14boo$boo12bobo$bb
oo12boo$bbo14bo$bboo$boo$$14b3o$13bobb3o$16boboo4boo$13boo4boo3boo$15b
3obbo$16bo3bo$17bobo$$6boo129bo$6boo115boo7boobbobo$123b3o6b4o3bo$123b
oobobo7bo$126boo10boboo$138bobo$139bo8boo$148boo4$111bo$109booboo$111b
o$126boo$125bobbo$112boo11booboo$111bobbo11bo$110boo3bo10b3o26boo$110b
o4bo34boo3boo$110bo3bo36b3obboo$111bobbo36boobb3o$112bo$$128bo$124bo3b
o$125bobbo$125booboo$126bobo$127bo$$115boo$115boo7$123boo$123boo5$121b
3o$121bo$122bo10$134bo$134bo5b3o$133bobo3boobbo$134bo3bo5bo$134bo3bo$
139bobboo$140boo11boo$153boo7$123b3o35boo$123b3o21bo13boo$124bo12boo9b
oo$125boo9bob3o8boo$126bo9bo3bo10bo$125bo11boobo5b5o$138bo10bo3$123boo
$123boo$124bo$124bo$123bobo$122bo$123bobboo$124bo3bo$126boo$126bo7$
128boo$128boo$141bo$141b3o$142boo$142bo$$140boobo$140b4o$142boo!

The lowest period for the puffer and spaceship is 384 (96 * 4) when the top Cordership is moved as close as possible to the lower one.

There is a second loaf-creating reaction which is very similar to the one shown above. In this one the top Cordership is flipped over. The phase is the same and so the puffer and spaceship using it have the same minimum populations.

Code: Select all

#C A second arrangement to create a high period puffer.
x = 109, y = 109
27bo$22bobbobobbo3bo$22bo4boob5o$22bo3bo4bobo$$24b3o$25bo18boo$44boo$$
6b3o$10bo$10boo$10bobbo3boo$11bobo3boo18bobo$11bo17bo6bobbo$10boo17boo
5bo3bo$9bobo19bo4b3oboo$11boo17b3o4bobbobo$8boo27boo$10bo27boobbo$39b
3o$16boo10bo$5bo10boo10bo$obbobobbo3bo$o4boob5o25boo$o3bo4bobo26boo$$
bb3o$3bo11$18b3o$7boboo7booboobo$3b3oboobo14bo$4bo3bobo9boobobo$5bo3bo
13boo5$10boo$10boo12$88bo$74boo7boobbobo$74b3o6b4o3bo$74boobobo7bo$77b
oo10boboo$89bobo$90bo8boo$99boo4$62bo$60booboo$62bo$77boo$76bobbo$63b
oo11booboo$62bobbo11bo$61boo3bo10b3o26boo$61bo4bo34boo3boo$61bo3bo36b
3obboo$62bobbo36boobb3o$63bo$$79bo$75bo3bo$76bobbo$76booboo$77bobo$78b
o$$66boo$66boo7$74boo$74boo5$72b3o$72bo$73bo!

Since the two Corderships are stacked on top of each other, the minimum period of this arrangement is raised to 576 (96 * 6)

EDIT:

I just want to clarify; the population 249 puffer above is the lowest population variable period puffer. The lowest population variable period spaceship is still the population 326 ping-pong spaceship from my previous post.

BCNU,
-dbell

[dbell]

My previous posts have described some Cordership-based variable period puffers and spaceships.

In this post, I will show minimum population variable period rakes that I built from those. Of course the population doesn't include any output gliders.

The absolute lowest population rake is the following simple boat-loop one. However, I don't consider this a 'proper' rake since it emits multiple gliders in each full period. (Is there a technical term for this?)

Code: Select all

#C A diagonal c/12 rake with a minimum population of 327 cells.
#C This emits an inverse-stream of gliders, where the gliders are
#C emitted every 96 generations except for a single gap in each full
#C period.  This uses a boat which is turned into a forward glider by a
#C sideways rake, and which is then turned back into a new boat.
#C The period of this particular rake is 2112.  Advancing the topmost
#C Cordership by 64 generations increases the period by 96 generations.
#C Only every third advancement preserves the lowest population, however.
#C David I. Bell, 3 June 2025
x = 226, y = 125
12bo$12bo5b3o$11bobo3boobbo$12bo3bo5bo$12bo3bo$17bobboo$18boo11boo$31b
oo6$205bo$b3o35boo150boo7boobbobo$b3o21bo13boo150b3o6b4o3bo$bbo12boo9b
oo163boobobo7bo$3boo9bob3o8boo165boo10boboo$4bo9bo3bo10bo176bobo$3bo
11boobo5b5o178bo8boo$16bo10bo188boo3$boo$boo176bo$bbo174booboo$bbo176b
o$bobo190boo$o192bobbo$bobboo174boo11booboo$bbo3bo172bobbo11bo$4boo
172boo3bo10b3o26boo$4bo173bo4bo34boo3boo$178bo3bo36b3obboo$179bobbo36b
oobb3o$180bo$$158boo36bo$159bobbo4bo24bo3bo$6boo148bobb3obobbobo24bobb
o$6boo148bobbo4b4o25booboo$19bo136bobbo34bobo$19b3o137bo6bo28bo$20boo
136boobo$20bo145bo11boo3boo$164boo12boo3boo$18boobo$18b4o$20boo$$149bo
$148bobo$148bobo35boo3boo$148bobbo34boo3boo$149bobo23bo$152bo22bobo$
151boo6bobbo12b3o$151bo8b3ob3o10bo$160boobobo$162b3o$163boo$149bo$148b
obo$150bo$150bo$150bo$$151bo42bo$147boob3o39boo$149b3oboo38boo$152bo7$
153boo$153boo$168bo$166boobo$165bo4bo$164bo4bo$164bo5bo$165boo3bo$166b
oobbo$168bo13$178bo$176boo$177boo21$152boo$151boo$153bo!

The following rakes are 'proper' rakes, only emitting a single glider for each full period.

The improper boat-loop rake can be upgraded to be a proper rake by the tricky use of a three-engine Cordership which both emits a glider when a boat is consumed and also deletes all the other incoming gliders.

Code: Select all

#C A diagonal c/12 rake with a minimum population of 471 cells.
#C This uses a boat which is turned into a forward glider by a
#C sideways rake, and which is then turned back into a new boat.
#C The period of this particular rake is 2112.  Advancing the
#C topmost Cordership by 64 generations increases the period by 96
#C generations.  Only every third advancement preserves the lowest
#C population, however.
#C David I. Bell, 3 June 2025
x = 226, y = 174
12bo$12bo5b3o$11bobo3boobbo$12bo3bo5bo$12bo3bo$17bobboo$18boo11boo$31b
oo6$205bo$b3o35boo150boo7boobbobo$b3o21bo13boo150b3o6b4o3bo$bbo12boo9b
oo163boobobo7bo$3boo9bob3o8boo165boo10boboo$4bo9bo3bo10bo176bobo$3bo
11boobo5b5o178bo8boo$16bo10bo188boo3$boo$boo176bo$bbo174booboo$bbo176b
o$bobo190boo$o192bobbo$bobboo174boo11booboo$bbo3bo172bobbo11bo$4boo
172boo3bo10b3o26boo$4bo173bo4bo34boo3boo$178bo3bo36b3obboo$179bobbo36b
oobb3o$180bo$$158boo36bo$159bobbo4bo24bo3bo$6boo148bobb3obobbobo24bobb
o$6boo148bobbo4b4o25booboo$19bo136bobbo34bobo$19b3o137bo6bo28bo$20boo
136boobo$20bo145bo11boo3boo$164boo12boo3boo$18boobo$18b4o$20boo$$149bo
$148bobo$148bobo35boo3boo$148bobbo34boo3boo$149bobo23bo$152bo22bobo$
151boo6bobbo12b3o$151bo8b3ob3o10bo$160boobobo$162b3o$163boo$149bo$148b
obo$150bo$150bo$150bo$$151bo42bo$147boob3o39boo$149b3oboo38boo$152bo7$
153boo$153boo$168bo$166boobo$165bo4bo$164bo4bo$164bo5bo$165boo3bo$166b
oobbo$168bo13$178bo$176boo$177boo24$127b3o$127b3o$128bo$129boo$130bo$
129bo14boo$144boo16bo$160boo$161boo$127boo$116bo10boo$111bobbobobbo3bo
4bo28boo$111bo4boob5o4bo15bo12bobo$111bo3bo4bobo4bobo15boo5boo4bo$126b
o16bobo6boo$113b3o11bobboo11bobbo$114bo13bo3bo10boobo$130boo12bobo$
130bo13bobo$125boo17b3o$116boo7boo17b3o$116boo$105b3o31bobbobo$105b3o
30bo6bo$106bo32bo5bo$107boo31bo$108bo$107bo4$105boo$105boo$106bo$106bo
$105bobo$104bo$105bobboo11boo$106bo3bo9bobbo$108boo13bo$108bo11bobbo$
119b4o$119bo$119bo4$110boo$110boo!

The ping-pong spaceship can be turned into a rake by the addition of a three-engine Cordership to detect the sparks when a backward glider is reflected.

Code: Select all

#C A diagonal c/12 rake with a minimum population of 465 cells.
#C This uses a glider which is reflected forwards and backwards
#C between two Corderships.  The period of this particular rake
#C is 864. Advancing the topmost Cordership by 128 generations
#C increases the period by 96 generations.  Only every third
#C advancement preserves the lowest population, however.
#C David I. Bell, 3 June 2025
x = 195, y = 186
48b3o$49bo$49bobbo$49bobbo$50bobo$65boo$65boo3$49bo$48bobo$49bo$66bo$
65bo7boo$47b4o22boo$47boo3bo10bo$48bo4bo9bobo$50boboo10bo$51bo3$59bobo
boo$42bo16bobo$41b3o17bobbo$60bo3bo$41b3o16b4obboo$42booboo14bo5boo$
44bo21bo13$25bo$24b3o$23booboo7bo$22boo3bo6bobo$23bobobobo5bo$24boobo
bbo$27boobo$bbo25boo12bobo$bobo39boo$o3bo13b3o22bo$o3bo8bo$obob3o4boob
3o$boobobbo5boboo$5bobo8bo$5boo11bobbo$18b3o11$7boo$7boo7$15boo$15boo
5$182bo$168boo7boobbobo$168b3o6b4o3bo$168boobobo7bo$171boo10boboo$183b
obo$184bo8boo$157b3o33boo$$161bo$157bo3boo$159bobo$156b3o7boo$158bo7b
oo$$157boo28b3o$158boo24boboo$158bo24bo3bo$158boo23bo3bo$157boo25b3o5$
158bo$150b3o3b4o$150bobo3booboo8boo$150b3obbo13boo$155boo3bo$156b4o$
157b3o3$130bobo$129bo47boo$130bobbo43boo$132bobo$135bo11b3o$134b3o$
134bo30bo$132boo31b3o$134bo30b3o$132bobbo12bobo5boo6bo3bo$132bobo11boo
bboo4boo6b4o$132bo13boobb3o11boboo$150boo$147b4o$148boo$148bo7$152boo$
120bo31boo$106boo7boobbobo$106b3o6b4o3bo$106boobobo7bo$109boo10boboo$
121bobo$122bo8boo$95b3o33boo$$99bo$95bo3boo$97bobo$94b3o7boo$96bo7boo
$$95boo28b3o$96boo24boboo$96bo24bo3bo$96boo23bo3bo$95boo25b3o$$103boo$
98bo4boo$84boo7boobbobo$84b3o6b4o3bo$84boobobo7bo$87boo10boboo$99bobo$
100bo6$107bo$106bobo$109bo$$106bo$98b3o$89boo5bo3b5obo$89boo6boo4boobb
oo$97bob6o6$97boo$97boo!

The loaf-loop block puffer can be turned into a rake by the addition of a three-engine Cordership which deletes the output blocks.

Code: Select all

#C A diagonal c/12 rake with a minimum population of 388 cells.
#C This uses a loaf which is turned into a forward glider by a
#C Cordership, and which is then turned back into a new loaf.
#C The period of this particular rake is 1344.  Advancing the
#C topmost Cordership by 64 generations increases the period by 96
#C generations.  Only every third advancement preserves the lowest
#C population, however.
#C David I. Bell, 3 June 2025
x = 197, y = 119
23b3o$$27bo$23bo3boo12bo$25bobo13boo$22b3o16bobo$9bo14bo$9bo30boo$9bo
8bo4boo16boo$16bobo5boo14bobbo$10b3obbo3bo4bo15b3o5boo$11bob5o6boo22b
oo$17bo5boo$12boo3$21boo$12boo7boo$12boo25boo$39boo$39bobbo$40bobo$b3o
36bo$42boo$5bo34bobbo$bo3boo34boo$3bobo$3o$bbo18boo$14boo$boo12bobo$bb
oo12boo$bbo14bo$bboo$boo$$14b3o$13bobb3o$16boboo4boo$13boo4boo3boo$15b
3obbo$16bo3bo$17bobo$$6boo129bo$6boo115boo7boobbobo$123b3o6b4o3bo$123b
oobobo7bo$126boo10boboo$138bobo$139bo8boo$148boo4$111bo$109booboo$111b
o$126boo$125bobbo$112boo11booboo$111bobbo11bo$110boo3bo10b3o26boo$110b
o4bo34boo3boo$110bo3bo36b3obboo$111bobbo36boobb3o$112bo$$128bo$124bo3b
o55bo$125bobbo41boo7boobbobo$125booboo40b3o6b4o3bo$126bobo41boobobo7bo
$127bo45boo10boboo$185bobo$115boo69bo8boo$115boo42b3o33boo$$163bo$159b
o3boo$161bobo$158b3o7boo$160bo7boo$123boo$123boo34boo28b3o$160boo24bob
oo$160bo24bo3bo$160boo23bo3bo$159boo25b3o$121b3o$121bo45boo$122bo39bo
4boo$148boo7boobbobo$148b3o6b4o3bo$148boobobo7bo$151boo10boboo$163bobo
$164bo6$171bo$170bobo$173bo$$170bo$162b3o$153boo5bo3b5obo$153boo6boo4b
oobboo$161bob6o6$161boo$161boo!

So the population 388 rake is the lowest population 'proper' variable period rake known.

Hopefully I haven't overlooked something which could reduce the population of any of these rakes. Performing adjustments is tricky so it would be easy to be wrong.

BCNU,
-dbell

[dvgrn]

That's a nice collection of new Corderstuff -- thanks!

Curiosity question: do the various new glider turns enable a Corderfleet that can escort a large moving memory loop? And maybe produce an output copy of the contents?

I haven't figured out how to convert binary information stored in a loop like that, into any kind of universal construction arm. But it seems like it might eventually be possible to construct a mighty Cordereplicator that flies along escorting its huge loop of gliders, and periodically drops a block off to the side and then aims backward gliders on it (on two different lanes chosen by the binary pattern in the memory loop, let's say) to turn the block into a construction elbow that builds a seed for a new Cordereplicator.

Copying the memory contents to the new Cordereplicator would be another tricky item, but in CGoL, where there's a will there usually seems to be a way.

[dbell]

Curiosity question: do the various new glider turns enable a Corderfleet that can escort a large moving memory loop? And maybe produce an output copy of the contents?

Maybe this is what you want.

Code: Select all

#C A period 3072 irregular rake created by gliders traveling in a loop.
#C This uses four Corderships which can turn gliders by 90 degrees at
#C each corner, with glider duplications being done by one of them.
#C This particular loop has 32 slots where gliders can be present
#C spaced at multiples of 96 generations apart.  Larger loops can be
#C easily constructed, aided by the fact that the phase of the lower
#C right Cordership can be greatly adjusted to join the first and
#C last segments together correctly.
#C David I. Bell, 3 June 2025
x = 386, y = 437
171bo$171bo$171bo$174boo$174boo12boo$169bo3b3o11boo$170b3o15bo$157b3o
11bo15b3o$156bo3bo9boo15b3o$155bo4bo9b3o16bo$154bo3bo13bo14bobbo$154bo
bbob3o8bo16b3o5boo$154bo7bo9bo15bo6boo$156bo3bobo7b3o$156bo3boboo$158b
3oboo$174boo$174boo$$185bobo$158boo25bobbo$158boo25bobbo$159bo25bo3bo$
186bobo$159bo27bo3$157bo5b3o$157bo7bo$157bo5bobo10boo$163boo10bobbo$
174bo3bo$176boo$$170bo$168boo$162boobboo5bo$162boo4boo$172bo$169b4o$
168bobo$167bobboobo$168bo4bo$169bo$170bobbo$170boo38$19boobo$18b3obo6b
obo$17bo4bobo4bo$18boo6bobo3bo$19bo3bobbobboo$22boboo3bo$21bobo16boo$
21bobo16boo3$bobo$o$bobbo$3bobo$6bo11b3o27boo$5b3o40boo$5bo41boo$3boo
40bobo$5bo13b3o$3bobbo12b3o21bo4bo$3bobo13boo21boob4o$3bo14bo24bo$16b
oobbo19b3o5boo$17bo3bo18boo$17bobbo19boo$18b3o6$7boo$7boo4$36b3o$38bo$
37bo$15boo$15boo13$18bo$18bobo$18boo26$359b3o$$363boo$365bo10b3o$359b
4obo11bo$359b5o$345bo$345bo30bobbo$347bo5bo5bobo14boboo$346bo6bobo3bob
o14bobbo$345bo3bobbo7bo15bobo5boo$346bobboboboo4bobo14b3o5boo$351boboo
5boo$360bo3$357boo$348boo7boo$348boo25boo$374bo$374boo$375boo$337b3o
36bobbo$377bobbo$341boo36bo$343bo34bo$337b4obo$337b5o$351bo$350bobo$
337bobo10bobboo$337bobo11bobbo$338bo13b3o$337bobo$338boo$338bo11b3o$
350bobo$353bobo$92b3o254bo6bo3boo$92bo260boboo3boo$93bo256bob3obbo$
350boob5o$355bo10$349bo$349bobo$349boo80$188b3o$188bo$189bo73$248bo$
246booboo$$249boo18bo$250bo18bobo$244bo3bo20boo$248bo3bo14bo$268bo$
264bo$246bo16bo6bo$247b3o20bo$264bo4bo$266boo$247b3o$247b3o$247booboo$
251bo13bo$249b3o14bo$266bo$265bobbo$265boobo$223bo11bo31bo$222b3o9b3o
14boo$221b3obo7bo10bobbo4bo16bobo$220bo3bo9booboo6b3obbobbo$219boobbo
bbo8b3oboo5boobbobbo15bobo$218b3obb4o10b4o9bobbo$220bo3bobbo23b3o$220b
o6bo$222bobbo47boo$224booboo44boo$224bo$270b3o$272bo$271bo$222boo$222b
oo$$236boo$236boo$$212bo$211bobo9b3o$210bo3bo7b3obo$211bobo8booboo$
212bo10bobbo$225boob5o11boo$212b4o13b4o11boo$211bo4bo10b3o$213bo$210bo
3bobbo$210bob3obo$211b3obo13bo$228bobo$230bo$225bo3bo$225bo8boo$225bo
bbo5boo$226b3o$228bo3$216boo$216boo!

BCNU,
-dbell

[dbell]

Here is a new smallest period 192 sideways rake.

Code: Select all

#C A diagonal c/12 period 192 five-engine sideways rake.
#C This uses the interaction of the two-engine Cordership and a
#C three-engine Cordership.  This is shown at its minimum population
#C of 250 cells (without counting output gliders).
#C David I. Bell, 7 June 2025
x = 90, y = 81
63b3o$63b3o$64bo$65boo$66bo$65bo14boo$80boo3$63boo$52bo10boo$47bobbobo
bbo3bo4bo$47bo4boob5o4bo15bo$47bo3bo4bobo4bobo15boo5boo$62bo16bobo6boo
$49b3o11bobboo11bobbo$50bo13bo3bo10boobo$66boo12bobo$66bo13bobo$61boo
17b3o$52boo7boo17b3o$52boo$41b3o31bobbobo$41b3o30bo6bo$42bo32bo5bo$43b
oo31bo$44bo$14boo27bo$$13bo3bo$18bo$11bo7bo21boo$10bo4bo25boo$11bobobo
4bo21bo$11bo8bo21bo$12bo4boobo20bobo$13boboob3o19bo$14b3oboo21bobboo
11boo$31boo9bo3bo9bobbo$31boo11boo13bo$44bo11bobbo$55b4o$55bo$55bo3$
39boo$39boo5boo$bbo18boo23boo$bbo11bo5bobboo$bobo10bo4b3obbo$bboobbo7b
o4bo4bo$bo5bo11b5o$bo5bo12boo$bo4bo$5bo$bb3o3$ooboo$5bo$oo$bb3o9$6boo
14bobo$6boo14bobbo$22bobbo$$19b3o$18bo$18bo$18bo3bo$14boobbo3bo$14boo
4bobo!

The previous smallest period 192 rake had a minimum population of 352, had a larger bounding box, and used six switch engines.

BCNU,
-dbell

[dbell]

I have been looking for a new smallish way to generate a backward glider rake. I haven't found that yet, but did find other things of interest.

The reactions I have been trying use a three-engine Cordership with an adjacent switch engine, such that the switch engine is stabilized on one side by consuming a block of the Cordership, and is stabilized on the other side by a glider released by the Cordership due to the missing block.

I will make another post to show some results for this type of reaction, but this post will just concentrate on one of them.

Here is a new useful Cordership.

Code: Select all

#C A diagonal c/12 period 192 spaceship with useful sparks.
#C This is based on a three-engine Cordership with an adjacent switch
#C engine which is stabilized by blocks and gliders from the Cordership.
#C The resulting spaceship creates useful sparks on its edge from a
#C period-doubled reaction.  The spaceship is shown at its minimum
#C population of 149 cells.
#C David I. Bell, 8 June 2025
x = 57, y = 53
52b3o$52b3o$$52boboo$23b3o26bo3bo$23b3o28b3o$24bo$25boo$26bo$25bo14boo
$40boo3$23boo$12bo10boo$7bobbobobbo3bo4bo$7bo4boob5o4bo15bo$7bo3bo4bob
o4bobo15boo$22bo16bobo$9b3o11bobboo11bobbo$10bo13bo3bo10boobo$26boo12b
obo$26bo13bobo$21boo17b3o$12boo7boo17b3o$12boo$b3o31bobbobo$b3o30bo6bo
$bbo32bo5bo$3boo31bo$4bo$3bo4$boo$boo$bbo$bbo$bobo$o$bobboo11boo$bbo3b
o9bobbo$4boo13bo$4bo11bobbo$15b4o$15bo$15bo4$6boo$6boo!

The period doubling is useful for the expected reasons. For example, it can turn a period 96 puffer into a period 192 puffer.

Code: Select all

#C A period 192 Cordership can thin out a diagonal row of blocks.
x = 82, y = 140
oo$oo7$8boo$8boo7$16boo$16boo7$24boo$24boo7$32boo$32boo7$40boo$40boo7$
48boo$48boo7$56boo$56boo7$64boo$64boo7$72boo$72boo7$80boo$80boo4$60b3o
$64bo$32boo30boo13b3o$31bo32bobbo12boo$31bobbo30bobo9bobbo$29boob4o29b
o11bobo$28bo20b3o12boo$28bo3b3obbo25bobo14boo$23bo4bobbobbob3o3bobo20b
oo11bobbo$22bobo5boo4b3o4bo18boo15boo$32boobobo26bo$22bobbo7boobo14bo
6boo13boo$24boo10bo12b4o5boo14boo$25bo22bo3bo20bo$48bobbo$49b3o$$31boo
$22boo7boo$22boo$$46bo6b3o$46bo8bo$52bobbo$10boo40bobo$9bo14boo26boo$
9bobbo11boo4bo$7boob4o16bobo$6bo26bo$6bo3b3obbo8b3o3bobo$6bobbobbob3o
10bo3bo$8boo4b3o5b3o$10boobobo9bo$11boobo10bobboo$14bo10bo4bo$30bo$26b
obbo$27b3o$$34boo$34boo4$31b3o$16boo13boo$16boo14bobo$31b3o$27bobb4o$
28b4o$29bo3$24boo$24boo!

But I found an unexpected result trying to thin a stream of backward gliders.

Code: Select all

#C A diagonal c/12 period 2592 (96 * 27) backwards glider rake.
#C This uses a period 96 backrake and three copies of a period 192
#C period-doubling Cordership which thin the base output stream.
#C Every other glider which reaches a Cordership is reflected back to
#C delete itself and another glider.  Every such reflection changes
#C the phase of that Cordership by 96 generations.  Each Cordership
#C triples the period of the glider stream passing through it.
#C With three such tripling reactions the resulting rake has its base
#C period multiplied by 27.
#C David I. Bell, 8 June 2025
x = 238, y = 262
58bo$57b3o14boo$56bo10bobbo4bo$57booboo6b3obbobbo$58b3oboo5boobbobbo$
60b4o9bobbo$74b3o6boo$83boo5$84b3o$82boob3o$87boobboo$85bobo3boo$79bo
3b4o$78bo3bo$63boo$63boo13boo$78boo$67b3o5boobo$67boboo4b4o$50b3o17bo
6bo$50b3o10boobbobbo$49bo3bo15bo$50boob3o11boo$35bo14boo4bo$31b5o7boo
8bobbo$31bo3bobo4b3o9boo$31b3o3b3o3b3o$37boobb3o$37bo$34b3o$34boo3$37b
o$36bobo$36bobo$37bo$$24bo$24bo$24bo$28bo16bo$24b3obbo14bobo$23bo4bo
15bobo$23bo3bo17bo$24b3o$3o$$4boo17bobo$6bo10b3o3bobo49bobo$4obo11bo5b
obo50boo$5o18bobo50bo$24boo$17bobbo$obo14boboo$obo14bobbo$bo15bobo$obo
14b3o$boo$bo5$16bo$14booboo$14b3oboo$15b5o$5boo9b3o$5boo10bo7$13boo$
13boo4$107bobo$108boo$108bo16$101bo3boobboobo$75bo25bo3boo4boboo$74boo
7bo17bo3boobbooboo$73bobob3obbobo20boo$72b3o3boo3bo19bobbo$73boboboobo
bo20bobo$74booboo25bo$75bob5obo$79b4o11boo$94boo$57bo$56boboo$60bo$54b
o3bobbo$52bo9bo4boo70bobo$52bo4boobboo4boo71boo$61boo15bo8b3o11boo37bo
$54bo5bo13boobobo7bo14boo$55bo4b3o17bo6boo12bo$56bo4boo12booboboo7bobo
$58b4o14bo12bobbo$76bo4bo7bobo$76bo13bo$53bo12boo8bobbo$52boo7bo4boo
10boo$51bobob3obbobo$50b3o3boo3bo26boo$51boboboobobo27boo$52booboo$53b
ob5obo$57b4o9$56bo$59bo6bobo$54bo11bobobo$53bo3bobbo10boboo$54b3obbo
10boobobo$55bo3bo13bobo$57boo15bo$57bo4$60boo$60boo$153bobo$153b3o15bo
$123bobo27boo15b3o$122bo45boo3bo$123bobbo41boob3o$125bobo28bo11boobboo
$128bo11b3o11bobo15boo$127b3o24b3o14b3o$113b3o11bo29bo13boo$113b3o9boo
26b5o13bo$127bo13b3o21boo$113boboo8bobbo12b3o5boo15boo$113bo3bo7bobo
13boo6boo14bo$115b3o7bo14bo$138boobbo$139bo3bo$139bobbo$122boo16b3o$
113boo7boo$113boo$145boo$148bo$145bobbo$146bobo$101bobo38boo$100bo14b
oo25boo$101bobbo10boo25boo$103bobo$106bo$105b3o14bo$105bo8b5o3boo$103b
oo8b6o$105bo8booboo$103bobbo7booboo$103bobo9bobo$103bo12b3o$117b3o$
117bobbo$117bobbo$118b3o4boo$125boo5$107boo$107boo3$118bobo$118boo$
119bo$$115boo$115boo4$213b3o19bobo$213bobo20boo$185bo27bobo14bo5bo$
185bo27bo4boo8boboobbo$185bo26b3o3boo7bobbobbobo$188boo28bo9b4o$188boo
12boo10b4o11bobo$183bo3b3o11boo12boo13booboobo$184b3o15bo12bo10boo3bo
3bo$185bo15b3o22bo$169b3o12boo15b3o12bo14bo$178bo5b3o16bo10bobo$171boo
5b3o5bo14bobbo8b4o$171b4o4bo4bo16b3o5b3ob3o$171boob3oboo6bo15bo6boo4bo
$176bobo5b3o4$182boo$173boo7boo$173boo25boo$199bobbo$200bo$163bo36boo$
163bo39boo$163bo38b3o$166boo36bo$166boo34boo$161bo3b3o$162b3o$163bo$
162boo11b3o$162b3o10boobo$164bo13boo$162bo14boo$164bo$162b3o$176bo$
175b3o$175bo3boo$174b4o3bo3boo$175bo5bo3boo$175b4obboo$176bobb3o3$167b
oo$167boo!

Why the period is tripled instead of just doubled is interesting. It must be because each reflected glider deletes one of the
forward gliders.

You might expect that each additional Cordership would have to be placed further down the output stream so that there is room
for the reflected glider to travel. But the stages can actually be packed close together without destruction.

Code: Select all

#C A diagonal c/12 period 6624 (96 * 3 * 23) backwards glider rake.
#C This uses a period 96 backrake and six copies of a period 192
#C period-doubling Cordership which thin the base output stream.
#C Every other glider which reaches a Cordership is reflected back to
#C delete itself and another glider.  Every such reflection changes
#C the phase of that Cordership by 96 generations.  The six Corderships
#C would normally multiply the base period by 729 if they had enough
#C room, but being packed closely together reduces the multiplication
#C factor to just 69.
#C David I. Bell, 8 June 2025
x = 279, y = 304
62bo$61b3o$60bobobo$59b3ob3o12bo$77bobo$61bob3o13boo$61b5o9bo3bo$61boo
bboo11bobboo$63boboo14bo$65boo9bobboo$61bobobbo11bo7boo$60bobobbo20boo
$61bo4$76boo$$76boo$94bo$77bobo9bo3bobo$78bo10b5oboo$66boo10booboo7bo
4bo$54b3o9b3oboo8boo9boobo$69bobbo8boo10bo$52bo5bo11b3ob5obobo3bo$52b
7o13bo3bobb3o4bo$54bo17bobboobbobbo$30bo23bo3bo14boo3b3obo$29bobo21bo
18boo6b3o$29bobboo20bo16boo$27b7o14bo6bo4bo10boobo$26bobbo3bo14bo6bo4b
o12bo$25b3obb7o11bo5boobobo$27b3obbo8bo11bobo$28booboo8bo12bo$29b3obo
bbo$30b3oboo13boo$33bo13boobo$46bo3bo$26b3o17bobboo$25bo3bo10bo6b3o$
24bo4bo9bobo6bo$23bo3bo11bobo$23bobbob3o9bo$23bo7bo$25bo3bobo$4bo20bo
3boboo$3b3o21b3oboo$bbooboo41bo$boobobo40bobo$3obb3o39bobo$bo6bo39bo$
bb5obo$3b4oboo$8bo$7bo12boo$20boo3$5bo$3boobo15booboboo$21boobo3bo$6bo
15bobobobo55bobo$3bobbo16bo61boo$4bo80bo$$9boo$bb3o5boo$9boo$9bo11b4o$
20boboo$20bobo$$15bo$13bobboo$8boo3bobb4o$8boo3boboobo$16boobo$16bo$
14bo4bo$14b3o$14boob3o$17b3o$16bobo$16boo9$116boo10$101bo$100b3o$99b3o
bo14bo$98boo3boo6bobbo3bo$97boobobboo6bo3bobbo$72bo25booboboo5bo$71b3o
14boo9b3oboo6boboo$70bo10bobbo4bo11bo4bo$71booboo6b3obbobbo11b4o$72b3o
boo5boobbobbo13bo12boboo$74b4o9bobbo26b3o$62bo25b3o6boo19bo$61bobo33b
oo$60booboo45boo$60boo49boo$66boo42bo$60b3obbo$64boboobboo$62bobbo4boo
$65bo$63boo23bo$88bo3bo55b3o$63bo23bobobobo54bo$63bo24boboobo55bo$88bo
3bo$64bo$61bob3obbobo$50bo10boobob3obo$49b3o8boo3booboo$48bo10bobbo4bo
$49booboo6b3obbobbo62bo$50b3oboo5boobbobbo61bobo$52b4o9bobbo61bobboo$
66b3o59b7o14bo$127bobbo3bo14bo$102b3o21b3obb7o11bo$101bo3bo22b3obbo8bo
$100bo4bo8boo3b3o7booboo8bo$100bobbobo7b4o13b3obobbo$73boo25boobobo6bo
3boo13b3oboo13boo$73boo27boobobbo4boobobo15bo13boobo$92b3o9boobbo38bo
3bo$92bobo10b3o13bo6boo17bobboo$91bo3bo22bobbo6boo12boo4b3o$67boo22bo
3bo23b3o21boo4bo$55boo9bo3boo19bo50bo$55boo9bo4bo19bo4boo$67bo3bo19bo
6bo$67boboo21bo5bobboo$68bo23boo7boo$$94bobbo20bo3bo$95bo21bo5bo$63boo
52bo6bo$63boo52bo3bobbo$95bo22b3oboo$94bo$80b3o11b3o3bo$79bo3bo8boo4b
4o$78bo4bo7b4o7bo59bo$78bobbobo6bob3o3b4o59bobo$78boobobo6bo5boo62bo3b
o$80boobobbo4bobb3o64bobo$82boobbo7bobbo36bo27bo14b3o$83b3o13bo31b4o
45bo$96bobbo62b4o10boo3bo$97b3o48b3o10bo4bo10bobbo$121b3o39bo15bo$120b
o3bo9bobo12boo9bo3bobbo10bo$119bo3boo10bo13boo9bob3obo12bo$104boo14bo
12boo13bobbo9b3obo13bo$104boo15b4o8bobbo11bo8boo$123boboo5booboo10b3o
7boo$123bobbo20boo$124boo24boo23bobo$102boo45bobbo26boo$86boo13b3o$86b
oo12bo3bo25boo15boo27bo3bo$99b5o17boo7boo15bobbo26b3o$99bo21boo25b3o$
99b3o53bo$100boo54boo$155b3o$$94boo54boo$94boo16bo10boo24bobbo$109b4o
9bobbo24boo$$123b3o$123bobbo3boo$112bobo10bobobboo$113bo12boo$111boo$
111bobbo$110booboo80bo$194bobo$128bo65bobboo$128boo62b7o14bo$125bobb3o
60bobbo3bo12b3o$125boobboobboo31b3o21b3obb7o5boobo3bo$126bobo4boo30bo
3bo22b3obbo15bo$126b3o35bo4bo8boo3b3o7booboo8bo6boo$164bobbobo7b4o13b
3obobbo5bo3bobbo$164boobobo6bo3boo13b3oboo8boobboo$166boobobbo4boobobo
15bo14boo$115boo39b3o9boobbo$115boo39bobo10b3o13bo6boo$155bo3bo22bobbo
6boo12boo$155bo3bo23b3o21boo$155bo50bo$125bobo27bo4boo$125boo28bo6bo$
124b3o29bo5bobboo$123boo31boo7boo$123boo$158bobbo20bo3bo$159bo21bo5bo$
181bo6bo$181bo3bobbo$159bo22b3oboo$158bo$144b3o11b3o3bo59b3o$143bo3bo
8boo4b4o$142bo4bo7b4o7bo55bo5bo$142bobbobo6bob3o3b4o56b7o12bo$142boobo
bo6bo5boo62bo15bobo$144boobobbo4bobb3o34b3o26bo3bo14boo$146boobbo7bobb
o33bobo25bo14bobb3obo$147b3o13bo20b3o8b3o26bo13b3o4bo$160bobbo19bo3bo
23boo12bo4bo11bobbo$161b3o18bo4bo22bobboo10bo4bo$181bo3bo11boo11booboo
9boobobo11bobo$181bobbob3o6booboo14bo8bobo15boo$181bo7bo5boobboo10boo
11bo$168boo13bo3bobo4boo3boo11bo7boo$168boo13bo3boboo4boobboo19boo$
185b3oboo5bobo3$166boo$150boo13b3o25boo17b3o$150boo12bo3bo15boo7boo14b
3obo$163b5o16boo24booboo25boo$163bo46booboo$163b3o46bo$164boo$$213boo$
158boo13b3o10boo24bobbo$158boo13bobo8boobbo24boo$173b3o8bo3bo$188boo
64b3o19bobo$185boobobobboo59bobo20boo$175boo13booboo31bo27bobo14bo5bo$
173booboo11boo35bo27bo4boo8boboobbo$173boobboo47bo26b3o3boo7bobbobbobo
$172boo3boo50boo28bo9b4o$173boobboo50boo12boo10b4o11bobo$174bobo47bo3b
3o11boo12boo13booboobo$190b3o32b3o15bo12bo10boo3bo3bo$190bobo33bo15b3o
22bo$188b4o18b3o12boo15b3o12bo14bo$187b3o6boo21bo5b3o16bo10bobo$187bo
8boo14boo5b3o5bo14bobbo8b4o$188b3o21b4o4bo4bo16b3o5b3ob3o$190bo21boob
3oboo6bo15bo6boo4bo$217bobo5b3o$$178boo$178boo$223boo$214boo7boo$214b
oo25boo$240bobbo$241bo$204bo36boo$204bo39boo$204bo38b3o$207boo36bo$
207boo34boo$202bo3b3o$203b3o$204bo$203boo11b3o$203b3o10boobo$205bo13b
oo$203bo14boo$205bo$203b3o$217bo$216b3o$216bo3boo$215b4o3bo3boo$216bo
5bo3boo$216b4obboo$217bobb3o3$208boo$208boo!

I don't understand what periods are possible for similar rakes. That factor of 23 appearing was unexpected.

EDIT:

The period multiplier spaceship can be placed on either side of the backward glider stream so that the reflection reactions can be placed closer together.

I still have no idea what periods are attainable, except that even multiples of 96 cannot work. This is because for those periods only a single backward glider can be reflected, with no further reactions for the following gliders.

Code: Select all

#C An even multiple of 96 backward glider stream not being period multiplied.
x = 369, y = 323
o$boo$oo62$64bo$65boo$64boo62$128bo$129boo$128boo62$192bo$193boo$192b
oo52$349bo$350boboobobo$344b3o3b4o3bo$350bobbooboo$349bo$347b3o$347b3o
17boo$367boo$330bo$330bo$256bo73bob3o$257boo73b3o$256boo75bo6boo$333b
oo5boo19bo$334bo17boo5b5o$334boo16boo4booboboo$352bobbo3bobobo$331boob
oo17b3o7bo$332b3o19bo5bo3bo$332bo27bo3bo$361b4o$339boo22bo$327bo11boo$
328boboobobo$322b3o3b4o3bo25boo$328bobbooboo25boo$327bo$325b3o$325b3o
10$342bo$341boboo$327bobooboo7bobbo$326b5obboo7bo3bobo$326bobb3obo11b
oobo$332bo12b3o5$333boo$333boo$333bo$324bo$320b5o7boo$320bo3bobo4b3o$
320b3o3b3o3b3o$326boobb3o$326bo$323b3o$323boo7$328boo$324bo3bo$323bobo
$325boo$322b4obo$323bob4obo$$324bobbo$323bo3bo$320bo3bo3bo$321boo4bo$
320boo!

Here is an arrangement to show that the multiplier value does not have to have a factor of 3, and can even be a large prime.

Code: Select all

#C A diagonal c/12 period 7008 (96 * 73) backward rake.
#C This uses a period 96 backward rake whose gliders interact
#C with six copies of a period multiplying Cordership.
#C David I. Bell, 18 June 2025
x = 283, y = 288
62b5o7bo$60boo5boo4bobo$60bo7bo4bo$60boo7bo3bobbo$62boo6bo3b3o$65bo$
65bo4bo13boo$66boobo14boo7$81bo3bo6boo$79bobbob3o5boo$82bobobo$70bobo
7bo$64boo4b3obobooboo$64boo6bobboo3bobo3bo$80bobo$68boo$56b3o8b4o$54b
7o5boobbo$53b9o3bob3o$52bo7b3o3boobo$53b3o6bo$34b3o6bo10boo$33bo4bo3bo
bo12bo$33bo4boo3bo14bo$33bo6bo18bo$34b3obobbobo$38b5o$43bo$$155bo$154b
3o14boo$38bo114bo10bobbo4bo$37bobo114booboo6b3obbobbo$37bobo115b3oboo
5boobbobbo$38bo118b4o9bobbo$145bo25b3o6boo$144bobo33boo$143booboo$143b
oo$24b3o19bo102boo$24bobo18bobo95b3obbo$24b3o18bobo99boboobboo$46bo98b
obbo4boo$148bo$26boo46bo71boo23bo$24booboo46boo94bo3bo$bbo21boobboo44b
oo70bo23bobobobo$ooboo18boo3boo116bo24boboobo$bbo21boobboo141bo3bo$17b
oo6bobo119bo$16bobbo124bob3obbobo$3boo11booboo112bo10boobob3obo$bbobbo
11bo114b3o8boo3booboo$boo3bo10b3o111bo10bobbo4bo$bo4bo125booboo6b3obbo
bbo$bo3bo127b3oboo5boobbobbo$bbobbo129b4o9bobbo$3bo145b3o$$19bo$15bo3b
o$16bobbo$16booboo$17bobo136boo$18bo137boo$$6boo191bo$6boo190boo7bo$
150boo45bobob3obbobo$138boo9bo3boo41b3o3boo3bo$138boo9bo4bo42boboboobo
bo$150bo3bo43booboo$150boboo45bob5obo$151bo51b4o11boo$14boo202boo$14b
oo165bo$106bo73boboo$107boo75bo$106boo22bo47bo3bobbo$129b3o44bo9bo4boo
$128b3obo43bo4boobboo4boo$127boo3boo51boo15bo8b3o$126boobobboo44bo5bo
13boobobo7bo$127booboboo45bo4b3o17bo6boo$128b3oboo46bo4boo12booboboo7b
obo$130bo4bo46b4o14bo12bobbo$131b4o65bo4bo7bobo$133bo66bo13bo$177bo12b
oo8bobbo$176boo7bo4boo10boo$175bobob3obbobo$174b3o3boo3bo26boo$175bobo
boobobo27boo$176booboo$177bob5obo$181b4o$105bo29bo$105bo5b3o21bo$104bo
bo3boobbo22boo$74b3o28bo3bo5bo21boo$83bo21bo3bo$76boo5b3o24bobboo$76b
4o4bo26boo17boo$76boob3oboo45bobo$81bobo46bo49bo$95boo86bo6bobo$95boo
81bo11bobobo$177bo3bobbo10boboo$178b3obbo10boobobo$179bo3bo13bobo$59bo
121boo15bo$58b3o7boo111bo$57bo10boo10bo$58booboo12boo$59b3oboo10boob3o
6boo$61b4o14boo6boo11bo83boo$80boo4booboo9boo82boo$81bo4boobbo8bobo$
86boobbo$87b3o81bo3boobboobo$67boo10boo90bo3boo4boboo$52b3o12boo10boo
90bo3boobbooboo$61bo113boo$54boo5b3o25boo82bobbo$54b4o4bo26boo82bobo$
54boob3oboo111bo$59bobo4$263bo$264boboobobo$258b3o3b4o3bo$264bobbooboo
$146bo32bobo81bo$146bo32bobbo78b3o$63boo81bo31boobo79b3o17boo$66bo80b
oo29bo102boo$56bo4boo4boo78b3o28bo65bo$56bo3boo6bo6bo40b3o28boo28bo66b
o$56bobb3obboobbo5bobo39bobo57boo66bob3o$64boobo6bobo38bo3bo56boo68b3o
$75bo39bo3bo127bo6boo$115bo17boo112boo5boo19bo$70boo43bo4boo11boo11bo
101bo17boo5b5o$71bo43bo6bo24bo100boo16boo4booboboo$71b3o42bo5bo23bo
119bobbo3bobobo$61boo40bo12boo127booboo17b3o7bo$61boo39boo7bo6bo3bo
123b3o19bo5bo3bo$101bobob3obbobo6bobo10boo112bo27bo3bo$100b3o3boo3bo
21bo141b4o$101boboboobobo21b3o118boo22bo$102booboo9b3o122bo11boo$103bo
b5obo3bo3bo13bo108boboobobo$107b4o5bobbo14bo101b3o3b4o3bo25boo$118boo
13boo107bobbooboo25boo$134bo106bo$114boo15b3o105b3o$105boo7boo14bo3bo
104b3o$105boo22b3oboo$129bobob3o$94b3o31b3obb3o$94bobo$93bo3bo$93bo3bo
$93bo$93bo4boo$93bo6bo$94bo5bo155bo$94boo159boboo$96bo3bo140bobooboo7b
obbo$97bobo140b5obboo7bo3bobo$240bobb3obo11boobo$246bo12b3o$94b3o$93bo
3bo$94bobbo11b3o$96boo12boo$108boboo135boo$109bo137boo$108bo5boo131bo$
107boo129bo$107boo125b5o7boo$234bo3bobo4b3o$234b3o3b3o3b3o$99boo139boo
bb3o$99boo139bo$237b3o$237boo7$242boo$238bo3bo$237bobo$239boo$236b4obo
$237bob4obo$$238bobbo$237bo3bo$234bo3bo3bo$235boo4bo$234boo22$241bo$
240bobo$240bobo$240bobbo$212bo28bobo$211bobo30bo$243boo$211bobbo28bo$
213boo$214bo$228boo$228boo3$211boo$199bo13bo$200boboobobo4boo$194b3o3b
4o3bo3b3o15bo$200bobbooboo3boo16boo$199bo10b3obo14bo$197b3o11bo3bo10b
oobbo$197b3o13bobbo10booboo$213b3o12boboo$214boo11booboo$209boo16bo3bo
$200boo7boo17bobo$190bo9boo25boo$189bobo$222boo4boo$189bobbo30bo$191b
oo$192bo5$189boo$191bo$190boo$189b3o$189boo$188b3obo$189bo3bo11boo$
191bobbo10bobo$191b3o12b3o$192boo9boobbo$203boboo$202boobo5$194boo$
194boo!

I have also found period 25 and 77 multiplying arrangements so that the multiplier possibilities seem pretty versatile.

BCNU,
-dbell

[dbell]

Here are all of the Corderships that I have found which use a three-engine Cordership with an adjacent switch engine.

Code: Select all

#C Diagonal c/12 spaceships which display sparks at their edge.
#C These use a three-engine Cordership and an adjacent switch
#C engine which is stabilized on one side by consuming one of
#C the blocks of the three-engine Cordership, and stabilized
#C on the other side by gliders released by the three-engine
#C Cordership due to the missing block.  These are sorted in rows
#C by their minimum populations of 147, 148, 149, 159, 163, 164,
#C and 197 cells.  All of these spaceships are period 96 except
#C for the one in the third row which has a period of 192.
#C David I. Bell, 10 June 2025
x = 328, y = 542
52b3o$53bo$53bobbo$53bobbo$54bobo$25b3o$25b3o$26bo$27boo$28bo$27bo14b
oo9boo$42boo3$25boo$14bo10boo$9bobbobobbo3bo4bo$9bo4boob5o4bo15bo$9bo
3bo4bobo4bobo15boo$24bo16bobo$11b3o11bobboo11bobbo$12bo13bo3bo10boobo$
28boo12bobo$28bo13bobo$23boo17b3o$14boo7boo17b3o$14boo$3b3o31bobbobo$
3b3o30bo6bo$4bo32bo5bo$5boo31bo$6bo$5bo4$3boo$3boo$4bo$4bo$3bobo$bbo$
3bobboo11boo$4bo3bo9bobbo$6boo13bo$6bo11bobbo$17b4o$17bo$17bo4$8boo$8b
oo25$53bo$52bobo$52bobo$52bobbo$53bobo$56bo$55boo$25b3o27bo$25b3o$26bo
$27boo$28bo$27bo14boo$42boo3$25boo$14bo10boo$9bobbobobbo3bo4bo$9bo4boo
b5o4bo15bo$9bo3bo4bobo4bobo15boo$24bo16bobo$11b3o11bobboo11bobbo$12bo
13bo3bo10boobo$28boo12bobo$28bo13bobo$23boo17b3o$14boo7boo17b3o$14boo$
3b3o31bobbobo$3b3o30bo6bo$4bo32bo5bo$5boo31bo$6bo$5bo4$3boo$3boo$4bo$
4bo$3bobo$bbo$3bobboo11boo$4bo3bo9bobbo$6boo13bo$6bo11bobbo$17b4o$17bo
$17bo4$8boo$8boo28$54b3o$54b3o$$54boboo$25b3o26bo3bo$25b3o28b3o$26bo$
27boo$28bo$27bo14boo$42boo3$25boo$14bo10boo$9bobbobobbo3bo4bo$9bo4boob
5o4bo15bo$9bo3bo4bobo4bobo15boo$24bo16bobo$11b3o11bobboo11bobbo$12bo
13bo3bo10boobo$28boo12bobo$28bo13bobo$23boo17b3o$14boo7boo17b3o$14boo$
3b3o31bobbobo$3b3o30bo6bo$4bo32bo5bo$5boo31bo$6bo$5bo4$3boo$3boo$4bo$
4bo$3bobo$bbo$3bobboo11boo$4bo3bo9bobbo$6boo13bo$6bo11bobbo$17b4o$17bo
$17bo4$8boo$8boo32$25b3o87b3o87b3o24bobo60b3o$25b3o87b3o26bo61bo25b3o
61bo26bobo$26bo28bo60bo25booboo59bobbo22boo62bobbo23b3o$27boo24booboo
59boo25bo61bobbo86bobbo23boo$28bo26bo62bo88bobo87bobo$27bo14boo73bo14b
oo88boo11bo76boo$42boo88boo11boo75boo9bobo76boo12bo$56boo86bobbo85b3o
88bobo$55bobbo84boo3bo87bo87b3o$25boo27boo3bo55boo26bo4bo57bo25b5o59bo
30bo$14bo10boo27bo4bo44bo10boo26bo3bo57bobo87bobo25b5o$9bobbobobbo3bo
4bo27bo3bo40bobbobobbo3bo4bo27bobbo45boo3b4o4bo76boo3b4o4bo$9bo4boob5o
4bo15bo12bobbo40bo4boob5o4bo15bo12bo42b3obobbo6bo19bobo53b3obobbo6bo
19bobo$9bo3bo4bobo4bobo15boo5boo4bo42bo3bo4bobo4bobo15boo5boo50bobbobb
5o27boo50bobbobb5o27boo$24bo16bobo6boo62bo16bobo6boo50bobbo8b4o17bo4b
oo50bobbo8b4o17bo4boo$11b3o11bobboo11bobbo56b3o11bobboo11bobbo59bo9boo
3bo10bo3bo59bo9boo3bo10bo3bo$12bo13bo3bo10boobo57bo13bo3bo10boobo56bob
o11bo4bo9bo4bo55bobo11bo4bo9bo4bo$28boo12bobo73boo12bobo57bo14boboo11b
o59bo14boboo11bo$28bo13bobo73bo13bobo73bo12boobboo71bo12boobboo$23boo
17b3o68boo17b3o68boo16bobo69boo16bobo$14boo7boo17b3o59boo7boo17b3o59b
oo7boo18boo59boo7boo18boo$14boo88boo88boo25bobbo59boo25bobbo$3b3o31bo
bbobo50b3o31bobbobo50b3o35bobo49b3o35bobo$3b3o30bo6bo49b3o30bo6bo50bo
31boo56bo31boo$4bo32bo5bo50bo32bo5bo50bobbo28boo56bobbo28boo$5boo31bo
56boo31bo55bobbo86bobbo$6bo89bo88bobo87bobo$5bo89bo4$3boo88boo89bo89bo
$3boo88boo88bobo87bobo$4bo89bo89bo89bo$4bo89bo$3bobo87bobo$bbo89bo89b
4o86b4o$3bobboo11boo72bobboo11boo71boo3bo11boo71boo3bo11boo$4bo3bo9bo
bbo72bo3bo9bobbo71bo4bo12bo71bo4bo12bo$6boo13bo74boo13bo73boboo8bobob
3o71boboo8bobob3o$6bo11bobbo74bo11bobbo74bo10bobboo74bo10bobboo$17b4o
86b4o85bo3boo84bo3boo$17bo89bo90b3o87b3o$17bo89bo4$8boo88boo88boo88boo
$8boo88boo88boo88boo27$55bo$54bobo$54bobo$22bo31bobbo$22bo32bobo$22bo
8bo26bo$29bobo25boo$23b3obbo3bo24bo$24bob5o$30bo$25boo15boo$42boo19boo
$63boo4$5b3o7boo10boo$4bo3bo6boo14bo$5boo15boobbo4bo$7booboo10boobbo7b
o$9boo15bo7boo$27bo8bo9b3o$28boobboobboo10bo$34b3o10bo$35bo$o13boo10b
oo$o13boo10boo$o8bo$7bobo26boo$b3obbo3bo25boo$bbob5o$8bo$3boo9$11bo$
10b4o$8b5obo$bb3obbo6boo6bo$6bo3bob3o6bobo$7bobobboo7bobo$22bo$18bo$
18bo$18bobo$19bo$8boo9bo$8boo27$51bo$51bo7bo$51bo5b3o$22bo27boo3bobo$
22bo33bobbo$24bo5bo24bobboo$23bo6bobo$22bo3bobbo$23bobboboboo$28boboo$
42boo$42boo4$5b3o$5b3o7boo$4bo3bo6boo$5boob3o11b3obbo$5boo4bo10b4obo6b
oo$8bobbo13bo21boo$9boo15bobo7boo8bobo$27boo3bo4boo9bo$37bo$33b4o$o13b
oo10boo7bo$o13boo10boo$bbo5bo$bo6bobo25boo$o3bobbo28boo$bobboboboo$6bo
boo11$9boo3bo$7b3o4boo$bb3obo8boo5bo$6bobobb5o5bobo$7bo3b3o7bobo$22bo
$$17boo$$18boo$8boo9bo$8boo34$58bo6boo$57bobo3bo3bo$56bo3bobo3boo$57bo
bobboboboo$58bo3bobboo$39bo22bo4bo$25boo7boobbobo22bobbo$25b3o6b4o3bo
23bo$25boobobo7bo$28boo10boboo$40bobo$41bo8boo$14b3o33boo$$18bo56bo$
14bo3boo41b3o10bobo$16bobo44bo11bo$13b3o7boo37bo$15bo7boo57bo$81bobo$
14boo28b3o34bobo$15boo24boboo37bo$15bo24bo3bo$15boo23bo3bo32boo$14boo
25b3o32bobbo$77boo$22boo$17bo4boo$3boo7boobbobo$3b3o6b4o3bo$3boobobo7b
o$6boo10boboo$18bobo$19bo6$26bo$25bobo$28bo$$25bo$17b3o$8boo5bo3b5obo$
8boo6boo4boobboo$16bob6o6$16boo$16boo!

The period 192 spaceship in the third row was discussed in my previous post.

The large beehive-pulling spaceship at the bottom contains sparks like previously known spaceships which can turn a sideways glider into a forward glider. But that reaction is useless in this spaceship since the glider runs into the front part of the spaceship.

The only remaining spaceship with sparks that I have found a use for is the first spaceship in the fourth row.

Code: Select all

#C A diagonal c/12 period 96 spaceship with a useful spark.
#C This is shown here using its two-cell diagonal spark to turn
#C two sideways gliders into forward and backward gliders.
#C The minimum population of this spaceship is 159 cells.
#C David I. Bell, 10 June 2025
x = 107, y = 112
105bo$104bo$104b3o30$88bo$88bobo$88boo32$25bo27bo$24b3o25bobo15bo$13b
oo8bobobo23bo3bo15bo$22b3ob3o12bo9bo3bo10bo$12bo3bo23bobo8bobob3o9bo$
17bo6bob3o13boo8boobobbo$10bo7bo5b5o9bo3bo13bobo12bo$9bo4bo9boobboo11b
obboo10boo13bo$10bobobo4bo6boboo14bo$10bo8bo8boo9bobboo$11bo4boobo4bob
obbo11bo7boo$12boboob3o3bobobbo20boo$13b3oboo5bo4$22boo15boo$13boo7boo
$13boo24boo$$40bobo$41boo$3bo$bb3o36b3o$bobobo10bo24bobbo$3ob3o9bobo
23boo$18b5o$bbob3o9bo$bb5o8bobbo4bo$bboobboo8bo5boo$4boboo9boo$6boo10b
obo$bbobobbo$bobobbo$bbo3$15b3o$15bobo7boo$15bobb3o4boo$21bo$18bobo$
19bo$$7boo$7boo!

This is now the smallest known Cordership which can turn a sideways glider into a forward glider. (The previous record holder had a minimum population of 172 cells, and was used in my recent variable period ping-pong spaceship.)

Amazingly, the population 159 spaceship can also reflect backward gliders by 180 degrees, similar to the population 172 one. The sparks of the two spaceships are different, and yet the reaction evolves into the exact same glider reflection.

This means I can replace the spaceship in the ping-pong spaceship with this smaller one.

Code: Select all

#C Two Corderships playing ping-pong with a glider.
#C The back Cordership uses an edge-spark to turn a backward
#C glider into a forward glider.  The front Cordership uses a
#C tub-deletion-to-release-a-glider reaction to turn a forward
#C glider into a backward glider.  Combining these results in a
#C spaceship where a glider travels back and forth between the
#C two Corderships.  This particular spaceship has period 864.
#C Shifting the topmost Cordership by 32 cells will change the
#C period by 288 generations, among other possible adjustments.
#C The spaceship is shown at its minimum population of 320 cells.
#C This is an improved version of similar spaceships.
#C David I. Bell, 10 June 2025
x = 182, y = 126
48b3o$49bo$49bobbo$49bobbo$50bobo$65boo$65boo3$49bo$48bobo$49bo$66bo$
65bo7boo$47b4o22boo$47boo3bo10bo$48bo4bo9bobo$50boboo10bo$51bo3$59bobo
boo$42bo16bobo$41b3o17bobbo$60bo3bo$41b3o16b4obboo$42booboo14bo5boo$
44bo21bo13$25bo$24b3o$23booboo7bo$22boo3bo6bobo$23bobobobo5bo$24boobo
bbo$27boobo$bbo25boo12bobo$bobo39boo$o3bo13b3o22bo$o3bo8bo$obob3o4boob
3o$boobobbo5boboo$5bobo8bo$5boo11bobbo$18b3o11$7boo$7boo$169boo$155bo
9bo3b3o$155b4o5bobobbo$155bo3bo5bo3bobbo$173bo$157b3o10bobo$15boo128bo
25boo7boo$15boo128bo34boo$145bo$149bo$145b3obbo$144bo4bo$144bo3bo4boo$
145b3o5boo$174bo$172boo$144bobo28bo$144bobo23bobobbo$144bobo23bobb3o$
144bobo24b4o$145boo25bo$152boo18bo$147boo3boo$133bo9bo3b3o$133b4o5bobo
bbo$133bo3bo5bo3bobbo$151bo$135b3o10bobo$149boo6$156boo$156boo3$148boo
$151booboo$138boo5bo4boo$138boo12boobo$145bobbo4boo$147bobobo$151bo4$
146boo$146boo$$136bo7bo$135b3o5bobo$134boob4obbobbo$135b3obbo$136bobb
oobbo$140boobobo$144bo!

Finally, here is a smaller ping-pong rake using the new ping-pong ship. The output glider's path is more straightforward than in the previous version.

Code: Select all

#C A diagonal c/12 rake with a minimum population of 459 cells.
#C This uses a glider which is reflected forwards and backwards
#C between two Corderships.  The period of this particular rake
#C is 864. Advancing the topmost Cordership by 128 generations
#C increases the period by 96 generations.  Only every third
#C advancement preserves the lowest population, however.
#C David I. Bell, 10 June 2025
x = 182, y = 178
48b3o$49bo$49bobbo$49bobbo$50bobo$65boo$65boo3$49bo$48bobo$49bo$66bo$
65bo7boo$47b4o22boo$47boo3bo10bo$48bo4bo9bobo$50boboo10bo$51bo3$59bobo
boo$42bo16bobo$41b3o17bobbo$60bo3bo$41b3o16b4obboo$42booboo14bo5boo$
44bo21bo13$25bo$24b3o$23booboo7bo$22boo3bo6bobo$23bobobobo5bo$24boobo
bbo$27boobo$bbo25boo$bobo$o3bo13b3o$o3bo8bo30boo$obob3o4boob3o27bo$boo
bobbo5boboo26bo$5bobo8bo$5boo11bobbo$18b3o11$7boo$7boo$169boo$155bo9bo
3b3o$155b4o5bobobbo$155bo3bo5bo3bobbo$173bo$157b3o10bobo$15boo128bo25b
oo7boo$15boo128bo34boo$145bo$149bo$145b3obbo$144bo4bo$144bo3bo4boo$
145b3o5boo$174bo$172boo$144bobo28bo$144bobo23bobobbo$144bobo23bobb3o$
144bobo24b4o$145boo25bo$152boo18bo$147boo3boo$133bo9bo3b3o$133b4o5bobo
bbo$133bo3bo5bo3bobbo$151bo$135b3o10bobo$149boo6$156boo$156boo3$148boo
$151booboo$138boo5bo4boo$138boo12boobo$145bobbo4boo$147bobobo$151bo4$
146boo$146boo$$136bo7bo$135b3o5bobo$134boob4obbobbo$135b3obbo$136bobb
oobbo$140boobobo$144bo4$106b3o$106b3o$107bo$108boo$109bo21bo$108bo14b
oo5boo$123boo5bobo3$106boo$95bo10boo$90bobbobobbo3bo4bo$90bo4boob5o4bo
15bo$90bo3bo4bobo4bobo15boo$105bo16bobo$92b3o11bobboo11bobbo$93bo13bo
3bo10boobo$109boo12bobo$109bo13bobo$104boo17b3o$95boo7boo17b3o$95boo$
84b3o31bobbobo$84b3o30bo6bo$85bo32bo5bo$86boo31bo$87bo$86bo4$84boo$84b
oo$85bo$85bo$84bobo$83bo$84bobboo11boo$85bo3bo9bobbo$87boo13bo$87bo11b
obbo$98b4o$98bo$98bo4$89boo$89boo!

EDIT:

I found a use for the sparking spaceship in the top row.

Code: Select all

#C A diagonal c/12 sparking ship detects a backward glider.
#C The sparks from a period 96 population 147 Cordership can act as a
#C Heisenburp device for a backward glider.  A block is created if a
#C glider is detected.  This shows two reactions that do this.
x = 201, y = 76
54bo$55bo$53b3o5$197bo$195bobo$196boo$52b3o$51bo$51bo3bo$49boo3boo$48b
obbobobbo$48bobbobobboo$26bo23booboobbo$25b3o23bo4bo137b3o$24booboo25b
ooboo134bo$23boobobo24b4o136bo3bo$22b3obb3o24boo135boo3boo$23bo6bo159b
obbobobbo$24b5obo159bobbobobboo$25b4oboo136bo23booboobbo$30bo136b3o23b
o4bo$29bo12boo122booboo25booboo$42boo121boobobo24b4o$164b3obb3o24boo$
165bo6bo$10b3o13boo138b5obo$8b7o9bo142b4oboo$7b9o11bo144bo$6bo7b3o154b
o12boo$7b3o12boobboboo154boo$8boo13bobbo$11bo10bo4bobo$12bo13boo3boo
119b3o13boo$13bo12boobboboo11bo104b7o9bo$4bo19boboo3boo10booboo101b9o
11bo$3b3o17booboo3bo116bo7b3o$bbooboo7boo7boobo14booboboo101b3o12boobb
oboo$boobobo7boo9bo18bo105boo13bobbo$3obb3o33bobbo108bo10bo4bobo$bo6bo
27boo4boo110bo13boo3boo$bb5obo27boo117bo12boobboboo11bo$3b4oboo136bo
19boboo3boo10booboo$8bo136b3o17booboo3bo$7bo136booboo7boo7boobo14boobo
boo$143boobobo7boo9bo18bo$142b3obb3o33bobbo$143bo6bo27boo4boo$5bo138b
5obo27boo$3boobo138b4oboo$150bo$6bo142bo$3bobbo12bo$4bo13b3o$18boobo$
9boo9b3o124bo$bb3o5boo8boo123boobo$9boo9boo$9bo10boo126bo$18boobo123bo
bbo12bo$19boo125bo13b3o$160boobo$151boo9b3o$144b3o5boo8boo$8boo141boo
9boo$8boo141bo10boo$160boobo$161boo4$150boo$150boo!

This allows the easy creation of a rather large fanout device.

Code: Select all

#C Corderships generating multiple output gliders from one glider.
#C This shows four Heisenburp reaction spaceships and block-to-glider
#C spaceships which turn a backward glider into four sideways gliders.
#C The backward glider emerges unchanged.  The timings of the output
#C gliders can be changed by adjusting the phases of the spaceships.
x = 281, y = 272
58bo$59bo$57b3o9$50bo7bo$49b3o5bobo$48boob4obbobbo$49b3obbo$50bobboobb
o$23bo30boobobo$23bo5b3o26bo$22bobo3boobbo$23bo3bo5bo$23bo3bo$28bobboo
$29boo11boo$42boo$$6bo$5b3o$4b3obo$3boo3boo5boo7bo$bboobobboo5boo6b4o$
3booboboo12bobboo$4b3oboo12bo13bo11boo$6bo4bo11b3obo8boo9bobo$7b4o14bo
bbo5bobboo10bo$9bo16b3o5bo3bo23b3o$33bobobbo$33boo31boo$14boo10boo40bo
10b3o$bo12boo10boo34b4obo11bo$bo5b3o52b5o$obo3boobbo25boo10bo$bo3bo5bo
24boo10bo30bobbo$bo3bo44bo5bo5bobo14boboo$6bobboo38bo6bobo3bobo14bobbo
$7boo39bo3bobbo7bo15bobo5boo$49bobboboboo4bobo14b3o5boo$54boboo5boo$
63bo3$60boo$51boo7boo$51boo25boo$14bo62bo$4boo9boo60boo$3bob3o8boo60b
oo$3bo3bo10bo3bo17b3o36bobbo$4boobo5b5o3bobo56bobbo$5bo10bo4bobo20boo
36bo$22bo23bo34bo$40b4obo$40b5o$54bo$19bo33bobo$8boo9bo20bobo10bobboo$
8boo30bobo11bobbo$41bo13b3o$40bobo$41boo$41bo11b3o$53bobo$56bobo$52bo
6bo3boo$56boboo3boo$53bob3obbo$53boob5o53bo7bo$58bo54b3o5bobo$112boob
4obbobbo$45boo66b3obbo$45boo67bobboobbo$87bo30boobobo$87bo5b3o26bo$86b
obo3boobbo$87bo3bo5bo$87bo3bo$92bobboo$93boo11boo$106boo$$70bo$69b3o$
68b3obo$67boo3boo5boo7bo$66boobobboo5boo6b4o$67booboboo12bobboo$68b3ob
oo12bo13bo11boo$70bo4bo11b3obo8boo9bobo$71b4o14bobbo5bobboo10bo$73bo
16b3o5bo3bo23b3o$97bobobbo$97boo31boo$78boo10boo40bo10b3o$65bo12boo10b
oo34b4obo11bo$65bo5b3o52b5o$64bobo3boobbo25boo10bo$65bo3bo5bo24boo10bo
30bobbo$65bo3bo44bo5bo5bobo14boboo$70bobboo38bo6bobo3bobo14bobbo$71boo
39bo3bobbo7bo15bobo5boo$113bobboboboo4bobo14b3o5boo$118boboo5boo$127bo
3$124boo$115boo7boo$115boo25boo$78bo62bo$68boo9boo60boo$67bob3o8boo60b
oo$67bo3bo10bo3bo17b3o36bobbo$68boobo5b5o3bobo56bobbo$69bo10bo4bobo20b
oo36bo$86bo23bo34bo$104b4obo$104b5o$118bo$83bo33bobo$72boo9bo20bobo10b
obboo$72boo30bobo11bobbo$105bo13b3o$104bobo$105boo$105bo11b3o$117bobo$
120bobo$116bo6bo3boo$120boboo3boo$117bob3obbo$117boob5o53bo7bo$122bo
54b3o5bobo$176boob4obbobbo$109boo66b3obbo$109boo67bobboobbo$151bo30boo
bobo$151bo5b3o26bo$150bobo3boobbo$151bo3bo5bo$151bo3bo$156bobboo$157b
oo11boo$170boo$$134bo$133b3o$132b3obo$131boo3boo5boo7bo$130boobobboo5b
oo6b4o$131booboboo12bobboo$132b3oboo12bo13bo11boo$134bo4bo11b3obo8boo
9bobo$135b4o14bobbo5bobboo10bo$137bo16b3o5bo3bo23b3o$161bobobbo$161boo
31boo$142boo10boo40bo10b3o$129bo12boo10boo34b4obo11bo$129bo5b3o52b5o$
128bobo3boobbo25boo10bo$129bo3bo5bo24boo10bo30bobbo$129bo3bo44bo5bo5bo
bo14boboo$134bobboo38bo6bobo3bobo14bobbo$135boo39bo3bobbo7bo15bobo5boo
$177bobboboboo4bobo14b3o5boo$182boboo5boo$191bo3$188boo$179boo7boo$
179boo25boo$142bo62bo$132boo9boo60boo$131bob3o8boo60boo$131bo3bo10bo3b
o17b3o36bobbo$132boobo5b5o3bobo56bobbo$133bo10bo4bobo20boo36bo$150bo
23bo34bo$168b4obo$168b5o$182bo$147bo33bobo$136boo9bo20bobo10bobboo$
136boo30bobo11bobbo$169bo13b3o$168bobo$169boo$169bo11b3o$181bobo$184bo
bo$180bo6bo3boo$184boboo3boo$181bob3obbo$181boob5o53bo7bo$186bo54b3o5b
obo$240boob4obbobbo$173boo66b3obbo$173boo67bobboobbo$215bo30boobobo$
215bo5b3o26bo$214bobo3boobbo$215bo3bo5bo$215bo3bo$220bobboo$221boo11b
oo$234boo$$198bo$197b3o$196b3obo$195boo3boo5boo7bo$194boobobboo5boo6b
4o$195booboboo12bobboo$196b3oboo12bo13bo11boo$198bo4bo11b3obo8boo9bobo
$199b4o14bobbo5bobboo10bo$201bo16b3o5bo3bo23b3o$225bobobbo$225boo31boo
$206boo10boo40bo10b3o$193bo12boo10boo34b4obo11bo$193bo5b3o52b5o$192bob
o3boobbo25boo10bo$193bo3bo5bo24boo10bo30bobbo$193bo3bo44bo5bo5bobo14bo
boo$198bobboo38bo6bobo3bobo14bobbo$199boo39bo3bobbo7bo15bobo5boo$241bo
bboboboo4bobo14b3o5boo$246boboo5boo$255bo3$252boo$243boo7boo$243boo25b
oo$206bo62bo$196boo9boo60boo$195bob3o8boo60boo$195bo3bo10bo3bo17b3o36b
obbo$196boobo5b5o3bobo56bobbo$197bo10bo4bobo20boo36bo$214bo23bo34bo$
232b4obo$232b5o$246bo$211bo33bobo$200boo9bo20bobo10bobboo$200boo30bobo
11bobbo$233bo13b3o$232bobo$233boo$233bo11b3o$245bobo$248bobo$244bo6bo
3boo$248boboo3boo$245bob3obbo$245boob5o$250bo$$237boo$237boo!

BCNU,
-dbell

[dbell]

I recently found this Cordership.

Code: Select all

#C A period 96 diagonal c/12 spaceship having a blocked glider.
#C The interaction between a two-engine Cordership and a wing
#C component creates a glider and a block which destroy each other.
#C There are many reactions using a forward glider which can
#C destroy the block, thereby releasing the glider.  So the
#C spaceship can be used to reflect gliders with several different
#C lanes and many glider phases.  The minimum population of the
#C spaceship is 205 cells.
#C David I. Bell, 7 June 2025
x = 70, y = 87
41bo$41bo5b3o$40bobo3boobbo$41bo3bo5bo$41bo3bo$46bobboo$47boo11boo$60b
oo6$36bobo$22bobo7bobbobbo29boo$21booboo5boboboobo29boo$22boboo6bo$26b
o11b3o$25bo13boo$25bo12boo24boo$63bobbo$62booboo$61bobo$59b3o$58bo5bo$
55bobbo5bo$54bobobbobboo$54bobboo$45boo9boo$44boboo5bo$42boo4bo3boo$
27boo12bo3bo3bo$27boo14boo3bo$42bobb3o$43b3o$43bo4$35boo$35boo9$28bo$
27boboo$31bo$25bo3bobbo6boo$23bo9bo6bo$23bo4boobboo5boo$32boo4b3o$5bo
19bo5bo6bobo$4bobo19bo4b3o5bo$4bobboo18bo4boo14bo$bb7o14bo5b4o16bo$bo
bbo3bo14bo23b3o$3obb7o11bo$bb3obbo8bo$3booboo8bo$4b3obobbo38boo$5b3ob
oo13boo24boo$8bo13boobo$21bo3bo$21bobboo$22b3o$23bo7$11boo$11boo7$19b
oo$19boo!

I thought that maybe the block could be deleted by a sideways glider released from a three-engine Cordership, reminiscent of my new sparking spaceships.

I found that there are lots of phases of the three-engine Cordership what can create gliders to delete the unwanted blocks, thereby releasing the gliders.

Code: Select all

#C A collection of similar period 96 diagonal c/12 backward rakes.
#C These use a two-engine Cordership, a three-engine Cordership,
#C and a bare switch engine.  These are shown at their minimum
#C populations of 267, 272, 278, 278, and 282 cells.
#C David I. Bell, 11 June 2025
x = 592, y = 102
58bo249bo123b3o$57bobo247bobo121bo139bo$56bo3bo13b3o229bo3bo13b3o103bo
4boo120boo7boobbobo$56bo3bo8bo236bo3bo8bo109bo3bo15b3o105b3o6b4o3bo$
56bobob3o4boob3o115bo117bobob3o4boob3o106bobbo4bo4boo113boobobo7bo$57b
oobobbo5boboo114bobo117boobobbo5boboo106bo3bo3bo4b3obo113boo10boboo$
61bobo8bo113bo3bo13b3o104bobo8bo107boobob3o134bobo$61boo11bobbo5boo
101bo3bo8bo111boo11bobbo5boo98bo139bo8boo$74b3o6boo101bobob3o4boob3o
121b3o6boo99b4o20boo122boo$46bo140boobobbo5boboo93bo139boo11boboo5boo$
46bo144bobo8bo93bo124bo27bobbo$46bo144boo11bobbo5boo81bo124bo27b3o$49b
oo153b3o6boo84boo119bobo122bo$49boo12boo111bo122boo12boo106boobbo11boo
104booboo$44bo3b3o11boo112bo117bo3b3o11boo106bo5bo9bobbo105bo$45b3o15b
o112bo118b3o15bo106bo5bo10boo121boo$46bo15b3o114boo115bo15b3o105bo4bo
12bo120bobbo$45boo15b3o23boo89boo12boo100boo15b3o23boo84bo13bo107boo
11booboo$45b3o16bo22b4o83bo3b3o11boo101b3o16bo22b4o80b3o13boobo21bo82b
obbo11bo$47bo14bobbo20bo3bo84b3o15bo103bo14bobbo20bo3bo95boo23bobbo79b
oo3bo10b3o26boo$45bo16b3o26bo84bo15b3o100bo16b3o26bo98bo20bo82bo4bo34b
oo3boo$47bo15bo27bo83boo15b3o23boo77bo15bo27bo77booboo12bob3o25bo77bo
3bo36b3obboo$45b3o44bo82b3o16bo22b4o74b3o44bo81bo12bobbo26bo77bobbo36b
oobb3o$177bo14bobbo20bo3bo198boo16b3o25boo79bo$175bo16b3o26bo199b3o$
177bo15bo27bo340bo$175b3o44bo335bo3bo$559bobbo$60bobo247bobo122boo122b
ooboo$60bobbo246bobbo124bo121bobo$60bobbo246bobbo121bobbo122bo$60bo3bo
245bo3bo121boo$50boo9bobo126bobo107boo9bobo122boo111boo$50boo10bo127bo
bbo106boo10bo112boo8bobbo110boo$190bobbo231boo8bo$190bo3bo241b3o$180b
oo9bobo$180boo10bo3$58boo248boo247boo$58boo248boo123boo122boo$433boo$$
188boo$188boo$52b3o247b3o123bo$52b3o247b3o122b3o$53bo220bo28bo248bo$
23b3o28boo218bo29boo121b3o122bo$23b3o29bo126b3o89bo30bo92b3o27booboo
118bobo$24bo29bo127b3o90boo27bo94bo30bo121boobbo$25boo126b3o27bo91b3o
121bobbo119b3o26bo5bo$26bo126b3o28boo89boo122bobbo148bo5bo$25bo14boo
143bo104boo108bobo123boo23bo4bo$40boo10boo99boboo27bo105boo10boo111boo
111bo10b3o13bo$52boo99bo3bo144boo111boo105b4obo11bo12b3o$53bo101b3o
145bo218b5o$23boo145boo102bo233bo$12bo10boo145boo10boo89bobo123bo108bo
30bobbo7booboo$7bobbobobbo3bo4bo157boo73bo3boobboobo4bobbo121bobo109bo
5bo5bobo14boboo12bo$7bo4boob5o4bo15bo142bo73bo3boo4boboo20boo93boo3b4o
4bo109bo6bobo3bobo14bobbo7boo$7bo3bo4bobo4bobo15boo111bo102bo3boobboob
oo20b3o88b3obobbo6bo19bobo90bo3bobbo7bo15bobo5boo3b3o$22bo16bobo105bob
o3bobo105boo9bobbo14boo93bobbobb5o113bobboboboo4bobo14b3o5boo$9b3o11bo
bboo11bobbo95bob3o4bobo4bo104bobbo9boob3o10boobboo91bobbo8b4o17bo95bob
oo5boo$10bo13bo3bo10boobo93boobo4bo6boboo104bobo12boobbo9bobo96bo9boo
3bo10bo3bo105bo$26boo12bobo95boo4bobbo5boo105bo14bobbo15bo89bobo11bo4b
o9bo4bo$26bo13bobo101bobbo3boobo120bobo11boo3bo90bo14boboo11bo$21boo
17b3o100bo4bobbobboo115boo16bo3bo107bo12boobboo100boo$12boo7boo17b3o
96bobbo10boboobo13bobo87boo7boo17boo104boo16bobo94boo7boo$12boo126boo
11bo4bo10boo81bo9boo25b3o95boo7boo18boo93boo25boo$b3o31bobbobo115bobo
10boboboo77bo36bobo95boo25bobbo119bo$b3o30bo6bo109boo18bo80bo31boo90b
3o35bobo120boo$bbo32bo5bo100boo7boo17boobo79boo29boo91bo31boo127boo$3b
oo31bo94b3o8boo28bo80b3o121bobbo28boo89b3o36bobbo$4bo126b3o119boo122bo
bbo159bobbo$3bo160boo212bobo123boo36bo$131boboo29boo340bo34bo$131bo3bo
364b4obo$133b3o364b5o$boo249bo261bo$boo248bobo123bo135bobo$bbo248bobbo
121bobo121bobo10bobboo$bbo374bo122bobo11bobbo$bobo128bo368bo13b3o$o
130bobo116bobbo246bobo$bobboo11boo113bo117boob3o11boo106b4o122boo$bbo
3bo9bobbo111boo119boobbo10bobbo104boo3bo11boo107bo11b3o$4boo13bo111boo
120bobbo9boobbo105bo4bo12bo118bobo$4bo11bobbo112bo120bobo9boo3bo107bob
oo8bobob3o119bobo$15b4o111boboo13boo118boo110bo10bobboo117bo6bo3boo$
15bo115boboobo9b3o115booboo120bo3boo121boboo3boo$15bo115bo4bo11bo242b
3o119bob3obbo$134bobo7bobbo365boob5o$144bo373bo$147boo$6boo139bo108boo
247boo$6boo248boo123boo122boo$381boo$$136boo$136boo!

These are not the smallest known backward rakes, but they can can still be used to create sawtooths with a smaller population than the ones using the older rakes. (This is because the need for a cleanup two-engine Cordership is unnecessary.)

BCNU,
-dbell

[hotdogPi]

This lumps of muck-based block puffer is known, but I don't think David Bell has seen it since he wasn't active at the time. When it was made, it was essentially a proof that something existed with no attempt to make it small. Could it be reduced?

Code: Select all

x = 171, y = 171, rule = B3/S23
28bo$20bo7bo$20b3o5bo$22bobo3b2o$20bo2bo$20b2o2bo$8b2o$8b2o7$2o$2o$14b
2o3b2o$13bobo3b4o3bo$13bo3bo2bo2b2obo$13b2o3bo4b2obo$18bo3bo$17bo3$27b
o6b3o$27bob2o3b2o$27bobo5b2o$27bob3o$27b2o14$28bo$29b2ob2o12bo$29b2ob
o12bobo$31bo12bo3bo$44bo3bo$42b3obobo$41bo2bob2o$41bobo$42b2o8$24b2o$
20bo$22bo$20bobo$65b2o6bo$64bo3bo3bobo$35b3o26b2o3bobo3bo$34bo4bo8bo15b
2obobo2bobo$38b2o8b4o13b2o2bo3bo$34bo3bo25bo4bo$34bo30bo2bo$34bobo29b
o$34bo11bobo$32bo3b2o9bo$36b2o10b2o$35bobo8bo2bo$30bo5bo9b2ob2o2$30b2o
b2o$32b3o24bo$57bo2bo7b3o$56bo3bo5b2obobo$56bo3bo5b2obobo$56bo3b2o5bo
3bo$57bo2bo7bobo$69bo4$65bo$64bobo$64bobo$65bo5$57bo48bo$56bobo46bobo
$56bobo45bo3bo$57bo47bobo$89b3o14bo$88bo3bo$87bo2b3o10b4o$88bo3bo9bo4b
o$49bo39b3o13bo$48bobo30b2o7b2o9bo2bo3bo$48bobo29bo2bo18bob3obo$49bo31b
2o20bob3o3$89bo$88b5o$93bo$73b2o$40bo31bo2bo12bo3bo$40bo32b2o14b3o2$38b
3o$40bo$21bo3b2o10bob2o$21b2o13b2o66bo$37b2o26b2o29bo7bo$37bob2o23bo2b
o28b3o5bo$24bo12b5o23b2o31bobo3b2o17b3o$23bobo10bobo2b2o53bo2bo22bo3b
o$23bo12b2o3b3o52b2o2bo21b2o3bo$24bo2bo13b2o83bo$13b2o9bo3bo11b2o80b4o
$13b2o9b2obo12bo5bo73b2obo$24bo20b3o72bo2bo$24b3o17b5o72b2o$14b2o27b2o
3b2o2b3ob2o$14b2o32b2o2bobo49b2o$47b2obo3bo48b2o$46bob5o44b3o6bo$46b2o
3bo44bob2obo4bo37bobo$97bo8bo37b3o$93b2o5b4obo39b2o$93b2o32bo$93bo5bo
26b2o$94bo30bo17bo$94bobo29b2o15bobo$126b2o15b3o21bo$44bo83bo13bo24b4o
$43bobo96b5o$41bo10bo98b3o$41bobo3bo4bo59bo$41b5o2bo63bo38b2o12bobo$46b
2o103b2o13bo$51bo57b2o39bo2bo13b2o$51b2o100bo11bo2bo$109bobo40b3o10b2o
b2o$153b2o$150b2o$149bo2bo2$39b2o112b2o$39b2o2b2o106bo2bo$43b2o106b3o
4$163b2o$163b2o7$155b2o$155b2o!

[dbell]

Here is an application of the period 192 sparking Cordership.

Blocks can be used to cleanly change the phase of the Cordership. (Examine this every 192 generations to see the subtle changes.)

Code: Select all

#C A diagonal c/12 period 192 spaceship showing phase changes.
#C This shows three blocks reacting with a period 192 sparking
#C Cordership so as to change its phase by 96 generations for
#C every block it consumes.  Blocks can be placed on the same
#C diagonal at any multiple of eight cells to make the changes,
#C even though an unperturbed spaceship moves 16 cells to
#C return to the same state.
x = 76, y = 123
5boo$5boo23$29boo$29boo31$61boo$61boo10$55bobo$54bo$55bobbo$27bo29bobo
$26boo32bo11b3o$25b5o29b3o$24bo19bo14bo$23boo5bo13bo12boo$22b3oboo8bob
o5bo14bo13b3o$23boboboobboo3bobo18bobbo12b3o$16b3o5bobbobboo5bo19bobo
13boo$16b3o7boo29bo14bo$17bo10boobo20boo13booboobbo$18boo11bo12b3o5boo
12bobobbo3bo$19bo22boobbo21bobbobbo$18bo24b3o26b3o$44bo$$25boo$16boo7b
oo$16boo$$41bo5boo$39boo7boo$47boo$5bo40boo$4boo12boo26bo$3b5o10boo4bo
$bbo21b3o$boo5bo16boo$3oboo10boboo5boo$boboboobboo6booboobbo$bbobbobb
oo6boobboo$4boo14bo$6boobo10b4o$9bo10boobbo$20boobbo$21b3o$22bo$$28boo
$28boo4$25boo$10boo14bobo$10boo16bo$22bo3boo$21bo3boo$22b3o4$18boo$18b
oo!

The sparks can be perturbed by another Cordership to create several different period 192 puffers, most usefully just blocks.

Code: Select all

#C A diagonal c/12 period 192 block puffer whose phase can be changed.
#C This uses a period 192 Cordership whose sparks are perturbed by a
#C two-engine Cordership so as to create blocks every 16 diagonal cells.
#C Also shown are two blocks laying in the path of the puffer which
#C change the phase of the sparking spaceship by 96 generations.
#C Each input block shifts the block output by eight cells.
x = 160, y = 187
oo$oo63$64boo$64boo15$133b3o$133b3o$$133boboo$133bo3bo$135b3o$150boo$
150boo5$118bo$117boo7bo$116bobob3obbobo30boo$115b3o3boo3bo31boo$116bob
oboobobo$117booboo29boo$118bob5obo24b3o$122b4o28bo$153boo$151b3o$150b
oo$148boo$149bo$$145b4o$144bo$121bo22bobboo$124bo6bobo11b3o$119bo11bob
obo10bo$118bo3bobbo10boo3boo$119b3obbo10bobo3b3o$120bo3bo13bobooboo$
122boo13b3obobbo$122bo14boboob3o4$125boo13boo$125boo$$135boo$136boo$
136bobo$136bobo$135boobbo$134bo3bo$135b3o$136bo$$114bobo$113bo$114bobb
o$86bo29bobo$85boo32bo11b3o$84b5o29b3o$83bo19bo14bo$82boo5bo13bo12boo$
81b3oboo8bobo5bo14bo13b3o$82boboboobboo3bobo18bobbo12b3o$75b3o5bobbobb
oo5bo19bobo13boo$75b3o7boo29bo14bo$76bo10boobo20boo13booboobbo$77boo
11bo12b3o5boo12bobobbo3bo$78bo22boobbo21bobbobbo$77bo24b3o26b3o$103bo
$$84boo$75boo7boo$75boo$$100bo5boo$98boo7boo$106boo$64bo40boo$63boo12b
oo26bo$62b5o10boo4bo$61bo21b3o$60boo5bo16boo$59b3oboo10boboo5boo$60bob
oboobboo6booboobbo$61bobbobboo6boobboo$63boo14bo$65boobo10b4o$68bo10b
oobbo$79boobbo$80b3o$81bo$$87boo$87boo4$84boo$69boo14bobo$69boo16bo$
81bo3boo$80bo3boo$81b3o4$77boo$77boo!

The period 192 sparking spaceship is able to distinguish between the two sets of blocks so as to delete one set. So adding this to the block puffer can create a block puffer which can be turned on or off.

Code: Select all

#C A diagonal c/12 period 192 block puffer which can be turned on and off.
#C This uses a period 192 block puffer with a following period 192
#C sparking spaceship which deletes the output blocks if they are on the
#C correct diagonal position.  In the initial state shown here the
#C blocks are allowed to live.  A block in the path of the puffer
#C changes the phase of the puffer which shifts the location of the
#C blocks so that they are deleted.  Another block in the path could
#C be used to re-enable the output.
x = 148, y = 144
boo$boo14$67boo$68bobbo4bo$65bobb3obobbobo$65bobbo4b4o$65bobbo$68bo6bo
$67boobo$75bo11boo$73boo12boo5$49bo$48b3o15bo$47booboo14bo28boo$46boo
3bo7b4o3bo28boo$47bobobobo5bo3bo$48boobobbo4boo3bo$51boobo7b3o25bobbo$
52boo10boobo21bo4bo$65b3o20boobobbo$66bo20boo3bobbo$88boo3boo$84bo4bo$
84boo$82b6o$82boob3o$82boobobo$73bo$69bobbo4bo$69bobbobb4obo$54boo15bo
bboob3o$54boo14boob3o$71b3o$71b3o5$62boo$62boo7$53bo$52bobo$51booboo$
51booboo$50b3o$24bo25b3o3bo12bo$23bobo24b3o4bo10boobboo$22booboo24boo
5bo9b3obo$22boo16boo9b3o12bobboo$28boo9bobbo9boo10boobbo$22b3obbo12bo
bbo9boo10bobo$26boboo36bo$24bobbo$17bo9bo11bo42boo$9b3o3b4o6boo11boo3b
o38boo$9bobo3booboo19bo3boo$9b3obbo10bo13boboboo10bo$14boo3bo3booboo
11bo3boo$15b4o7bo13b3o$16b3o4bo16b3o$25bo$$21boo$12boo7boo16bo$12boo
24b3o$37boobbo$36boobboo$bbo37bo$bobo38boo$ooboo37boo37bo16boo$oo78bob
o15boo$6boo71booboo$3obbo73booboo$4boboo70b3o$bbobbo46bo25b3o3bo$5bo9b
obboo31bobo24b3o4bo$3boo8boo5bo29booboo24boo5bo$20bo29boo16boo9b3o$3bo
52boo9bobbo9boo$booboo9bo3bo30b3obbo12bobbo9boo$4bo10bo38boboo37boo$bo
14bo35bobbo41bo$3bo11b3o27bo9bo11bo27boo$37b3o3b4o6boo11boo3bo$20bobo
14bobo3booboo19bo3boo$21bo3bo11b3obbo10bo13boboboo10bo30boo$14boo4bo3b
o17boo3bo3booboo11bo3boo41boo$14boo4bo22b4o7bo13b3o$44b3o4bo16b3o$53bo
$6boo$6boo41boo$40boo7boo16bo$40boo24b3o$65boobbo$64boobboo$30bo37bo$
29bobo38boo$28booboo37boo$28boo$34boo$28b3obbo96boo$32boboo94boo$30bo
bbo$33bo9bobboo$31boo8boo5bo$48bo$31bo$29booboo9bo3bo$32bo10bo$29bo14b
o$31bo11b3o$$48bobo$49bo3bo$42boo4bo3bo$42boo4bo$146boo$146boo$34boo$
34boo!

Here is the toggable puffer being repeatedly triggered.

Code: Select all

#C A diagonal c/12 period 2496 (96 * 13 * 2) irregular block puffer.
#C This uses a period 1234 sideways rake whose gliders are turned
#C into blocks by a two-engine Cordership, and those blocks are
#C then consumed by a toggable block puffer.  The result is a puffer
#C which emits six blocks in a row and gaps of seven missing blocks.
x = 229, y = 230
45boo$41boo3bo$30b3o7bo6bo$33b3o5bo3b5o$33b3o6bo3bo$34bo11bobbo$47boo
7boo$56boo5$57bo$57boo$55boobbo4boo$53bo4boo4boo$54boo$54bo$36boo6bobb
oobo$36boo5bo3bo3boo$47b3obo$41bo7boo$40bobbo$39bobbo$24bo14bo$24b4o6b
o4b3o27boo$24bo3bo5bo34bobo$70bo$26b3o$66bo65boo$15boo48boo$11boo3bo
48bobo63bo3bo$3o7bo6bo118bo$3b3o5bo3b5o57boo50bo7bo$3b3o6bo3bo60bobo
48bo4bo$4bo11bobbo58bo50bobobo4bo$17boo110bo8bo$130bo4boobo$131boboob
3o$132b3oboo$149boo$22boo61boo62boo$25bo59bobo$22bo3bo59bo$23bobbo$23b
oboo$16boo4b4o$16boo4bobo92bo$6boo6b4o9bo85boobobo7bo30boo$6boo5bobo
10bo66boo18bobbooboobbooboo29boo$13bobo10b3o64bobo17bo5bobo5bo$94bo19b
oobbo8bo$118bobb3obbo24boo$118b3o29b3o$150bobbo$150boobo$14boo135boo$
14boo85boo$101bobo$102bo39b3o$78bo63bobo$77bobo18bo42boobobboo$76boob
oo16boo35bo7bobbobboo$76booboo16bobo21bobbo9boo6bo3boboo$75b3o46b5oboo
3bo6bo5boo$75b3o3bo12boo13boo5boo3boob6oboobo5bo7bo$75b3o4bo11boo13bob
o4boo9bobo4bo$76boo5bo26bo19b3oboo3bo3bo3bo$76b3o52bobbo3boo$77boo44bo
8b4oboo$78boo54boo3bo$93boo41b3o$136boo$61b3o6bo22b3o6boo13boo5boo$62b
oo3boobo6bo4bo10bobo6boo13bobo4boo$61boo5bobo5bobbo3bo34bo$66b3obo7boo
15bo$69boo7boobboo10boo18bo$94boo17boo$113bobo$93boo$93b3o29boo$91b3o
31bobo$91bo34bo$$90b3o$90bo$90b3o$71bo3boo$65boboo3boboobo$63boobo3bob
o4boo$66bobobb3obboo7boo$67bo4boo10bobbo$85boo43bo$43boo40boo42boo$43b
3o35boobo44bobo$43boobo34bobbo$47bo13bo20b3o$39bo3boo3bo12bo7boo$49bo
11bo7boo$46bobo31boo$46bo33b3o$41bo4bobo13bo18bo21bo93b5o7bo$60booboo
4boo7booboo20boo90boo5boo4bobo$45b4o20boo7booboo19bobo90bo7bo4bo$45boo
12bobo18bo114boo7bo3bobbo$59bo3bo133boo6bo3b3o$59boobbo9boo125bo$60b3o
9bo127bo4bo13boo$61bo5bobbo130boobo14boo$38bo28bobb5o82boo$34b5o7boo
19boob4o83boo$34bo3bobo4b3o25boo$34b3o3b3o3b3o24b3o107bo$40boobb3obo
24b3o104b4o$40bo7b3o12bo$37b3o9boo10booboo131b3o$37boo26bo$61bo3bo117b
obo12boo26bo$62b3o119bo13boo27boo$182boo13bobbo21boobb3o$182bobbo11bo
23b3obbo$181booboo10b3o23bo$196boo24bobb4o$199boo22bobo$198bobbo$52bob
4o$37bo3b3obo6boo4bo137boo$36bobo3bobobo5bo3boboo136bobbo$36bob7oboo5b
3obo139b3o$37b3oboo3bo$43b3o$44bo$186boo$186boo$$44boo$44boo4$194boo$
194boo4$184b3o$183bobbo$182bo4bo$182bobb3o$156bo25bo5bo$155bobo25b7o$
155bobo31bo$155bobbo30bo$156bobo28boo17boo$159bo46boo$158boo$158bo13b
oo$172boo3$156bo$143bo11bobo$139b5o8bobobbo$139bo3bobo4bo3bobbo$139b3o
3b3o5bo3bo$145boobboobboo$145bo7bo4bo$142b3o9boob3o$142boo12b3oboo9b4o
bo$154bo4bo11boboo47boo$153boo18boboo45boo$134bo9boo7boo17boo$133bobo
8boo27boo$133bobo$133bobbo29boo44b3o$134bobo29boo43bobbo$137bo72bo4bo$
136boo72bobb3o$136bo47bo25bo5bo$183bobo25b7o$183bobo31bo$183bobbo30bo$
134bo49bobo28boo$133bobo51bo$135bo50boo$135bo50bo13boo$135bo64boo$$
136bo11bobo$132boob3o10bobbo32bo$134b3oboo8bobo20bo11bobo$137bo29b5o8b
obobbo$149boo16bo3bobo4bo3bobbo$149boo16b3o3b3o5bo3bo$149boo22boobboo
bboo$173bo7bo4bo$170b3o9boob3o$170boo12b3oboo9b4obo$138boo42bo4bo11bob
oo$138boo41boo18boboo$162bo9boo7boo17boo$161bobo8boo27boo$161bobo$161b
obbo29boo$162bobo29boo$165bo$164boo$164bo4$162bo$161bobo$163bo$163bo$
163bo$$164bo11bobo$160boob3o10bobbo$162b3oboo8bobo$165bo$177boo$177boo
$177boo4$166boo$166boo!

Note that a boat-loop based rake can create such irregular output by itself, so the above pattern is pointless except as a demonstration.

The important feature is that the block output can be triggered on and off as desired. (However I don't know of any useful application for such a toggled puffer.)

BCNU,
-dbell

[dbell]

Here is an interesting period 96 Cordership based on another one of the recent sparking spaceships.

Code: Select all

#C A diagonal c/12 period 96 spaceship with an integral tagalong.
#C This uses a period 96 sparking Cordership which is perturbed
#C by the sparks from a two-engine Cordership.  The interaction
#C creates and supports a tagalong composed of loafs and blocks.
#C David I. Bell, 1 July 2025
x = 94, y = 96
62bo3boobboobo$62bo3boo4boboo$62bo3boobbooboo$66boo$64bobbo$64bobo17b
oo$65bo18boo3$46bo$45boo$44b5o$43bo19bo$42boo5bo13bo28boo$41b3oboo8bob
o5bo28boo$42boboboobboo3bobo$43bobbobboo5bo$45boo38b3o$47boobo33b4obb
3o$50bo12b3o18b3o3boboo$61boobbo17boo4bobboo$62b3o25boo$63bo22bo3bo$
85boo$84b3o$84boo5$51boo$51boo7$59boo$59boo10$24bo27bobo$24bo26bobbo$
23bobo26bobo$24boobbo11boo21bo$23bo5bo9bobbo19bobo$23bo5bo10boo12bo6bo
bbo$23bo4bo12bo11boboo5boo$27bo13bo11boboo$10bo13b3o13boobo8bo3bo$9bob
o5bo21boo12b4o$15booboo23bo9b3o15boo$9b3obbo3boobbooboo12bob3o4boo22b
oo$15booboo7bo12bobbo4boo21b3o$15b4o3boo16b3o26booboo$24b3o42booboo$
70b3o$71bo$21boo$12boo7boo58bo$12boo25bo40bobo$37booboo38bobbo$37boob
oo39boo$bbo34boo$bbo36b5o$bobo35boo3bo$bboobbo36bo$bo5bo$bo5bo74booboo
$bo4bo75booboo$5bo9bo$bb3o9bobbo$14boobboo$15boobbo$ooboo11bobbo$5bo9b
obbo$oo13bobbo$bb3o$15b3o$20bo$19bobobboo$19bo3b3o$14bo6boo$14boo5bo3$
6boo$6boo!

If the rear loaf and blocks are deleted they will be regenerated. If both loafs and blocks are deleted, they will also be regenerated after leaving a bit of a mess.

However, if just the blocks are deleted, the spaceship is converted into a puffer.

Code: Select all

#C A diagonal c/12 period 96 tub puffer with cleanup.
#C The puffer is created by a simple perturbation of a Cordership
#C which has an integral tagalong.  This also shows one way a
#C two-engine Cordership can delete the tubs to make a spaceship.
#C David I. Bell, 1 July 2025
x = 195, y = 151
66bo7bo$65b3o5bobo$64boob4obbobbo$65b3obbo$66bobboobbo$70boobobo$74bo
10boo$85boo6$47bo$46b3o14boo28boo$45bo10bobbo4bo28boo$46booboo6b3obbo
bbo$47b3oboo5boobbobbo$49b4o9bobbo23bo$63b3o21b4o$87boobbo$91bo$88bob
oo$87boo$82boo$80boboo$79bo4boo$70boo8bo3bo$70boo12bo$68bo8boo3boo$77b
oo$52boo13boo4b3o$52boo13bobboobbo$66bo6bo$66bo4bo$67boboo$68bo3$60boo
$60boo9$52boo$52b3o$24b3o25boobo$56bo$22bo5bo19bo3boo3bo6bo$13bo8b7o
12bo16bo4bobo$24bo17boo11bobo4bobbo$17bo6bo3bo13boo11bo7boo$23bo17boob
o5bo4bobo$9b3obo10bo18b3o$9b3obo11bo4bo11boboo8b4o16bo$10bo8boo4bo4bo
11boo10boo13bo5bo$11bo3b3oboo3boobobo12bo6boo17bo5boo$12bo6bo3bobo23b
oo$13bobobobo4bo43bobb4o$14bo55b3obo3$22boo$13boo7boo58bo$13boo66bobo$
39b3o39bobbo$42bo39boo$41boo$bb3o38bo$41b3o$o5bo10bo23bobbo$7o11boboo
20boo$bbo15b4o$bbo3bo10boob3o$bo13b3o4boo$bbo13bobo3boo$3bo4bo8b3o74bo
$3bo4bo8b3o73bobo$bboobobo86bo$bobo$bbo$$16bo$15bobo$14boobobo5boo75bo
$16bob3o4boo74bobo$18bobbo80bo$19boo$19bo$$7boo$7boo$110bo$109bobo$
110bo6$118bo$117bobo$118bo$$165bo$165bo$165bo8bo$172bobo$126bo39b3obbo
3bo$125bobo39bob5o$126bo46bo$168boo15boo$185boo4$134bo$133bobo15b3o$
134bo14b7o6bo$148b9o4bo31boo$147bo7b3obboo31boo$148b3o6bo3bobbo$149boo
11b3o$152bo10bo23bo$142bo10bo31bo4bo$141bobo10bo29bo5bo$142bo47bo$185b
obbo$186b3o$180bo$178b4o$177b3oboobo$177boobbo$171bo5bo4bobbo$167bo4bo
5bo3boobo$158boboo5bo3boo5bo$152boo4bo$152boo6bo5bo6boo$165b3ob7o$165b
ooboo5bo$172boo$175bo$172bobbo$173bo$160boo$160boo!

If the temporary loaf in the puffer is deleted, then the puffer is converted back to the original loafs and blocks spaceship.

The changes back and forth between a spaceship and a puffer can be done using single glider impacts. There are some impacts that can be supplied by a rake to repeatedly toggle the Cordership back and forth between the two forms.

Here is the most useful such reaction.

Code: Select all

#C A diagonal c/12 fleet of Corderships which can period double.
#C This uses a toggable ship/puffer which is repeatedly hit by
#C the output stream from a rake.  Every other impact releases a
#C sideways glider.  A two-engine Cordership is present to delete
#C tubs which would otherwise be left behind.  The result is that a
#C glider stream is period doubled.  In the example shown here, a
#C period 192 output rake is created from a period 96 input rake.
#C David I. Bell, 1 July 2025
x = 272, y = 247
212bo$211bobo$210booboo$211bobbo$213b3o$213bobo$214boo$214boo12boo$
228boo5$195boo$198boo4bo$195boob4o3bo30boo$192b5o4b4o31boo$195b3o6bo$
196bo$195b3o33boo$202bo28boo$202bo29boo$227bob4o$226bobboo3$223bo3bo$
223bobbo$222bo3bo$222booboo$213bo8boobbo19bo$211boobo7b4o19bobo$197bob
oobo9booboo5b3o19booboo$196bo4b3o9boboo4boo22bobbo$197bo5bo10bobo5boo
23b3o$198bo3bo11b3ob3obbo23bobo$199bobo14bob5o25boo$218booboo25boo12b
oo$262boo$$203boo$203boo$214bo$214bo14boo$232boo4bo$213booboo11boob4o
3bo30boo$226b5o4b4o31boo$213boo14b3o6bo$212bo3boo12bo$212bo3bo12b3o33b
oo$213bobo20bo28boo$214bo21bo29boo$261bob4o$202bo57bobboo$198b4oboo5b
3o$167bo29boob3oboo4b3o$166b3o15bo13bob3obo7boo43bo3bo$165booboo14bo
14bo3b4o4boo44bobbo$164boo3bo7b4o3bo17boob3o48bo3bo$165bobobobo5bo3bo
21b5o48booboo$166boobobbo4boo3bo21bo42bo8boobbo$157bo11boobo7b3o62boob
o7b4o$156b3o11boo10boobo6boo21bo15boboobo9booboo5b3o$156bobbo23b3o6boo
12boo6bobo13bo4b3o9boboo4boo$156b3o25bo20bobo5bobbo14bo5bo10bobo5boo$
156b3o48bo6boo16bo3bo11b3ob3obbo$155boboobo72bobo14bob5o$156bobb3o90b
ooboo$156b4oboobboo$157bob3o3boo58bo$159b3o62bobo10boo$158bobo22boo39b
obbo9boo$159bo22b6o37boo21bo$181b3oboobo59bo$182booboobo$159boo22bo3bo
39boo18booboo$158bo68bobo$145bo13boo67b3o16boo$144b3o12bo3b3o72bo7bo3b
oo$143booboo7b8obbo59boboo8b3o6bo3bo$142boo3bo6bo5b3oboo60boo4boobboob
oo6bobo$143bobobobo4bo72bo3bobbo5boo6bo$144boobobbo4boobbo71bobbo5b3o$
147boobo7b3o71boo5bobo$148boo10boobo75boo$161b3o$162bo4$168boo$168boo
4$166bo$150boo14boo$150boo12bo3bo40boo$164b4o42boo$163bo45bo$164boo$
164bo3$158boo$158boo8$177boo$178boo$177bo$215bo$214bo$214b3o7$44boo$
45bobbo4bo$42bobb3obobbobo$42bobbo4b4o$42bobbo99boo$45bo6bo93boo$44boo
bo97bo$52bo11boo$50boo12boo5$26bo$25b3o15bo$24booboo14bo28boo$23boo3bo
7b4o3bo28boo$24bobobobo5bo3bo$25boobobbo4boo3bo$28boobo7b3o25bobbo$29b
oo10boobo21bo4bo41boo$42b3o20boobobbo42boo$43bo20boo3bobbo40bo$65boo3b
oo$61bo4bo$61boo$59b6o$59boob3o$59boobobo$50bo$46bobbo4bo$15bo30bobbo
bb4obo$14b3o14boo15bobboob3o$31boo14boob3o$14b3o31b3o$15booboo28b3o$
17bo63boo$31boo49boo$31boo48bo$$39boo$15bo23boo$14bobo$15bo$$14boo23b
oo$13bobo23boo$$13b3obobo$17b3o$bbo14boo$ooboo26bo$bbo27bobbo15boo$30b
oboboo14boo$29bobbobo14bo$3boo23bobboboo148bo$bbobbo22boo3bo148bo$boo
3bo22bo3bo148b3o$bo4bo23bobo$bo3bo25bo$bbobbo$3bo$30bo$29boo$26boo$25b
o$26bobo$27boo$24boobo$23bobbo$6boo15bo$6boo14boo$21bo4bo$20b3o3bo$19b
o4boo$19bobo$20boo$$14boo$14boo40$151bo$150bo$150b3o!

The reaction can be cascaded to produce very high period rakes.

Code: Select all

#C A diagonal c/12 period 6144 (96 * 2^6) sideways rake.
#C This uses six copies of a period doubling Cordership convoy to
#C multiply the period of a period 96 input stream by 64.
#C More convoys can be added to increase the period further.
#C David I. Bell, 1 July 2025
x = 365, y = 384
178b3o$176b7o6bo$175b9o4bo$174bo7b3obboo$175b3o6bo3bobbo$176boo11b3o$
179bo10bo$180bo18boo$181bo17boo4$161bobo$161b3o$161boo15bo$178bo$177bo
$164bo13boo27bo$162bobo12bobbo27bo$162b3o12bobo21bobobbobo$165bo35bo4b
o$161b5o12bo26bo$176bobbo22b6o$177b4o23boobo$179boo$177bo$176boo$176bo
bbo$177b3o$178bo$212b3o$210b7o6bo$166boo41b9o4bo$166boo40bo7b3obboo$
209b3o6bo3bobbo$210boo11b3o$213bo10bo$214bo18boo$215bo17boo$$174boo$
174boo$195bobo$195b3o$195boo15bo$212bo$211bo$198bo13boo27bo$139bo28bo
27bobo12bobbo27bo$138bobo27bo27b3o12bobo21bobobbobo$168bo30bo35bo4bo$
138bobbo29boo22b5o12bo26bo$140boo29boo37bobbo22b6o$141bo24bo3b3o38b4o
23boobo$155boo10b3o8bo34boo$155boo11bo8bobo31bo$167boo7bobbo30boo$167b
3o7boo31bobbo$138boo29bo41b3o$126bo13bo26bo44bo$127boboobobo4boo28bo
16b3o$121b3o3b4o3bo3b3o15bo10b3o15bo3bo$127bobbooboo3boo16boo5boo20bo
4bo9boo$126bo10b3obo14bo6boo21bo13boo$124b3o11bo3bo10boobbo29bo3bo47bo
$124b3o13bobbo10booboo29bobo47b3o$140b3o12boboo30bo47b3obo14bo$141boo
11booboo25boo50boo3boo6bobbo3bo$136boo16bo3bo28bo47boobobboo6bo3bobbo$
127boo7boo17bobo38bo39booboboo5bo$117bo9boo25boo29b3o7bobo10boo27b3ob
oo6boboo$116bobo76bobbo9boo29bo4bo$149boo4boo39boo42b4o20boo$116bobbo
30bo91bo12boboo5boo$118boo135b3o$119bo106b3o27bo$$227bo15boo$197booboo
25boob3o10boo$197booboo24bob4o11boo$116boo108bob3o$118bo108b3o15bo$
117boo109bo14boobbo$116b3o123bo4bo19b3o$116boo123bo25b4o$115b3obo105b
ooboo15boo22b4o$116bo3bo11boo91booboo12booboo24boo$118bobbo10bobo55boo
34boboo14bo27bo$118b3o12b3o53bobo35boo$119boo9boobbo56bo$130boboo$129b
oobo$242bo$241b4o$193bo47b4o28bo$191boo79b3o$121boo69boo77b3obo14bo$
121boo108boo8b4o25boo3boo6bobbo3bo$231boo9b3o24boobobboo6bo3bobbo$243b
o26booboboo5bo$271b3oboo6boboo$273bo4bo$274b4o20boo$158boo116bo12boboo
5boo$157bobo129b3o$159bo79boo19b3o27bo$239boo$261bo15boo$44bo216boob3o
10boo$41b4o158b3o54bob4o11boo$202bo30bo26bob3o$58b3o141bo3bo25bobo26b
3o15bo$200boo3boo55bo14boobbo$44bobo12boo138bobbobobbo24bobbo40bo4bo
19b3o$45bo13boo138bobbobobboo25boo39bo25b4o$30bo12boo13bobbo139booboo
bbo26bo23booboo15boo22b4o$29bobo11bobbo11bo8boo133bo4bo51booboo12boob
oo24boo$42booboo10b3o7boo136booboo50boboo14bo27bo$29bobbo24boo145b4o
53boo$31boo27boo64boo77boo13boo21bo$32bo26bobbo62bobo92boo10boo8bobo$
46boo79bo106bo6bobbo$46boo9boo173boo8boo32bo$57bobbo214b4o$58b3o214b4o
$29boo95bo57bobo6boo11bo43b4o$31bo92booboo54bo9boo11bo42bo4bo$30boo92b
ooboo55bobbo12boobbobo58boo8b4o$29b3o15bo76boo60b3o11boobbobb3o39bob5o
9boo9b3o$29boo16boo77boobo74bo6bo42bobo20bo27bo$28b3obo14boo78bobbo74b
o6bo10bo30bobbo45booboo$29bo3bo11bobo79bobbo50b3o24bo3bo11bo28bo3bo47b
o$31bobbo11boo80boo12boo36bo27bobboo11boo28bobo63boo$31b3o14bo93boo36b
o3bo16boobo4boo12boo30bo63bobbo$32boo12bobbo128boo3boo7boo11bo13boob3o
36bo44boo11booboo$49bo44boo81bobbobobbo6boo8bobo14b5o36bobo10boo30bobb
o11bo$46b3o44bobo30bo50bobbobobboo16bo15bobboo36bobbo9boo17bo11boo3bo
10b3o$95bo13bobo13boboo50booboobbo27boo5bo39boo28b3o10bo4bo19boo$44bo
64bobobo9bo56bo4bo28boo88bo3bo20boo$42bobo63bobboobo11bobo54booboo103b
3o11bobbo$15bo28bo64boo3bobobo3bobbobo22boo30b4o106booboo9bo$11boobobo
7bo9boo5bobo65boo3booboo3bo5bo21boo31boo109bo$11bobbooboobbooboo8boo5b
o71boboo5bobbooboo178boo12bo$11bo5bobo5bo15bobo68bobo8bo3boobo11b3o
163boo8bo3bo$12boobbo8bo16boo82b3oboo9bob3o173bobbo$16bobb3obbo98bo3b
4o13bobo36bo135booboo$16b3o15boo89booboo15boo37bo107bo27bobo$34boo68bo
9boo8bo17bobbo37bo107bobo27bo$4boo96booboo7boo26b3o147bo$42boo58booboo
36bo52boo60b3o$3bo3bo34boo58boo32boo122bo30boo$8bo53boo40boobo28boo50b
oo69bo30bobo$bo7bo51bobo41bobbo72bo5bobbo118bo$o4bo57bo41bobbo72bo5bo
bbo99b3obobo11bo$bobobo4bo31boo62boo73bo4booboo103b3o13boo$bo8bo20bo3b
oo5boo143boo9b3o93boo14boo$bbo4boobo8bobbo6boobooboo159bo3bo110bo$3bob
oob3o11b3o3bo7bo159bobbo108bobbo$4b3oboo4boo3boob4o3bo6boo123bo34b3o
109bobo$14boo9boo4boobboo67b3o52boo145boo31bo$31boobboo123boo143bo31b
ooboo$104bobo79boo119bo31bo$21bo83bo80boo108boo5b4o47boo$106bo189boo4b
obbo47bobbo$106boo10b3o181bobbo34boo11booboo$103boboobo9bobo182b3o33bo
bbo11bo$103b4oboo8boobo204bo11boo3bo10b3o$104b5o11bo204b3o10bo4bo19boo
$106boo11b3o216bo3bo20boo$11boo105bobbo203b3o11bobbo$4bo5bobboo104boo
183boo20booboo9bo$4bo4b3obbo282b3o4boo22bo$4bo4bo4bo281bo45boo12bo$9b
5o282bo3bo41boo8bo3bo$10boo96boo184boo3boo52bobbo$62bo45boo183bobbobo
bbo51booboo$61b3o229bobbobobboo23bo27bobo$60bobobo230booboobbo22bobo
27bo$59b3ob3o12bo187bo7bo21bo4bo24bo$9boo66bobo185b3o5bobo23booboo$9b
oo50bob3o13boo20bo162boob4obbobbo21b4o23boo$61b5o9bo3bo19booboo161b3o
bbo28boo23bobo$61boobboo11bobboo19boo162bobboobbo69bo$63boboo14bo17b3o
168boobobo48b3obobo11bo$65boo9bobboo20bo3bo168bo10boo21bo19b3o13boo$
61bobobbo11bo7boo12bo3bo180boo20bobo18boo14boo$60bobobbo20boo13b3obo
142boo56bobbo35bo$61bo41boo5bo136bo59boo33bobbo$102bobo5bobo134bobbo
91bobo$103bo6boo133boob4o88boo$102boo83bo56bo13boo5bobbo70bo$76boo23b
3o83bo56bo3b3obbo4boo8bo49bo22bo$101boboo84bo5bo48bobbobbob3o9bo14bo
12bo24bobo10boo5b4o$47booboo24boo22b5o83bo6bobo48boo4b3o10bo3bo9boo11b
oo23bobbo9boo4bobbo$47boo45bo92bo3bobbo53boobobo12booboo8bobo9bobo24b
oo16bobbo$47boobobo24bobo9bo3bobo14bo77bobboboboo52boobo14bobo67b3o$
50bobo25bo10b5oboo12bobo81boboo55bo16boboo7b3o$51boo25booboo7bo4bo12bo
bbo95boo59bobbo3bo5bo41bo$80boo9boobo14boo96boo59bo7boo45b3o$81boo10bo
163boo9bobbo51bobbo$80bobo3bo157bo7bo4boo10boo49bo3boboo10boo$78b4o4bo
156b3o5bobo66bo3boobbo9boo$78boobbo87b3o69boob4obbobbo24boo39bo4b3o$
79boobo87b3o7boo61b3obbo30boo$74boo4b3o86bo3bo6boo62bobboobbo$73bobbo
93boob3o11b3obbo22boo31boobobo$73bobboo38boo52boo4bo10b4obo6boo14boo
35bo$73boboo38bobbo5boo47bobbo13bo21boo$70bobbobo40bobo4bobbo47boo15bo
bo7boo8bobo113booboo$70boo20bo24bo4b5o65boo3bo4boo9bo113booboo$53boo
14bo21b3o27booboo76bo$53boo9boobboo20bobobo28bo74b4o$64boobbo20b3ob3o
12bo56bo13boo10boo7bo$65boboo38bobo20b3o32bo13boo10boo$66boo23bob3o13b
oo21bo34bo5bo$91b5o9bo3bo21bo34bo6bobo25boo45bo$91boobboo11bobboo52bo
3bobbo28boo44b4o6boo$93boboo14bo54bobboboboo71bo4bo4b3oboo$61boo32boo
9bobboo60boboo70boo10boob3obbo$61boo28bobobbo11bo7boo128boboboo4b3oboo
bbobo$90bobobbo20boo129b3o6boo6bobo$91bo156bo16bo4$106boo$251boo$77boo
boo24boo143boo$77boo45bo$77boobobo24bobo9bo3bobo48boo3bo$80bobo25bo10b
5oboo45b3o4boo$81boo25booboo7bo4bo41b3obo8boo5bo$110boo9boobo46bobobb
5o5bobo$111boo10bo48bo3b3o7bobo$110bobo3bo70bo$108b4o4bo$108boobbo69b
oo$109boobo$104boo4b3o13b3o54boo$103bobbo19bobo44boo9bo$103bobboo17bo
3bo43boo$103boboo18bo3bo36bo$100bobbobo19bo17boo19booboo$100boo23bo4b
oo11boo19booboo$83boo14bo25bo6bo31boo$83boo9boobboo26bo5bo33boobo$94b
oobbo27boo39bobbo$95boboo29bo3bo34bobbo$96boo31bobo10boo24boo$143bo$
142b3o6boo$126b3o13bo8boo$91boo32bo3bo$91boo33bobbo36b3o$112bobo13boo$
111bo33bo20bobo3bo$112bobbo26bobboo20bo3bo$114bobo24bo3bo21boobb3o76bo
3boobboobo$117bo23bo4bo19b4o80bo3boo4boboo$116b3o26boo18bobbobo79bo3b
oobbooboo$116bo23bo4bo20b3oboo3bo78boo$114boo24bobbobo21b4o3bobo75bobb
o$116bo24boobbobo20boo3bobbo75bobo17boo$114bobbo27bob4o23boo77bo18boo$
114bobo28bobboo$114bo30boobbo84boobbo$237bobo$138booboo93bo$138boo105b
oo$136bo4bo96boo5boo19bo$137bo119boo4boo3boo$137bobbo40boo56boo15bobbo
3bo5bo$138bobo15b3o21bobbo6boo46bo18bobbobboo3bo$139boo15bobo22bobo4bo
47booboo17bobo4bob3o$138b3o14bo3bo22bo4bobb4o45boo17b3o7boo$118boo11b
3o6bobo12bo3bo30bo46bo27boboboo$118boo11b4o20bo17boo11bo79boobo$130boo
bboo19bo4boo11boo11boboo54boo22boo$131boobo20bo6bo31bo49boo$131b3o22bo
5bo24b4oboboo32bo3boobboobo$132bo23boo37boo31bo3boo4boboo24boo$158bo3b
o31b3o31bo3boobbooboo25boo$159bobo10boo20b3o35boo$126boo45bo19bobo34bo
bbo$126boo44b3o6boo10boo35bobo$156b3o13bo8boo4bo4boo37bo$155bo3bo26bob
o3boo$156bobbo$142bobo13boo$141bo33bo$142bobbo26bobboo13boo$144bobo24b
o3bo15bobo$147bo23bo4bo15bo$146b3o26boo$146bo23bo4bo71boo$144boo24bobb
obo70boboo$146bo24boobbobo53boobb5o6bobboo$144bobbo27bob4o50bo7bo11bo$
144bobo28bobboo51bo4boboo13bo$144bo30boobbo11b3o41b3o12bobo$190bobbo
57bo$168booboo16bo4bo$168boo19bobb3o$166bo4bo17bo5bo$167bo22b7o41boo
91b3o$167bobbo25bo41boo93bo$168bobo25bo30bo104bo$169boo23boo12boo17bo$
168b3o37boo19bo5bo$148boo11b3o6bobo55bo6bobo$148boo11b4o62bo3bobbo$
160boobboo27bo34bobboboboo$161boobo27bobo38boboo$161b3o27boobo$162bo
28boo$192b3o21boo$193bo22boo$156boo21bo14bobbo34bo$156boo21bo11bo6bo
32bobo$179bo11bo6bo31bobbo$176bob3obo8bo4b3o32boo$176bob5o$180bobo$
177boo28bobo$177boo28boobbo$178bo27boo4bo27boo$178boo26boo3bo27bobbo$
179bo3boo22bo30bobbo$179bo27bobo28boobo$177boboo28bo28bobbo$178bo27bo
30boo$206bobbo$208bo$221b3o$203bo16bobbo$202bobo14bo4bo$204bo14bobb3o
21boo$200bo18bo5bo19bobbo$200bo3bo15b7o19bobo5boo$226bo20bo6boo$183boo
12b3obbobo21bo$183boo11bo3bobbo20boo12boo14boo$196booboo37boo14boo$
197boo$$198bo24bo$196boobo22bobo$196boobo21boobo$191boo4boo22boo$191b
oo29b3o21boo$223bo22boo$209bo14bobbo$209bo11bo6bo$209bo11bo6bo$206bob
3obo8bo4b3o$206bob5o$210bobo$207boo28bobo$207boo28boobbo$208bo27boo4bo
$208boo26boo3bo$209bo3boo22bo$209bo27bobo$207boboo28bo$208bo27bo$236bo
bbo$238bo$$233bo$232bobo$234bo$230bo$230bo3bo$$213boo12b3obbobo$213boo
11bo3bobbo$226booboo$227boo$$228bo$226boobo$226boobo$221boo4boo$221boo
!

The tub deletions can be done by sharing a Cordership from a later period doubling stage. This can make final convoy smaller.

Code: Select all

#C A diagonal c/12 period 768 (96 * 8) sideways rake.
#C This uses a period 96 input rake and three stages of a period
#C doubling convoy to multiply the period by eight.  Tubs created
#C from the first stage are deleted using a Cordership which is
#C part of the third stage.
#C David I. Bell, 1 July 2025
x = 367, y = 257
245boo3b4o$240b3obobbo6bo$244bobbobb5o$244bobbo$246bo$243bobo17boo$
244bo18boo3$224boo$223bo$223bobbo$221boob4o$220bo20b3o27boo$220bo3b3o
bbo41boo$220bobbobbob3o3bobo$222boo4b3o4bo29bo$224boobobo33bobbo3bo$
225boobo14bo25boboo$228bo12b4o21boboo$240bo3bo17boo4bo3bo$240bobbo24b
4o$241b3o20boo3boo$263bobbo$$263bobo5$230boo$230boo7$238boo$238boo10$
232bo$202b3o25booboo$202bobo27bo$202bobo14boo21bo$202bo4boo9bobbo19bob
o$201b3o3boo10b3o11boo5bobbo$207bo12boo10bobbo5boo$203b4o13bo10boo3bo$
189bo14boo12boboo9bo4bo$189bo5b3o6bo13b4o9bo3bo$188bobo3boobbo19bobobo
9bobbo14b3o$189bo3bo5bo5bo13booboo3boo4bo$189bo3bo9bobo12bo3bo4boo20bo
3bo$194bobboo3b4o13b3o26bo4bo$195boo5b3o15bo$204bo43bo3bo$249b3o$200b
oo$191boo7boo58bo$191boo24b3o39bobo42bo$216bo3bo38bobbo40boo7bo$215bo
3boo39boo40bobob3obbobo$216bo84b3o3boo3bo$180b3o37b3o79boboboobobo$
180bobo35bo4bo79booboo$180bobo121bob5obo$180bo4boo121b4o11boo$179b3o3b
oo74booboo57boo$185bo75booboo$181b4o$182boo9bobobo$182bo10bobb3o$193bo
booboo85bo$183bo11b4o85bobo$181bobo10b5o84bo3bo13b3o27boo$180b4o99bo3b
o8bo34boo$180b3o11bobo86bobob3o4boob3o$182bo12bo88boobobbo5boboo$195bo
3bo52bo35bobo8bo27boo$198bo3bobo47boo26bo7boo11bobbo21b4o$200bobobo46b
obo25bobo19b3o20booboboo$193boo4b5o54bo21bo43bo5bo$193boo5boo56bobo63b
o4boo$258boo60bo4bo$319bobo4bo$185boo135bo$185boo131boobboo$307bobo8bo
bbo$307bobo12bo$306b3o5bobo21bo$305boo4boobobo20boo7bo$290boo15bo3bo3b
o20bobob3obbobo$290boo15bobbobbo21b3o3boo3bo$303bo3boobo25boboboobobo$
220bo116booboo$220boo82bo3bo29bob5obo$219bobo83bobbo33b4o11boo$357boo
$$298boo$298boo$$319bo$318bobo$317bo3bo13b3o27boo$317bo3bo8bo34boo$
317bobob3o4boob3o$318boobobbo5boboo$322bobo8bo27boo$322boo11bobbo21b4o
$188bo100b3o43b3o20booboboo$188boo72b3o28bo64bo5bo$187bobo103boo63bo4b
oo$266bo26bobbo5bo51bo4bo$262bo3boo12bo13bobo4bobo49bobo4bo$264bobo13b
oo12bo5bobbo52bo$261b3o16bobo10boo6boo49boobboo$248bo14bo28bobo46bobo
8bobbo$248bo30boo13boo45bobo12bo$248bo8bo4boo16boo9boo47b3o5bobo$255bo
bo5boo14bobbo10bo18boo25boo4boobobo$249b3obbo3bo4bo15b3o5boo23b3o9boo
15bo3bo3bo$250bob5o6boo22boo22bobo10boo15bobbobbo$256bo5boo45bob3o23bo
3boobo$251boo55boo$338bo3bo$156bo27b3o152bobbo$156boo26bobo73boo$155bo
bo15b3o8b3o64boo7boo58bo$40boo130bo3bo23boo49boo25boo39bobo10boo$40b3o
128bo4bo22bobboo74boo39bobbo9boo$40boobo126bo3bo11boo11booboo74bobbo
38boo$44bo13bo111bobbob3o6booboo14bo75bobo$36bo3boo3bo12bo111bo7bo5boo
bboo10boo38b3o36bo$46bo11bo113bo3bobo4boo3boo11bo7boo70boo$43bobo126bo
3boboo4boobboo19boo33bo34bobbo$43bo130b3oboo5bobo52bo3boo34boo$38bo4bo
bo13bo182bobo76booboo$57booboo4boo171b3o79booboo$29bo12b4o20boo173bo
18boo$28b3o11boo12bobo123boo17b3o49boo$28bobbo24bo3bo112boo7boo14b3obo
37boo12bobo$28b3o25boobbo63bo48boo24booboo37boo12boo$28b3o14boo10b3o
64boo73booboo37bo14bo$27boboobo12boo11bo64bobo75bo39boo$28bobb3o192bo
13boo$28b4oboo191bobo$29bob3o168boo22boo25b3o$31b3o10bo117b3o10boo24bo
bbo47bobb3o$32boo10bo117bobo8boobbo24boo51boboo4boo$45bo116b3o8bo3bo
74boo4boo3boo45boo$43bobo131boo75b3obbo51boo$28boo16bo127boobobobboo
71bo3bo50bo$28boobo132boo13booboo72bobo$28b4o12bobo115booboo11boo$30bo
14boo115boobboo77boo$161boo3boo77boo$44bo117boobboo$43bo48bo70bobo$42b
3obo45boo85b3o$42boobboo43bobo85bobo$42boobboo129b4o$21boo153b3o6boo$
11bo3boo4b3o9boo7boo132bo8boo$11boboobbo6bo8boo7bo4bo129b3o$11bobb5obb
4o17bo4bo131bo$15b3o3b3o19bobo$14b3o$14boo17boo132boo$14bo18boo132boo
$$41boo$4bo36boo$3b3o128boo$bbooboo53bo69boo3bo40bobo$boobobo53boo57b
3o7bo6bo39boo$3obb3o33boo16bobo60b3o5bo3b5o38bo$bo6bo32boo79b3o6bo3bo
22b3o$bb5obo11bo8boobbo89bo11bobbo18bo$3b4oboo9bobbo5b3obboo101boo7boo
9bo4boo$8bo4b3obbo3bo6boobb3o109boo8bo3bo$7bo5b3obbo4bo5boobboo120bobb
o4bo$17bo3boo132bo3bo3bo$21boo133boobob3o$18boo139bo$5bo140bo13b4o$3b
oobo139boo14boo$112b3o6bo22boobbo4boo$6bo106boo3boobo20bo4boo4boo$3bo
bbo105boo5bobo21boo24bo$4bo112b3obo21bo24bobo$120boo3boo6bobboobo27bo
bbo$9boo114boo5bo3bo3boo26boo$bb3o5boo120bo3b3obo$9boo127boo$9bo4$176b
o$175bo$8boo165boo$8boo112bo3boo48bo$116boboo3boboobo48bo5b3o$19boo93b
oobo3bobo4boo$19boo96bobobb3obboo52bo$19b3o96bo4boo56bo$20boo142boo15b
3o$21boo137boo3bo17boo$21b3o125b3o7bo6bo15bobbo8bo$152b3o5bo3b5o14bobo
8bobo$152b3o6bo3bo18bo9boo$120boo31bo11bobbo$120boo44boo7boo$175boo5$
176bo$176boo$142b3o6bo22boobbo4boo$143boo3boobo20bo4boo4boo$142boo5bob
o21boo$147b3obo21bo$150boo3boo6bobboobo$155boo5bo3bo3boo$162bo3b3obo$
168boo8$152bo3boo$146boboo3boboobo$144boobo3bobo4boo$147bobobb3obboo$
148bo4boo5$272bo$150boo119bo$150boo119b3o!

It is tricky to use shared Corderships for more stages since each doubling convoy must be shifted inwards by a few cells in order to be properly aligned to delete the tubs. This means that the total convoy must be made wider at the front so that it can taper for each stage. (I haven't tried to do this.)

If the tubs are not deleted and the output gliders are deleted instead, then another on-off type puffer could be made.

Finally, this is not the first period doubling reaction known for Cordership technology.

I found period doubling convoys in 2005 which were based on two interacting beehive-shooting Corderships. But that reaction is larger than the one shown here, and required turning sideways gliders into forward gliders for each doubling stage.

EDIT:

Here is a larger rake which shares Corderships.

Code: Select all

#C A diagonal c/12 period 98304 (96 * 2^10) sideways rake.
#C This uses ten period multiplication convoys in series to
#C multiply the period from an input period 96 rake by 1024.
#C Tubs created by earlier stages are deleted by shared
#C Corderships from later stages, except for the final two
#C stages which use single Corderships to delete the tubs.
#C More stages can be added to increase the period further,
#C however the components become increasingly spaced out.
#C David I. Bell, 2 July 2025
x = 566, y = 589
210bo$210bo$210bo$211boo$211b3o$211boo$226boo$226boo3$210bo$211bo$210b
o$194bo6boo24boo$193bobo3bo3bo22bo7boo$192bo3bobo3boo30boo$193bobobbob
oboo$194bo3bobboo7bo15b3o$198bo4bo6bo15bobo$199bobbo25boo$201bo24bobbo
$227boo$227bo$223bo$224boo$222bobo$222bo$220boo$208bo12bobo$197b3o7bo
bbo11boo$196boboboo5bo3bo$196boboboo5bo3bo$196bo3bo5boo3bo4b3o$197bobo
7bobbo4boobbo$198bo15bo3boo$213bobb3o$212bobboo$212bobbo$213bobbo$201b
oo13bo$201boo11bobo$$212bo$210boboo$209bobboo$210boobo$210booboo$211bo
bo$212bo4$207bobo$198bob3o4bobo$196boobo4bo5bo$180bo17boo4bobbobbo$
164booboo6boboobboo21bobbobbo$164boo8bob5o22bo4bo$164boobobo5bo4boo17b
obbo$167bobo11bobo16boo$168boo$155bo25b3o6boo21bo$155bo34boo20bobo$
154bobo46bo7bobbo$155boobbo43boo7boo$154bo5bo41bobo$154bo5bo$154bo4bo
3boo$158bo4boo58bo$155b3o25boo37bobo$222bobbo$181bo41boo$153booboo22b
ooboboo$158bo21b3obbo$153boo$$155boboo3boo61b3o$157bo4boo60bobo$142boo
boo6boboobboo62boo$142boo8bob5o$142boobobo5bo4boo$145bobo11bobo$146boo
83bo$159b3o67boo$230boo5$166boo75bo$166boo74bobo$243bo3$160boo132bo$
148boo10bobbo129b3o$148boo11b3o$159bo4bo41boo85b3o$161bobo41bobo86boob
oo$159bobo45bo88bo$310boo$310boo$$156boo$156boo$259bo$258bobo$259bo17b
3o6bo$276bo4bo3bobo30boo$276bo4boo3bo31boo$276bo6bo27bo$277b3obobbobo
23bo$281b5o26boo$174boo110bo25boo$173bobo137bo$175bo134bobbo$310bobo$
308boo$48b3o256bo$47bo261bo$47bo3bo253b4o$45boo3boo252bobbo$44bobbobo
bbo228boo21bobbo$44bobbobobboo227b4o5boboo11b3o$46booboobbo225boob3o5b
o3bobo$47bo4bo226boo3boo10bo4boo$50booboo224boobobo9bobobbobbo$49b4o
231bo5bobo5bo4bo$50boo13boo214b3o13boobooboo$65boo75boo152bo5boo$141bo
bo156bo$143bo152bo$297bo3bo$285boo14bo$285boo13bo$31boobo261bo$30b3obo
6bobo29boo221bo$29bo4bobo4bo31boo221boo$30boo6bobo3bo$31bo3bobbobboo
254boo$34boboo3bo252bob3o$33bobo30b3o226bobbo$33bobo33bo225b3o$66bobbo
$67boo$110boo$59bo49bobo87bo82boobo$58bobo50bo85boo82b3obo6bobo$63bo
134boo80bo4bobo4bo$58b3obbo185bo31boo6bobo3bo$59bobboo184b3o14boo15bo
3bobbobboo$38bo10boo9b4o183bo10bobbo4bo18boboo3bo$33bo3b5o5bobboo7bo4b
o183booboo6b3obbobbo16bobo$32bobo7boob3oboo3boobbo5bo184b3oboo5boobbo
bbo16bobo$32bo7boboobbo3boo4bobb5o187b4o9bobbo$16bo16bo8boo3boobo5bobb
o179bo25b3o6boo21bo$16bo17bo3b4o6bobo5bo181bobo33boo20bobo$16bo22b3o7b
oobo184booboo45boo6bobbo$19boo30booboo181boo49boo6boo$19boo12boo16b3o
189boo42bo$14bo3b3o11boo203b3obbo$15b3o15bo6boo36boo161boboobboo$16bo
15b3o5boo35bobo159bobbo4boo58bo$15boo15b3o44bo162bo63bobo$15b3o16bo
205boo23bo40bobbo$17bo14bobbo229bo3bo37boo$15bo16b3o5boo198bo23bobobob
o$17bo15bo6boo198bo24boboobo$15b3o247bo3bo$241bo67b3o$238bob3obbobo60b
o$227bo10boobob3obo59bo3bo$bbo223b3o8boo3booboo60boboo$bobo46boo173bo
10bobbo4bo63bo5boo3b3o$o3bo26boo193booboo6b3obbobbo67bobbobbobbo$o3bo
25bobboo13bobbo175b3oboo5boobbobbo67bobbo6bo$obob3o23b5o194b4o9bobbo
68boo4bobo$boobobbo22b3obo8boobbo3bo191b3o75bo$5bobo23boobboo8boboobbo
$5boo25bo3bo$34boobo10boo$34bobo$34boo$30bobboo94bo120boo75bo$28b3o97b
3o119boo74bobo40b3o$27b4o3b3o91bobbo195bo$27bobo4b3o91b3o239bo15boo$
28b3ob4o92b3o14boo223boob3o10boo$27bo3boo94boboobo12boo97boo111bo11bob
4o11boo$27bo3bo96bobb3o98boo9bo3boo107boo11bob3o$27bobbo97b4oboo97boo
9bo4bo106boboo11b3o15bo$7boo13boo4bo100bob3o110bo3bo86bo19bobboo11bo
14boobbo$7boo13boo90b3o6bo7b3o10bo99boboo86bobo16b4ob3o24bo4bo$113bo4b
o3bobo7boo10bo100bo89bo16bobbobobboo22bo$113bo4boo3bo21bo207bobobob3o
6booboo15boo4boo$20b3o90bo6bo22bobo7boo199boob3obo6booboo12booboo4boo$
21boo91b3obobbobo4boo16bo6boo199b4obbobo6boboo14bo$118b5o5boobo108boo
115bo3bo8boo$123bo4b4o12bobo93boo115bo3bo$15boo113bo14boo210bobbo12boo
$15boo356boo$126boo15b3o239bo$117boo7boo14bo3bo237b4o$117boo23boobbo
237b4o$141bo4boo210boo$107bo33bobbobbo$106b3o32bobbo239b4o$106bobbo37b
o110b3o124b3o$106b3o151bo125bo$106b3o150bo103boo$105boboobo56bo194bobb
o$106bobb3o53boo188b3o4bobboo8bo$106b4oboo53boo193bobboo9boo$107bob3o
249b4o9bobbo$109b3o263bobo$110boo263boo$$367bo$106boo260boo$106boobo
251boobbobbo$106b4o12bo238boobbobbo$108bo11boboo245bo$120bobo245b4o$
121bo4bo239bobbobo$127bo237boo4boo$119boo5bo243bo$119boo3$111boo$111b
oo$63bobo$62bo304bo$63bobbo292b3o3b4o$65bobo291bobo3booboo$68bo11b3o
246boobo26b3obbo$67b3o258b3obo6bobo22boo3bo$67bo35b3o221bo4bobo4bo25b
4o$65boo35bo3bo221boo6bobo3bo23b3o$67bo13b3o18bo3bo9bo212bo3bobbobboo$
65bobbo12b3o5boo11bo3bo9bobo213boboo3bo$65bobo13boo6boo25boo213bobo16b
oo21bo$65bo14bo22booboo223bobo16boo20bobo$78boobbo21bobbo263bobbo$79bo
3bo9bo11bobo206b3o55boo$79bobbo10bo12boo206bobo$80b3o7bo12bo3bo206b3o
43bo$55boobo27boo6bo7bobobobo214boo35boo$54b3obo6bobo19b4o12bo219boo
11bo22bobo21bo$53bo4bobo4bo25bo3bo220boo18bo9boo34bobo$54boo6bobo3bo
23bo20bo200booboo16bo3boobo3boo34bobbo$55bo3bobbobboo26bobo16bobo199b
oobboo21boo40boo$58boboo3boboobo11b3o9bo16bobbo198boo3boo22bo$57bobo8b
obo11b4o26boo200boobboo15bo$57bobo21boobboo228bobo17bo3bo49boo$82boobo
250boo6boboo43bo$82b3o237boo21bo38bobo4bo$83bo223boobo11boo20bo38bo3b
oobo$306b3obo6bobo64b3o$305bo4bobo4bo28bo47boo$306boo6bobo3bo24bo45bo
bboo$119boo186bo3bobbobboo73b3o$75boo41bobbo6bo181boboo3bo75bo$62bo9bo
b4o41bobo5bobo179bobo$57bo3b5o5boobo3boo40bo6bobo179bobo$56bobo7boo4bo
bbooboo49bo97boo$56bo7boboo5b6o48boo88bo3boo4b3o206b3o$57bo8boo6bo52b
oo88boboobbo6bo205b3o14boo$58bo3b4o151bobb5obb4o204bo3bo7bobo4boo$63b
3o59boo94b3o3b3o173bo32boob3o5bobbobb3o$125boo4boo87b3o179bobo31boo4bo
4bobob6o$130bobbo86boo17boo85bo76bo35bobbo9bobboo$130bo89bo18boo84boo
113boo11b3o6boo$64boo63boo183bo9boo128bo7boo$64boo64bo3boo67bobo103bo
3b5o5boo$203b3o102bobo7boo4boboo96b3o$134boo67boo103bo7boboo5boo$212b
oo95bo8boo8boo81bo16bo$212boo96bo3b4o10boo80bobo11bo3boo12bo$206bo17b
oo4bo4boo78b3o93bo14bobo13boo$204bobo16bobbobbo6bo186b3o16bobo$140bo
63b3o16bo3bob3o3bo189bo$139bobo65bo19booboo209boo$140bo62b5o16booboo
87boo106boo16boo22b4o$226bo6boo81boo107boo14bobbo20bo4bo$233bobbo188bo
15b3o20bobbo$211boo20b3o189boo42bobo$205boo4boo22bo188boo45bo$195bo3b
oo4b3o256bo5bo$148bo46boboobbo6bo24boo230bo$147bobo45bobb5obb4o24boo
232bobo$148bo50b3o3b3o$198b3o$198boo240boo$198bo240b3o$439bobbo$440b3o
$429boo9b3o$429boo4$215bo$204bo9b3o$203bobbo6bo3bo$197b3obbo3bo7booboo
218boo$197b3obbo4bo7bobo219boo$158b3o40bo3boo10bobo$157bo3bo43boo10bo$
156bo4bo40boo14boo$155bo3bo$155bobbob3o238b3o$155bo7bo236bobbo26b3o$
157bo3bobo41boo192bo4bo25bobo$157bo3boboo40boo192bobb3o24bo3bo$159b3ob
oo234bo5bo23bo3bo$175boo223b7o22bo$175boo17b3o6bo202bo22bo4boo$195boo
3boobo202bo22bo6bo$194boo5bobo200boo12boo10bo5bo4bo$159boo38b3obo214b
oo10boo8bobo$159boo41boo228bo3bobbobbo$160bo272bobo4boo$402boo$160bo
22boo200b5o11bobbo$183boo198boo5boo8b3o27bo18boo$146bo52bo183bo7bo8b3o
28bobo15boo$146bo11bo5b3o31bobo182boo8bo4boobooboo42bobbo$146bo11bo7bo
30bobbo184boo7bobbobo4bo27boo14bobbo$149boo7bo5bobo31boo188bo10bo3boo
bbo41bo3boo$149boo13boo222bo4bo9bobobbo41boobbo$144bo3b3o238boo9bobo5b
o43b3o$145b3o252bobo3b3o11b3o$146bo232b3o17boobo16booboo$145boo60boo
169bobbo8boo8bobo15boboboo35bo46bo$145b3o58bobbo167bo4bo7boo9bo15boobo
37bobo44b3o$147bo56bo5bo166bobb3o34boobo37bobbo42boobbo$145bo58b3obbo
167bo5bo28boo5bo39boo42boobboo$147bo59boo90bo78b7o27boo90boo$145b3o
150bobo83bo120b5o$298bobboo81bo124boo$296b7o14bo64boo123bobbo$295bobbo
3bo14bo190boo12boo$294b3obb7o11bo142booboo57boo$170boo63boo53bo5b3obbo
8bo149booboo$213boo19bobo53bo6booboo8bo70bo$212bobbo20bo53bo7b3obobbo
74bobo$213bobo5boo68boo6b3oboo13boo5boo52boobo$164bobo47bo6boo68b3o8bo
13boobo5boo52boo$150boo12bo5boo119boo22bo3bo60b3o$150boo11bo4boo51boo
92bobboo61bo12b3o90bo3boobboobo31boo$162boo4bo52boo93b3o63bobbo7bo3bo
89bo3boo4boboo29boo$163bo3bo149bo61bo6bo10bo89bo3boobbooboo$298boo79bo
6bo10bo93boo$163bobbo122boo7boo79bo4b3o9bo92bobbo$164bobo122boo102bo3b
o91bobo34boo$163bobbo154bo72bobbo92bo34bo$158boo4boo155boo72boo125boo
bboo$158boo4bo155boboo198boo$320b3o$277bo40boobo$276bobo12boo26boo63b
oo134bo$276bobboo10boo5bo85boo129b7o$274b7o17bo221boo$273bobbo3bo11bo
6boo206bo10boo20bo$234bo37b3obb7o8boo4boo206bobbo4bo3bobo18b3o$233bobo
38b3obbo13bo4bo206bo4bo4bobobbo17boobbo$234bo40booboo10boo198boobb5o6b
o4bo7bobo16boobboo$276b3obobbo6bobo197bo7bo6bo4b3oboo22boo$277b3oboo8b
3obbo193bo4boboo7boboboobbobobbo19b5o$280bo16bo196b3o10bobo4bo28boo$
296boo211bobbo3bobo22bobbo$294boboo212boo30boo12boo$242bo51b3o259boo$
241bobo51bo$242bo58boo194boo$301boo194boo3$299bo208boo$298bobo220bo3b
oobboobo31boo$283boo223boo11bo3boo4boboo29boo$283boo223b3o10bo3boobboo
boo$297bo3bo205b3o15boo$295bo4bo204b3obbo12bobbo$295bo210bobo14bobo34b
oo$249bobo43boo198bo11boo15bo34bo$240bob3o4bobo256bo47boobboo$238boobo
4bo5bo238bo7bo56boo$240boo4bobbobbo207b3o28bo8bobb3o$246bobbobbo206bo
30bo4boo3bobb3o$245bo4bo207bo4boo26bobo6bobboobbo46bo$241bobbo16boo
194bo3bo15b3o11boboo10bobo41b7o$242boo17boo194bobbo4bo4boo33b3o46boo$
274b3o7bobo170bo3bo3bo4b3obo21bo44bo10boo$277b3o5bo165bo6boobob3o74bo
bbo4bo3bobo$231b3o43b3o169booboo7bo77bo4bo4bobobbo$230bo3bo43bo183b4o
20boo13bo7bo14boobb5o6bo4bo7bobo$229bo4bo217boo10boo11boboo5boo13boo5b
obo13bo7bo6bo4b3oboo$228bo3bo220bo23bobbo19bobo4bobbo13bo4boboo7bobob
oobbobobbo$228bobbob3o33boo176bo3bo25b3o28boo18b3o10bobo4bo$228bo7bo
32boo180bo3bo87bobbo3bobo$230bo3bobo19bobobboo22bo258boo$230bo3boboo4b
o4bobo6bobboobbo20bobo172boo$232b3oboo3bobobboobboo7boobbo19bobbo162bo
bbo6boo58bo$241bob4obbobo5boobbobo20boo164boo66bobo10boo$242bo6bobo
266bobbo9boo$246bob3o128bo94bobo4boo36boo$377booboo92bo3boobbo$232boo
134bo10bo94bo7bo59boo$232boo133b3o24boo85bo39boo$233bo55b3o74booboo22b
obbo41b3o11bo23booboo39bo3bo17boo$288b3o74boobobo9boo11booboo39bo14boo
3bobo60booboo17b3o$233bo54b6o70b3obb3o7bobbo11bo41bo4boo14bobbo59bo20b
3o$289booboboo69bo6bo5boo3bo10b3o38bo3bo20bo59bobo16b3obbo$292bob3o69b
5obo5bo4bo19boo30bobbo4bo5bo3bo5bo62bo17bobo$231bo5b3o51boob4o69b4oboo
4bo3bo20boo30bo3bo3bo5boboobo4bo81boo$231bo7bo53b4o75bo6bobbo53boobob
3o7bobboboo84bo$231bo5bobo54boo75bo8bo58bo13bo$237boo201b4o11b3o$396bo
45boo11bobbo$299boo75boo14bo3bo58bobbo$298bobbo65boo7boo15bobbo58b3o$
299bobo5boo58boo24booboo$300bo6boo85bobo$236boo157bo66boo$236boo69boo
93boo58boo$307boo$247boo147boo$246bo110bo11boo24bobbo$355booboo8bobbo
24boo62bo$247bo109bo9boobbo72boo12bob3o$251bo116booboo71boo13bobbo$
249bobo116boo3bobboo78b3oboo$250bo107boo11bobobboo78boobo$357bobbo11b
oo82boo$356boo3bo$356bo4bo$356bo3bo$357bobbo91boo$358bo15boo76boo$372b
oobo$374bo$370boo7boo$371boo6boo$372b3o4$361boo$361boo4$328bo42bo$314b
obo6bobb4o40bo$313bo9bob4o41b3o$314bobbo6b3o3boo$316b3o9bobboo20bo$
329boboo19b3o$330bo8boo10b3obo$339boo9boo3boo$349boobobboo$350booboboo
$351b3oboo$353bo4bo$354b4o$307bo31b3o14bo89b3o$307bo7bo21bo4bo4boo101b
o$307bo5b3o23boboo4boo101boo13bo$306boo3bobo22b3o24bo86bobbo11bo$312bo
bbo13bo32bobo73bo12bobo11bo$311bobboo3boo9bobobo26bobbo72bobo11bo$319b
oo5b5o3bo27boo73bobo10boo14bo$327boobbobbo102bobbo8bobo13bobo$332boo
104bobo10boo11bo8boo$441bo6boo14bobbo5boo$440boo8bo12boobo$440bo21b3o$
463booboo$370boo91bobboo$369bo5boo69boo16b3o$369bo67boo7boo17bo$315boo
3boo48bo7bo58boo$309bo3b4o3bobo48bo6bo$309boboobbobbo3bo49bo5bo90b3o$
309boboo4bo3boo149boo$313bo3bo56b3o94bo$318bo147boo$377boo45b3o12boo
24bobbo$376bobbo48bo10boo25boo$377bobo5boo41boo$378bo6boo41bobbo$314b
oo113bobo7b3o4boo$314boo69boo42bo7bo4bo3boo$385boo41boo7bo5bo$427bobo
13bo$429boo$426boo10boo$428bo14bo$443bo$440boobbo$441bobboo$442b3o4boo
$443bo5boo5$431boo107b3o$431boo109bo$541bo$$442bo$390bo51bobo$386boobo
bo7bo42boo$386bobbooboobbooboo$386bo5bobo5bo$387boobbo8bo$391bobb3obbo
$391b3o15boo$409boo11b3o$379boo40bo3bo$422boo$378bo3bo41booboo$383bo
42boo$376bo7bo$375bo4bo$376bobobo4bo31boo$376bo8bo20bo3boo5boo$377bo4b
oobo8bobbo6boobooboo21bo$378boboob3o11b3o3bo7bo20bobo$379b3oboo4boo3b
oob4o3bo6boo18bobbo$389boo9boo4boobboo20boo$406boobboo$$396bo4$440boo$
439bobbo$439bobo$386boo52bo4bo$379bo5bobboo53booboo$379bo4b3obbo50bo4b
o$379bo4bo4bo50bo$384b5o$385boo33bo$416boobobo7bo17boo$416bobbooboobb
ooboo15bobbo$416bo5bobo5bo16bobo5boo$417boobbo8bo17bo6boo$384boo35bobb
3obbo$384boo35b3o15boo14boo$439boo14boo$409boo$$408bo3bo$413bo$406bo7b
o$405bo4bo$406bobobo4bo31boo$406bo8bo20bo3boo5boo$407bo4boobo8bobbo6b
oobooboo$408boboob3o11b3o3bo7bo$409b3oboo4boo3boob4o3bo6boo$419boo9boo
4boobboo$436boobboo$$426bo7$416boo$409bo5bobboo$409bo4b3obbo$409bo4bo
4bo$414b5o$415boo5$414boo$414boo!

You can see how the components are spaced out more at the top of the convoy, and how there are more gliders and tubs between them.

At some number of stages it will be worth starting a new independent period doubling convoy using the output of the previous convoy to get a better bounding box or population.

EDIT 2:

Partial resets can be used to keep the width of a single convoy small so that there is no need to use multiple convoys to get high periods.

Code: Select all

#C A diagonal c/12 period 393216 (96 * 2^12) sideways rake.
#C This uses twelve period multiplication convoys in series to
#C multiply the period from an input period 96 rake by 4096.
#C Tubs created by earlier stages are deleted by shared
#C Corderships from later stages, except for the final two
#C stages which use single Corderships to delete the tubs and
#C another single Cordership to reset the width of the convoy.
#C More stages can be added to increase the period further,
#C with the occasional reset to keep the width small.
#C David I. Bell, 4 July 2025
x = 598, y = 611
147bo6boo$146bobo3bo3bo$145bo3bobo3boo$146bobobboboboo$147bo3bobboo$
151bo4bo$152bobbo10boo$154bo11boo6$144bo$127b3o8bo5bo29boo$126bo3bo6bo
7bo28boo$127boo9b4obboo$129booboo9b3o$131boo11bobo$145bo23b3o$145bo22b
oobbo$171boo$167bob3o$165bobboo$163bo$161b3obbo$161boobbo$152bo8booboo
$150boobo9boo$148bo9boo3bo$148bo6bobboo$133boo20bo$133boo13boobbobbo$
147bo3b4o$148b3obo$148b3o4$141boo$141boo9$133bo$132boboo$106bo29bo$
105b3o22bo3bobbo$94boo8bobobo19bo9bo6bo$103b3ob3o12bo5bo4boobboo5bobo$
93bo3bo23bobo13boo4bobbo$98bo6bob3o13boo5bo5bo7boo$91bo7bo5b5o9bo3bo7b
o4b3o$90bo4bo9boobboo11bobboo5bo4boo$91bobobo4bo6boboo14bo8b4o16bo$91b
o8bo8boo9bobboo26boobboo$92bo4boobo4bobobbo11bo7boo18b6o$93boboob3o3bo
bobbo20boo17boobbo$94b3oboo5bo43booboboo$151bo3bo$151bobbo$$103boo15b
oo$94boo7boo58bo$94boo24boo40bobo$162bobbo$121bobo39boo$122boo$84bo$
83b3o36b3o44bo$82bobobo10bo24bobbo43bo39b3o$81b3ob3o9bobo23boo83bo3bo$
99b5o104bo3bo$83bob3o9bo110bo3bo12b3o$83b5o8bobbo4bo120b3o$83boobboo8b
o5boo104booboo9boo4bo$85boboo9boo75bo34bobbo9b3obobo$87boo10bobo72bobo
20bo13bobo10boo3bo$83bobobbo86bo19booboo12boo10b5o$82bobobbo107booboo
9bo3bo12bo7boo$83bo111boo11bobobobo19boo$197boobo8bo$198bobbo$96b3o99b
obbo$96bobo7boo91boo12boo9boobbo$96bobb3o4boo105boo$102bo49b3o69bo3bo$
99bobo52bo69bo$56bo43bo52bo71bobo$40booboo6boboobboo138b3o$40boo8bob5o
31boo135b3o$40boobobo5bo4boo30boo107bobo$43bobo11bobo138bo$44boo153bo$
57b3o6boo131boo$66boo128boboobo$196b4oboo13boo$29bo167b5o$28b3o168boo
17bo$27bobobo181boobboo$26b3ob3o12bo167boo28b3o$44bobo195bo3bo$28bob3o
13boo72b3o119bo3bo$28b5o9bo3bo75bo119bo3bo12b3o$28boobboo11bobboo71bo
79boo4boobboo46b3o$30boboo14bo152boo4boboboo30booboo9boo4bo$32boo9bobb
oo22b4o132bobb4o31bobbo9b3obobo$28bobobbo11bo24boobo137bo19bo13bobo10b
oo3bo$27bobobbo36bobobbo132bobbo18booboo12boo10b5o$28bo40b3oboo133b3o
18booboo9bo3bo12bo7boo$69b3oboo154boo11bobobobo19boo$73bo157boobo8bo
87bo$209boo21bobbo81boo7boobbobo$43boo164boo21bobbo81b3o6b4o3bo$233boo
12boo9boobbo54boobobo7bo$43boo202boo71boo10boboo$147bobo49bo58bo3bo69b
obo$44bobo100boo49bobo57bo74bo8boo$14bo30bo42b3o57bo110bobo80boo$13bob
o5bo11boo10bo44bo79boo26bobbo3bob3o21b3o$19booboo9boo54bo83boo4bo20bo
4bo53b3o$13b3obbo3boo146boob4o3bo20boboobobo22bobo$19booboo143b5o4b4o
22boo3bo24bo72bo$19b4o147b3o6bo23bo29bo69booboo$33boo136bo61boo70bo$
33boo135b3o57boboobo84boo$177bo12boo21bo16b4oboo13boo67bobbo$41boo134b
o12boo20bobo16b5o70boo11booboo$41boo110bobo55bobbo18boo17bo52bobbo11bo
$152bo59boo33boobboo51boo3bo10b3o26boo$153bobbo90boo55bo4bo34boo3boo$
155bobo146bo3bo36b3obboo$4bo36boo115bo4boo140bobbo36boobb3o$bbooboo34b
oo114b3o3boo18boo13bo24bo82bo$26b3o27b3o98bo16boo7b3o12boo22bobo10boo
4boobboo$5boo9b4o4b4oboo27bo96boo19bo5bobbo11bobo22bobbo9boo4boboboo
75bo$6bo9boboboo4boobbo26bo99bo13bo5bo5boobo36boo15bobb4o71bo3bo$o3bo
12boo9b3o55b3o66bobbo12bo6bo4bobboo57bo73bobbo$4bo3bo10bo3bobo58b7o6bo
57bobo16boobo6bobboo39bo12bobbo74booboo$83b9o4bo58bo28booboo38bobo12b
3o75bobo$82bo7b3obboo74bo14bo39boobobo89bo$bbo80b3o6bo3bobbo48boo12boo
11bo50bobb4o$3b3o78boo11b3o51boo4bo4boo9bobo50b3o4bo9boo64boo$87bo10bo
49boob4o3bo66bo3boboboo8boo64boo$88bo18boo36b5o4b4o26boo43bo3bo$3b3o
65b3o15bo17boo39b3o6bo26boo44bobo$3b3o143bo81bo$3booboo61bo5bo72b3o$7b
o61b7o79bo$5b3o63bo83bo$71bo3bo4boo235boo$70bo9boo151boo82boo$71bo30bo
bo127bobo$72bo4bo23boobo129bo$72bo4bo20bobb3o$71boobobo20bo3bo$70bobo
25bobo$8boo61bo27bo$8boo301bo$64b3o12boo83boo115b3o27bo$20b3o39b7o6bo
3boo69boboobo9boboboo111bo28bo$22boo37b9o4bo74bo4b3o9boo3bo110bobbo29b
o$60bo7b3obboo75bo5bo10b3obo110bobbo25b3obbo$21bo39b3o6bo3bobbo73bo3bo
13boo112bobo24bo4bo$21bo40boo11b3o74bobo143boo10bo3bo6bo$21b4o40bo10bo
221boo11b3o6bobo$19bo46bo252bobbo$67bo252boo$156boo124bo27bobo$156boo
123bobo26bobo16b3o$269boo3b4o4bo27bobo19bo$264b3obobbo6bo19bobo9bobo
15bo3bo$268bobbobb5o27boo3boo15bobbo$83bo184bobbo8b4o17bo4boo20b3o$80b
ooboo185bo9boo3bo10bo3bo29b3o$83bo183bobo11bo4bo9bo4bo29b3o$79boboo
185bo14boboo11bo32b3o$71boboo4bo3bo200bo12boobboo$65boo4bobo3bobo3bo
195boo16bobo$65boo6boob5o3bo185boo7boo18boo38bo$77bo5bo31bobo152boo25b
obbo28boo7bobo$115boo142b3o35bobo38bobbo$116bo143bo31boo45boo$22b3o
235bobbo28boo$31bo228bobbo$24boo5b3o227bobo$24b4o4bo40boo$24boob3oboo
40boo$29bobo30boo276booboo$43boo18bobbo4bo268booboo$43boo15bobb3obobbo
bo187bo$60bobbo4b4o187bobo$60bobbo196bo$63bo6bo$62boobo$70bo187b4o$68b
oo188boo3bo11boo$51boo206bo4bo12bo123bo$33boo16boo106bo101boboo8bobob
3o116bobbobobbo3bo$13b3o20bo30bo87b5o7boo93bo10bobboo118bo4boob5o$13bo
bbo9bo4boo4boo27bobo86bo3bobo4b3o103bo3boo118bo3bo4bobo$16bo9bo3boo6bo
26bobbo86b3o3b3o3b3o104b3o$13boo11bobb3obboobbo27boo93boobb3o230b3o$
12bobo19boobo123bo237bo18boo$13bobb3o139b3o16boo239boo$14boobbo139boo
17boo$14bo3bo245boo$15bobo59boo63bo121boo$17bo59b3o60booboo235bo$14bo
bbo54b3o4boo61bo236b3o$14bo57bob6o70boo226b3obo14bo$72b7o71boo225boo3b
oo6bobbo3bo28boo$13boobbo125boo17b3o8boo201boobobboo6bo3bobbo28boo$14b
3o125bobbo20bobo4boo202booboboo5bo$141boo3bo15bob3obboo207b3oboo6boboo
$105boo34bo4bo16b4obo211bo4bo$104bobo34bo3bo16booboo214b4o34b3obbobo$
106bo35bobbo17b4o4bo211bo12boboo18bobb3obbo$81boo60bo20bo5bobbo222b3o
18boobb3obbo$80bobbo65boo21b3o222bo19booboobboo$81bobo5boo46bo11boo22b
oo244boo$35bo46bo6boo42b5o7boo24b3o245bo$18boo16bo96bo3bobo4b3o26bo$
18boo13bo55boo42b3o3b3o3b3o23boo239bobobb3o$31bo57boo48boobb3o267bo$
30bo3bo104bo$31bobo102b3o$30boobo102boo263bo3bo3bo$28b6o351boo17bobbo$
27bo357boo$29b5o$27bo4bo370bo$403bo$$153bo$152bobo$151bo241boo$136bo3b
3obo6bo4bo236boo$102bo32bobo3bobobo5bobo$96b3obbobo31bob7oboo5boobo$
95bo6bo33b3oboo3bo9bo$95bo3bo42b3o10bo$93boo3boo43bo12bo$92bobbobobbo$
92bobbobobboo$94booboobbo$95bo4bo42boo$98booboo40boo213bo29bo$97b4o
257bo26b4o$98boo13boo18bo224bo$113boo18bo5b3o220bo12bo21bo$132bobo3boo
bbo215b3obbo10boo20bobo$133bo3bo5bo213bo4bo11bo13bobo4bobbo$98bo34bo3b
o219bo3bo27bo6boo$99bo38bobboo215b3o26boo$98bo40boo203bo30b3o9bobbo$
344bo7bo20boob3o7booboo$121boo221bo5b3o4bobo13boobbo28bobo$121boo220b
oo3bobo6bobo13booboo4boo21boobo$84bo18boo32bo211bobbo4bobo14bobo5boo
20bobo$84bo11bo5bobbo30bobo209bobboo4bobo15bo27bo3bo$84bo11bo5bobbo29b
obbo219boo43boboo$88bo7bo4booboo30boo266b3o$84b3obbo12boo$83bo4bo266b
oo$83bo3bo258boo7boo58bo$84b3o259boo25bo40bobo$145bobo224bobo39bobbo$
144bo3bo223bobo40boo$83bobo56bo5bo187bo35bobo$83bobo56bo5bo187bo36b3o$
83bobo56bo4bo188bo39b3o$83bobo58boo194bo35boo$84boo250b3obbo$335bo4bo
75booboo$335bo3bo76booboo49bo$336b3o10bo119b3o$348boboo$151boo93b3o99b
ob3o116b3o$150bobbo181bobo11bo3bo116booboo$151bobo96bo84bobo12b3o119bo
$103bo48bo93bo3boo12bo70bobo13bo134boo$88boo10bobbobbobo139bobo13boo
69bobo11bo136boo$88boo15bo139b3o16bobo69boo10bobo$99bo5bobbo123bo14bo
100boboo$100bobo3bo125bo30boo$232bo8bo4boo16boo88bo3boo$102b3o134bobo
5boo14bobbo83boob3obboo$101booboo127b3obbo3bo4bo15b3o5boo75bo6bo97b3o
6bo$100bo3boo128bob5o6boo22boo75boo5bo96bo4bo3bobo30boo$96boo3bobbo59b
o75bo5boo105bo98bo4boo3bo31boo$96boo3bobo59bobo69boo215bo6bo27bo$164bo
175boo111b3obobbobo23bo$340boo115b5o26boo$244boo216bo25boo$235boo7boo
243bo$235boo25boo222bobbo$262boo222bobo$172bo89bobbo218boo$171bobo89bo
bo217bo$172bo51b3o36bo221bo$265boo214b4o$228bo34bobbo213bobbo$224bo3b
oo34boo191boo21bobbo$226bobo228b4o5boboo11b3o$223b3o229boob3o5bo3bobo$
180bo44bo18boo209boo3boo10bo4boo$179bobo55boo216boobobo9bobobbobbo$
180bo43boo12bobo219bo5bobo5bo4bo$225boo12boo216b3o13boobooboo$225bo14b
o231bo5boo$225boo249bo$224boo246bo$473bo3bo$188bo48b3o221boo14bo$187bo
bo46bobb3o219boo13bo$188bo50boboo4boo223bo$236boo4boo3boo223bo$238b3o
bbo228boo$239bo3bo$240bobo230boo$470bob3o$229boo240bobbo$229boo240b3o
3$182bo$181bobo274boobo$180bo3bo13b3o256b3obo6bobo$180bo3bo8bo43bo218b
o4bobo4bo$180bobob3o4boob3o39bo188bo31boo6bobo3bo$181boobobbo5boboo22b
3o14b3o185b3o14boo15bo3bobbobboo$185bobo8bo26bo199bo10bobbo4bo18boboo
3bo$185boo11bobbo5boo14boo199booboo6b3obbobbo16bobo$198b3o6boo14bobbo
198b3oboo5boobbobbo16bobo$224bobo200b4o9bobbo$224bo190bo25b3o6boo21bo$
223boo189bobo33boo20bobo$208bo13bobo188booboo45boo6bobbo$175bo31boo15b
oo187boo49boo6boo$174boo7bo23boboboo8boo196boo42bo$173bobob3obbobo23b
3obooboo6bo189b3obbo$172b3o3boo3bo23bo3boobboo200boboobboo$173boboboob
obo24bo3bo19bo183bobbo4boo58bo$174booboo28bobbo19bobo185bo63bobo$175bo
b5obo3boo13boo4bo20bobbo183boo23bo40bobbo$179b4o4boo13boo26boo209bo3bo
37boo$333bo82bo23bobobobo$332b3o81bo24boboobo$200b3o128booboo105bo3bo$
201boo127boobobo81bo67b3o$329b3obb3o77bob3obbobo60bo$330bo6bo65bo10boo
bob3obo59bo3bo$331b5obo64b3o8boo3booboo60boboo58bo$237boo93b4oboo62bo
10bobbo4bo63bo43b3o8bo5bo$178bo57bobbo97bo64booboo6b3obbobbo105bo3bo6b
o7bo$181bo6bobo46bobo96bo12boo52b3oboo5boobbobbo106boo9b4obboo$176bo
11bobobo45bo5boo103boo54b4o9bobbo108booboo9b3o$175bo3bobbo10boo47boob
oo172b3o110boo11bobo$176b3obbo10bo49booboo299bo7boo$177bo3bo59bo3bo71b
3o13boo159bo51bo7boo$179boo61b3oboo9bo57b7o9bo162bo$179bo62bo3bobo9bo
55b9o11bo181b3o$243boobb3obb3obb3o53bo7b3o$243boo3bo3b3obboo55b3o12boo
bboboo20boo67boo86bo5bo$245b3o8bo58boo13bobbo23boo67boo86b7o12bo$182b
oo61b3o3bobobo62bo10bo4bobo179bo17boo$182boo67bo3bo63bo13boo3boo176bo
3bo13boo$253boo65bo12boobboboo11bo162bo17boobo$311bo19boboo3boo10boob
oo65boo94bo18b3o$310b3o17booboo3bo69boo9bo3boo92bo4bo11boboo21boo$309b
ooboo7boo7boobo14booboboo53boo9bo4bo92bo4bo11boo22bobbo$308boobobo7boo
9bo18bo68bo3bo91boobobo12bo22bo3boo$307b3obb3o33bobbo68boboo91bobo39bo
4bo$308bo6bo27boo4boo70bo94bo39bo6bo$309b5obo27boo212bobo$310b4oboo
241bob3o$315bo$314bo101boo$416boo$$531b3o$312bo220bo$310boobo218b3o44b
o$521boo39b3o8bo5bo$313bo207boo38bo3bo6bo7bo$310bobbo12bo235boo9b4obb
oo$311bo13b3o236booboo9b3o$325boobo237boo11bobo$316boo9b3o250bo7boo$
309b3o5boo8boo251bo7boo$316boo9boo$316bo10boo200boo19b3o$325boobo200b
oo$326boo220bo5bo$548b7o12bo$550bo17boo$550bo3bo13boo$269bo45boo232bo
17boobo$269bo45boo176b3o54bo18b3o$269bo222bo3bo25b3o26bo4bo11boboo21b
oo$272boo217bo3boo25bobbo25bo4bo11boo22bobbo$272boo12boo20bo183bo32bo
24boobobo12bo22bo3boo$267bo3b3o11boo20bobo183b4o25boo25bobo39bo4bo$
268b3o15bo19booboo184boboo22bobo26bo39bo6bo$269bo15b3o18booboo184bobbo
23bobb3o63bobo$268boo15b3o17b3o188boo12boo11boobbo5bo58bob3o$268b3o16b
o17b3o3bo198boo11bo3bo4bobo$270bo14bobbo16b3o4bo211bobo4bobbo$268bo16b
3o5boo11boo5bo212bo5boo$270bo15bo6boo11b3o185boo27bobbo$268b3o36boo
171bo13boo26bo42b3o$308boo6bo159boobobo12bobo25bo44bo$316bobo157bobboo
boo10boo30bo14b3o22b3o$316boo158bo5bobobo7b3o22bo3b3o15bo13boo$255bo
52bo168boobbo4bobb3obobboo43boobo10boo$254bobo50b3o171bobboo4boobbo16b
o30bobbo$253bo3bo26boo20bo3bo96bo73b3o9bo4boo10bobbo29bobo$253bo3bo25b
obboo13b3o6boo95bo86bo4bo44boo$253bobob3o23b5o16bo4boo6bo91bo5bo77bo5b
o11bobbo$254boobobbo22b3obo8boobbo3bo11bobo89bo6bobo74b3o3bo13bobo$
258bobo23boobboo8boboobbo10bobbo88bo3bobbo56b3o8boo9bo16bobboo36bo$
258boo25bo3bo26boo90bobboboboo53bo3bo7boo26bobo37bobo10boo$287boobo10b
oo110boboo52bo3boo35b3o37bobbo9boo$287bobo137boo41bo33boo45boo$287boo
138boo42b4o29boo$283bobboo185boboo$281b3o189bobbo$280b4o3b3o184boo$
280bobo4b3o100b3o$281b3ob4o34boo65b3o7boo150booboo$280bo3boo36bobbo63b
o3bo6boo150booboo$280bo3bo38bobo7bo56boob3o11b3obbo22boo36bo$280bobbo
40bo3b5o57boo4bo10b4obo6boo14boo36bo$260boo13boo4bo46boboboo59bobbo13b
o21boo38bobo$260boo13boo53bo63boo15bobo7boo8bobo39bo$329boo81boo3bo4b
oo9bo39boo$422bo50b3o11bo$273b3o142b4o64bobo$274boo109bo13boo10boo7bo
50bo4boo7bo3bo$385bo13boo10boo58bo5bo8bobbo$387bo5bo77bo5bo8bo$268boo
116bo6bobo25boo53bo10bobo$268boo115bo3bobbo28boo63bobbo$386bobboboboo
92boo$391boboo3$476boo$476boo7$394boo3bo$392b3o4boo$387b3obo8boo5bo$
391bobobb5o5bobo$392bo3b3o7bobo$407bo$$402boo$$346b3o54boo$346bobo44b
oo9bo$345bo3bo43boo$345bo3bo36bo$345bo17boo19booboo$345bo4boo11boo19b
ooboo$345bo6bo31boo$346bo5bo33boobo$346boo39bobbo90bo$348bo3bo34bobbo
89boo$349bobo10boo24boo89boboo$363bo115bobboo$362b3o6boo104b4ob3o$346b
3o13bo8boo103bobbobobboo$345bo3bo127bobobob3o$346bobbo36b3o89boob3obo$
332bobo13boo128b4obbobo$331bo33bo20bobo3bo88bo3bo$332bobbo26bobboo20bo
3bo89bo3bo$334bobo24bo3bo21boobb3o87bobbo12boo$337bo23bo4bo19b4o107boo
$336b3o26boo18bobbobo$336bo23bo4bo20b3oboo3bo$334boo24bobbobo21b4o3bob
o$336bo24boobbobo20boo3bobbo$334bobbo27bob4o23boo74boo$334bobo28bobboo
90b3o7boo11boo$334bo30boobbo93b3o11boo4bobo19boo$463b3o11booboobboo19b
oo$358booboo101bo16boobbo$358boo99bo28boo$356bo4bo96boo29boo9b3o$357bo
99boboo24bob3o12bo$357bobbo40boo54bobboo24b3o10bo$358bobo39bobbo6boo
43b4ob3o6boo7booboo13bo$359boo40bobo5bobboo40bobbobobboo5boo9boo13bo$
358b3o41bo6bo3bo41bobobob3o16bo15bo3bo$338boo11b3o6bobo43bobo47boob3ob
o27boo6bo$338boo11b4o50bobbob3o43b4obbobo26boo$350boobboo50bo52bo3bo$
351boobo104bo3bo$351b3o105bobbo$352bo3$346boo$346boo112boo5$465boo$
464bobbo$457b3o4bobboo$463bobboo8bo$463b4o9boo$474boobo$472booboo$473b
3o$474bo$$417bo45boo$417bo45boo$416bobo$417boobbo11boo21bo$416bo5bo9bo
bbo20bo$416bo5bo10boo21bo94b3o$416bo4bo12bo22boo94bo$420bo13bo22b3o92b
o$417b3o13boobo20boo$432boo$436bo$415booboo12bob3o4boo$420bo12bobbo4b
oo$415boo16b3o20bo$417b3o35bobo$455bobbo4bo$402b3o58bobo$401bo31bo29b
oo$400bo4boo25b3o19bobbo$399bo3bo27bob3o18boob3o$399bobbo4bo23bo24boo
bbo$399bo3bo3bo24b5o15bo4bobbo4bo$400boobob3o27boboo14boobbobo4bobo$
403bo28bo3bobo24bobbo$404b4o31bo24boo$406boo24bobb4o$433boo3$428bo4boo
$427boo3b3o$426bo3bobboo$426bo3bo40boo$432bo37bobbo$428boboboo13bo23bo
bo5boo$430bobo14bo24bo7boo$408boo13bo22bobo30boo$408boo12bo24boobbo11b
oo11boo$421bobbo21bo5bo9bobbo11bobo$421bobbo21bo5bo10boo13bo$422boo22b
o4bo12bo$450bo13bo$447b3o13boobo$462boo$416boo48bo$416boo27booboo12bob
3o4boo$450bo12bobbo4boo$445boo16b3o$447b3o$$432b3o$431bo31bo$430bo4boo
25b3o$429bo3bo27bob3o$429bobbo4bo23bo$429bo3bo3bo24b5o15bo$430boobob3o
27boboo14boo$433bo28bo3bobo$434b4o31bo$436boo24bobb4o$463boo3$458bo4b
oo$457boo3b3o$456bo3bobboo$456bo3bo$462bo$458boboboo$460bobo$438boo13b
o$438boo12bo$451bobbo$451bobbo$452boo4$446boo$446boo!

BCNU,
-dbell

[dbell]

Here are two period 96 edge puffers made from the three-engine Cordership with an attached switch engine.

Code: Select all

#C A diagonal c/12 period 96 loaf puffer.
#C The loafs are created on the edge of the puffer.
#C David I. Bell, 6 July 2025
x = 87, y = 53
52bo$50booboo$$53boo$54bo$48bo3bo$24bo27bo3bo11bo$22booboo40bobo$25boo
40bobbo$22b3o15boo8bo17boo$24bo3bo10bobbo8bobo$23bo3bo26bo$24b3obo23b
oo$26boo23bobo$10bo6boo6bobo10boo11bobo22bo$9bobo3bo3bo6bo11b3obboo7bo
bo20bobo$8bo3bobo3boo5boo12bo13boo20bobbo$9bobobboboboo4b3o11boo5bo30b
oo$10bo3bobboo5boboo11bo4bo$14bo4bo3b5o11bo$15bobbo21bobo$17bo23bo$84b
o$21boo60bobo$12boo7boo15b3o42bobbo$12boo23bobbo43boo$36bo4bo$36b6o$bb
o37bobo$ooboo36b3o$3boo37boo$3o$bbo3bo$bo3bo$bb3obo$4boo$3bobo8bo4bo$
4bo9bo5bo$3boo$bb3o$bboboo$b5o9boo$17bo$15b3o$16bo$21bo$20boo$14boo4b
oo$14boo3$6boo$6boo!

Code: Select all

#C A diagonal c/12 period 96 ship puffer.
#C The ships are created on the edge of the puffer.
#C David I. Bell, 6 July 2025
x = 91, y = 52
51bo$51bo$51bo$48bob3obo$48bob5o$24bo27bobo$22booboo22boo15b3o$25boo
22boo$22b3o15boo8bo$24bo3bo10bobbo7boo$23bo3bo23bo3boo$24b3obo22bo$26b
oo21boboo$10bo6boo6bobo10boo10bo$9bobo3bo3bo6bo11b3obboo27boo$8bo3bobo
3boo5boo12bo32bobo$9bobobboboboo4b3o11boo5bobboo23boo$10bo3bobboo5bob
oo11bo4bo3boo$14bo4bo3b5o11bo$15bobbo21bobo$17bo23bo$$21boo57boo$12boo
7boo15b3o39bobo$12boo23bobbo40boo$36bo4bo$36b6o$bbo37bobo$ooboo36b3o$
3boo37boo$3o85boo$bbo3bo81bobo$bo3bo83boo$bb3obo$4boo$3bobo8bo4bo$4bo
9bo5bo$3boo$bb3o$bboboo$b5o9boo$17bo$15b3o$16bo$21bo$20boo$14boo4boo$
14boo3$6boo$6boo!

Here are some period 192 puffers based on thinning period 96 puffers.

Code: Select all

#C A diagonal c/12 period 192 block puffer.
#C The blocks are created on the edge of the puffer.
#C This uses a period 96 block puffer whose output is thinned by a
#C period 192 sparking spaceship.
#C David I. Bell, 6 July 2025
x = 135, y = 97
36b3o$36b3o$37bo$38boo$39bo$38bo14boo$53boo3$36boo$36boo$37bo$37bo15bo
$36bobo15boo5boo$35bo16bobo6boo$36bobboo11bo$37bo3bo11boo$24bo14boo14b
o$24bo14bo13b3o$24bob3o25bo$26b3o23boo$27bo13boo26boo$27boo12boo8boo
16boo$28bo22boo$28boo$3o$4bo20booboo24boo$4boo13bo6b3o25boo$4bobbo11bo
6bo$5bobo11bo57boo$5bo71boo$4boo14bo$3bobo13bobo$5boo11bo$bboo14bobbo$
4bo12boobo$16b3o$17booboo63boo$17bobboo63boo$18b3o$19bo3$46b3o23bo$45b
o26bo$7boo36bo3bo22bo8bo$7boo34boo3boo29bobo$42bobbobobbo22b3obbo3bo$
42bobbobobboo22bob5o$44booboobbo28bo$45bo4bo24boo$48booboo34bo$47b4o
35bobo$15boo31boo13boo22bo13boo$15boo46boo36boo5$27bobo6boo11bo$26bo9b
oo11bo$27bobbo12boobbobo$29b3o11boobbobb3o$47bo6bo$48bo6bo10bo$24b3o
24bo3bo11bo$23bo27bobboo11boo$23bo3bo16boobo4boo12boo$21boo3boo7boo11b
o13boob3o$20bobbobobbo6boo8bobo14b5o50boo$20bobbobobboo16bo15bobboo50b
oo$22booboobbo27boo5bo$23bo4bo28boo$26booboo$25b4o$26boo4$26bo$27bo$
26bo$$39boo$$31boo100boo$24bo5bobbo99boo$24bo5bobbo$24bo4booboo$30boo
9b3o$39bo3bo$39bobbo$39b3o3$29boo$29boo!

Code: Select all

#C A diagonal c/12 period 192 ship puffer.
#C The ships are created on the edge of the puffer.
#C This uses a period 96 ship puffer whose output is thinned by a
#C period 192 sparking spaceship and a two-engine Cordership.
#C David I. Bell, 6 July 2025
x = 163, y = 103
51bo$50b3o$49booboo$50b3o$23b3o25bo14b3o$51bobo$24bo15boo9b4o$24boob3o
10boo12bo$23bob4o11boo27bo$23bob3o22booboo15bo$24b3o15bo6bo5bo$25bo14b
oobbo5bo3bo$9b3o6bo20bo4bo6bo22b3o$10boo3boobo19bo29bobboo$9boo5bobo3b
ooboo15boo4boo22bo$14b3obo3booboo12booboo4boo17bo3boo$17boo4boboo14bo
25bobo$24boo3$21boo57boo$12boo7boo57bobo$12boo25bo41boo$38bobo$37boob
oo$38bo$b3o35b5o$40bo3bo$bbo39bobo43boo$bboob3o80bobo$bob4o82boo$bob3o
$bb3o10boo$3bo10bo3bo$14bo3bo$15bo3bo54bo$ooboo11b3o54b3o20boo$ooboo
12boo53bobobo19bobo$boboo10boo54b3ob3o19boo$bboo10boboo70bo4bo$16boo
27bo27bob3o8b3obboobo$43booboo25b5o8b5o4bo$19b3obboo8bo10bo27boobboo7b
oo3boobbo$19bobobboo7b3o24boo13boboo8boo$14bobo4boo9booboo22bobbo14boo
9bo$14boo4bo10boobobo9boo11booboo9bobobbo10bo$30b3obb3o7bobbo11bo11bob
obbo8bobbo$31bo6bo5boo3bo10b3o10bo14bo$6boo24b5obo5bo4bo19boo$6boo25b
4oboo4bo3bo20boo$38bo6bobbo53boo$37bo8bo50b3obboo$96bo15boo$62bo33bo3b
o11bobo$42boo14bo3bo31boo3boo12boo$33boo7boo15bobbo30bobbobobbo$33boo
24booboo29bobbobobboo$60bobo32booboobbo$61bo34bo4bo$68boo29booboo$98b
4o$62boo35boo13boo$23bo11boo24bobbo49boo$21booboo8bobbo24boo$23bo9boo
bbo$34booboo$34boo3bobboo$24boo11bobobboo$23bobbo11boo40boobo44boo$22b
oo3bo51b3obo6bobo29boo4bobo$22bo4bo50bo4bobo4bo31boo5boo$22bo3bo52boo
6bobo3bo$23bobbo53bo3bobbobboo$24bo15boo41boboo3bo$38boobo40bobo30b3o$
40bo41bobo33bo$36boo7boo68bobbo$37boo6boo69boo$38b3o$108bo$107bobo$
112bo$27boo78b3obbo$27boo79bobboo$87bo10boo9b4o31boo$82bo3b5o5bobboo7b
o4bo30bobo$81bobo7boob3oboo3boobbo5bo31boo$81bo7boboobbo3boo4bobb5o$
82bo8boo3boobo5bobbo$83bo3b4o6bobo5bo$88b3o7boobo$100booboo$100b3o$$
89boo$89boo5$160boo$160bobo$161boo!

Code: Select all

#C A diagonal c/12 period 192 ship puffer.
#C This uses a period 96 ship puffer whose output is thinned by a
#C period 192 sparking spaceship.
#C David I. Bell, 6 July 2025
x = 127, y = 112
100b3o$100bobbo$103bo$100boo15boo$99bobo15boo$100bobb3o$101boobbo$101b
o3bo$87bo7bo6bobo10bobo$86b3o5bobo7bo12bo$85boob4obbobbo3bobbo16bo$86b
3obbo9bo13b3o7boo$87bobboobbo21boo7boo$91boobobo3boobbo11boo$95bo5b3o
13boo$118bo$$98boo16bo$89boo7boo15b3o$89boo23booboo$113bo4bo$113b4obbo
$78b3o33boo4bo$78bobbo$81bo36bobo$78boo$77bobo$78bobb3o$79boobbo$79bo
3bo$80bobo$82bo$79bobbo$79bo$$78boobbo10bo$79b3o12bo$92bobo$92b3o$97b
oo$99bo$91boo4boo$91boo3$83boo$83boo3$75b3o$75b3o$76bo$77boo$78bo$77bo
$88bobo$88boo$89bo$75boo$75boo$51bo24bo$51bo24bo$51bo23bobo$48bob3obo
19bo$48bob5o20bobboo$24bo27bobo21bo3bo$22booboo22boo15b3o9boo$25boo22b
oo27bo$22b3o15boo8bo$24bo3bo10bobbo7boo$23bo3bo23bo3boo$24b3obo22bo$
26boo21boboo$10bo6boo6bobo10boo10bo$9bobo3bo3bo6bo11b3obboo27boo$8bo3b
obo3boo5boo12bo32bobo$9bobobboboboo4b3o11boo5bobboo23boo$10bo3bobboo5b
oboo11bo4bo3boo$14bo4bo3b5o11bo$15bobbo21bobo$17bo23bo$$21boo$12boo7b
oo15b3o$12boo23bobbo$36bo4bo$36b6o$bbo37bobo$ooboo36b3o$3boo37boo$3o
85boo$bbo3bo81bobo$bo3bo83boo$bb3obo$4boo$3bobo8bo4bo$4bo9bo5bo$3boo$
bb3o$bboboo$b5o9boo$17bo$15b3o$16bo$21bo$20boo$14boo4boo82boo$14boo88b
obo$105boo$$6boo$6boo!

And here is a new breeder making use of the new puffers.

Code: Select all

#C A breeder based on Corderships building Gosper glider guns.
#C This uses large and small period 192 ship puffers, two
#C period 192 block puffers, and two period 192 glider guns.
#C David I. Bell, 6 July 2025
x = 344, y = 322
102bo$88boo7boobbobo$88b3o6b4o3bo$88boobobo7bo$91boo10boboo$103bobo$
104bo8boo$77b3o33boo$$81bo$77bo3boo$79bobo$76b3o7boo$78bo7boo$$77boo
28b3o$78boo24boboo$78bo24bo3bo$78boo23bo3bo$77boo25b3o$123b3o$85boo$
80bo4boo34bo5bo$66boo7boobbobo30bo8b7o12bo$66b3o6b4o3bo40bo17boo$66boo
bobo7bo36bo6bo3bo13boo$69boo10boboo37bo17boobo$81bobo24b3obo10bo18b3o$
82bo25b3obo11bo4bo11boboo$109bo8boo4bo4bo11boo$110bo3b3oboo3boobobo12b
o6boo$111bo6bo3bobo23boo$112bobobobo4bo$113bo$89bo$88bobo$91bo29boo$
112boo7boo$88bo23boo$80b3o55b3o$71boo5bo3b5obo52bo$71boo6boo4boobboo
49boo$79bob6o14b3o38bo$140b3o12b3o$99bo5bo10bo23bobbo15bo$99b7o11boboo
20boo16boo13bo$101bo15b4o38bobbo11bo$101bo3bo10boob3o25bo12bobo11bo$
79boo19bo13b3o4boo23bobo11bo$74bobobboo20bo13bobo3boo23bobo10boo14bo$
65bob3o4bobo25bo4bo8b3o27bobbo8bobo13bobo$63boobo4bo5bo24bo4bo8b3o28bo
bo10boo11bo8boo$65boo4bobbobbo23boobobo43bo6boo14bobbo5boo$71bobbobbo
22bobo46boo8bo12boobo$70bo4bo25bo47bo21b3o$66bobbo102booboo$67boo46bo
56bobboo$114bobo38boo16b3o$113boobobo5boo20boo7boo17bo$115bob3o4boo20b
oo$117bobbo$118boo58b3o$118bo62boo$180bo$106boo67boo$106boo25b3o12boo
24bobbo$69bo67bo10boo25boo$69bo67boo$69bo67bobbo$138bobo7b3o4boo$138bo
7bo4bo3boo$98bo15bo22boo7bo5bo$77boo16b4o15bobo19bobo13bo$77bobo34boo
22boo$68bo9boo55boo10boo$51b3o8bo5bo68bo14bo$50bo3bo6bo7bo28bobo51bo$
37bo13boo9b4obboo29bo49boobbo$23bobo6bobb4o14booboo9b3o27boo51bobboo$
22bo9bob4o17boo11bobo26bobbo50b3o4boo$23bobbo6b3o3boo28bo26booboo51bo
5boo$25b3o9bobboo27bo$38boboo$13bo25bo8boo$13bo34boo$13bo126boo$16boo
42bo79boo$16boo42boo$11bo3b3o41bobo31boo$12b3o6boo70bobo55bo$13bo7boo
71boo8bo46bobo$12boo29bo60bo46boo$12b3o26b3o60bo$14bo26bo$12bo25boobb
oo88bobo$14bo23bobobo88bobbo$12b3o24b3o70boo18bobo$40bo71bobo$20boo91b
oo$15bo4boo112bo33bo$bobo6bobb4o116boboo32boboobobo$o9bob4o117boboo26b
3o3b4o3bo$bobbo6b3o3boo113bo3bo32bobbooboo$3b3o9bobboo113b4o31bo$16bob
oo89boo9boo11b3o30b3o$17bo91bobo8bobo43b3o17boo$110boo9boo63boo5$24bo
131b3o$24boo102boo25bo3bo$128bobo23bo3boo34boo$129boo24bo38boo23b3o$
16bo139b4o22b4o32bo3bo$16booboobo135boboo24bo30bo4bo$6boo9b3oboobo133b
obbo6bobooboo7bo4bo28bo3bo$6boo5b3o8bo134boo6b5obboo7boobo29bobbob3o$
14bob4obo145bobb3obo10bo30bo7bo$17b4o104boo9boo35bo44bo3bobo$125bobo8b
obo79bo3boboo$126boo9boo19bo61b3oboo$158bo77boo$157bobo76boo$14boo142b
o$14boo142boo$158b3o59boo$220boo$156bo4boo58bo$156bo5bo$156bo5bo58bo
22boo$161bo82boo$$219bo5b3o$219bo7bo$141boo9boo59bo5bo5bobo$141bobo8bo
bo57b3o10boo$142boo9boo6boo48b3obo$161boo47bo3bo45b3o$209boobbobbo43b
3o14boo$173bo34b3obb4o42bo3bo7bobo4boo$172bo37bo3bobbo42boob3o5bobbobb
3o$171boo37bo6bo42boo4bo4bobob6o$171boo39bobbo47bobbo9bobboo$172boo40b
ooboo32bo12boo11b3o6boo$174boo38bo34booboo24bo7boo$176bo75boo$249b3o$
251bo3bo$250bo3bo$195boobo52b3obo3boo$157boo9boo24b3obo6bobo45boo4boo$
157bobo8bobo22bo4bobo4bo46bobo$158boo9boo23boo6bobo3bo44bo$195bo3bobbo
bboo45boo22b3obbo$198boboo3bo70bobobobo$197bobo12boo62booboobo$197bobo
12boo64boboo$252b3o$250bo4bobo$238b3o18bo$238b3o8bobbobo3bo$218bo18bo
3bo6bobbobbobobo61bobo$217bobo18boob3o5bobbobb3o62bobobo7bo$146bo70boo
19boo4bo4bobob6o60bobboobo4b3o$145bobo67boboo22bobbo9bobboo61boo3bobob
oobo$144booboo53bo9bob5o23boo11b3o62boo3boob5o$144boo16boo9boo9boo11bo
3b5o5boobo3boo36bo67boboo3boo$150boo9bobbo8bobo8bobo9bobo7boo4bobboob
oo103bobo16boo$144b3obbo12bobbo8boo9boo9bo7boboo5b6o123boo$148boboo45b
o8boo6bo92bo$146bobbo48bo3b4o100bobo$149bo11bo41b3o56boo41bo3bo$147boo
11boo3bo96boo42bobo$161bo3boo140bo7boo$147bo13boboboo3boo143boo$145boo
boo11bo3boo3boo32boo101b4o16boo9boo$148bo13b3o39boo50bo49bo4bo20bobo3b
oo$145bo16b3o79boo9bo3boo47bo23boboo$134bo12bo96boo9boo3boo43bo3bobbo
20boo$133boo120b3obbo44bob3obo$132b5o119boboo46b3obo16bo$131bo29bo95b
oo69bo8boo$130boo5bo12boo8b3o15boo9boo9boo112boo20b3o$129b3oboo15boo
11bo14boo9bobo8bobo9boo84bobo13boo$130boboboobboo20booboo25boo9boo9boo
84bobobo7bo$131bobbobboo20booboo133bobboobo4b3o$110b3o20boo25boboo71b
3o60boo3boboboobo$109bo25boobo18b4obbo70bo63boo3boob5o$108bo4boo23bo
17bob6o69bo4boo62boboo3boo$107bo3bo15b3o27bo3boo69bo3bo64bobo$107bobbo
4bo4boo64boo44bobbo4bo$107bo3bo3bo4b3obo61boo32boo10bo3bo3bo$108boobob
3o104boo11boobob3o$111bo124bo30b3o$112b4o121b4o25bo3bo$114boo11boboo
108boo24bo4bo8boo3b3o$127bobbo134bobbobo7b4o$127b3o135boobobo6bo3boo
34boo$194boo9boo9boo49boobobbo4boobobo32bobo$194boo9bobo8bobo9boo14bo
24boobbo31boobo6bobbo$206boo9boo9boo12b3o25b3o13bo6boo6bo3b6o4bobbo$
242boobo37bobbo6boo5bo5bo4bo3booboo$184b3o97b3o13bo11bo4boobo$183bo3bo
50boo4bo4boo50bo9bo7b3o$182bo4bo51bo66bo13boo$181bo3bo54b3o50boo11bobb
o$116boo63bobbob3o13boo36boo18boo30boo4bo9bo$116boo38bo24bo7bo12boo32b
oo25boo4bo22boobboboobo$154booboo24bo3bobo8bo37boo22boob4o3bo21boobbo
5bo$154booboo24bo3boboo7boo57b5o4b4o25bobo4bo$154boo29b3oboo9boo58b3o
6bo22bo3b6o$156boobo40boo59bo30boboobo$157bobbo34boo3bo59b3o10boo13boo
$157bobbo34boo70bo5boo13boo$124boo32boo12boo20boobbo11boo9boo9boo33bo
20bo$124boo46boo22bo13boo9bobo8bobo9boo41bo$222boo9boo9boo40bobo$$156b
o$139bobo13boboo39bo$139bobobo9bo44bo$138bobboobo11bobo$139boo3bobobo
3bobbobo$139boo3booboo3bo5bo119bo$143boboo5bobbooboo116boobo$142bobo8b
o3boobo11b3o87boboobo9boboo$156b3oboo9bob3o85bo4b3o10bo$153bo3b4o13bob
o85bo5bo$155booboo15boo86bo3bo$134bo9boo8bo17bobbo88bobo$132booboo7boo
26b3o51boo9boo9boo$132booboo36bo52boo9bobo8bobo9boo$132boo32boo70boo9b
oo9boo$134boobo28boo100boo$135bobbo129boo$135bobbo$136boo73bo$209boob
oo$211bo$226boo$225bobbo$134b3o75boo11booboo$211bobbo11bo$134bobo61bo
11boo3bo10b3o$135bo61b3o10bo4bo19boo$136bo73bo3bo20boo$136boo10b3o46b
3o11bobbo27boo9boo9boo$133boboobo9bobo47booboo9bo29boo9bobo8bobo9boo$
133b4oboo8boobo48bo53boo9boo9boo$134b5o11bo63boo12bo$136boo11b3o62boo
8bo3bo$148bobbo73bobbo$149boo74booboo$198bo27bobo$197bobo27bo$198bo$
138boo$138boo57boo$196bobo$215bo$196b3obobo11bo$200b3o13boo$200boo14b
oo40boo9boo9boo4bo$217bo40boo3boo4bobo8bobobbo6boo$214bobbo46boo4boo9b
oobb3o4boo$214bobo46bo$212boo$211bo$213bo$202boo5b4o$202boo4bobbo$208b
obbo$209b3o$187bo$187bo$187bo$190boo$190boo12boo4boo$185bo3b3o11boo5b
oo$186b3o15bo$187bo15b3o$171b3o12boo15b3o$180bo5b3o16bo$173boo5b3o5bo
14bobbo$173b4o4bo4bo16b3o$173boob3oboo6bo15bo$178bobo5b3o4$184boo$175b
oo7boo$175boo25boo$201bobbo$202bo$165bo36boo$165bo39boo$165bo38b3o$
168boo36bo$168boo34boo$163bo3b3o$164b3o$165bo$164boo11b3o$164b3o10boob
o$166bo13boo$164bo14boo$166bo$164b3o$178bo$177b3o$177bo3boo$176b4o3bo
3boo$177bo5bo3boo$177b4obboo$178bobb3o3$169boo$169boo!

EDIT:

OOPS, I didn't use the smaller p192 side rake! The breeder has been updated.

BCNU,
-dbell

[dbell]

Here is a smaller Cordership backrake then previous ones.

Code: Select all

#C A diagonal c/12 backwards rake with a population of 182 cells.
#C This is based on a previous Cordership rake with an adjustment of
#C its components which creates output gliders using a new mechanism.
#C This is shown at its minimum population.
#C David I. Bell, 10 July 2025
x = 92, y = 88
65bo$60bobbobobbo3bo$60bo4boob5o$60bo3bo4bobo$$62b3o$63bo18boo$82boo7$
90boo$90boo$79boo$78booboo$67boboo7booboo$63b3oboobo9b3o$64bo3bobo$65b
o3bo$$57bo$58boboobobo$52b3o3b4o3bo$58bobbooboo$57bo$55b3o$55b3o4$36bo
$36bo5b3o$35bobo3boobbo$36bo3bo5bo$36bo3bo$41bobboo$42boo4$39bo$38bobo
$38bobo$39bo5$27bo19bo$24b4o18bobo$46bobo$47bo$$27bobo$28bo$oobbo21boo
$3bobo20bobbo$bbo16bo5booboo$19bo$4boo13bo$$5boo12boo$4bo13bobbo$bboob
oo11bobo$5boo10boo$3bo13bo$20boo$20boo$20boo$17boobo$18b3o$19bo4$7boo$
7boo7$15boo$15boo!

The previous smallest backrake which this is based on has a population of 187 cells.

The adjustment I found seems like it should have been known, but I guess not. I found another rake where the adjustment also works, but it is larger. There might be other Corderships where the glider generation reaction could be used.

This is a nice backwards rake in that a sawtooth can be made using it, as shown in another thread.

BCNU,
-dbell

[dbell]

Here is a smaller period 192 sideways rake.

Code: Select all

#C A diagonal c/12 period 192 sideways glider rake.
#C This uses the interaction of a pair of period 96 two-engine
#C Corderships.  This is shown at its minimum population of 240 cells.
#C David I. Bell, 15 July 2025
x = 79, y = 75, rule = B3/S23
49bo$49bo$51bo5bo$50bo6bobo$49bo3bobbo$50bobboboboo$55boboo$69boo$69b
oo6$45bo$31boo7boobbobo30boo$31b3o6b4o3bo29boo$31boobobo7bo$34boo10bob
oo$46bobo$47bo26bo$14boo57boo$$13bo3bo52bobbo$18bo51bobbo$11bo7bo45bo
4b3o$10bo4bo50bo$11bobobo4bo43boboo$11bo8bo43bo3bo$12bo4boobo39boobo$
13boboob3o34boo4boobbobbo$14b3oboo24bo10bo11bo$31boo3boo6bo5bo3bobbo$
31boo3boo12bobbo3boo$49bobo4bob3o$52boobobboo$58boo$58boo$58bo$$39boo
3boo$39boo3boo$bbo18boo$bbo11bo5bobboo30bo$bobo10bo4b3obbo29bobo$bboo
bbo7bo4bo4bo31boo$bo5bo11b5o30bobo$bo5bo12boo32boo$bo4bo46bo$5bo48bo$
bb3o$$51b3o$ooboo$5bo$oo$bb3o9$6boo14bobo$6boo14bobbo$22bobbo$$19b3o$
18bo$18bo$18bo3bo$14boobbo3bo$14boo4bobo!

The previous smallest period 192 sideways rake has a population of 250 cells.

The glider producing reaction is many cells behind the Corderships so that it can be reached by sideways gliders. Even though the smoke from the reaction is rather large, other gliders can join the stream to form convoys.

For example, here is a pseudo-period 96 rake producing a glider stream identical to a real period 96 sideways rake.

Code: Select all

#C A pseudo-period 96 glider rake made from two period 192 rakes.
x = 387, y = 187, rule = B3/S23
277bo$275booboo$275booboo$275boo$277boobo$278bobbo$278bobbo$279boo12b
oo$293boo5$384b3o$263bo122bo$258bobbobobbo3bo30boo82bo$258bo4boob5o30b
oo$258bo3bo4bobo$$260b3o33boo$261bo$298bo$293boobboo$293boo4$238b3o46b
oobboo$239bo47boboboo$239bobbo43bobb4o59b3o$239bobbo34boo7bo4bo62bo$
240bobo33bobboo5bo3bo62bo$255boo8boboo7bo4bo8bo$255boo4b3oboobo8boo3bo
3bobbo$262bo3bobo9bo5boobbo$263bo3bo11bobobo4bo$239bo41bo6bo$238bobo
41boo3bo$239bo$$263boo3boo$237b4o22boo3boo$237boo3bo$238bo4bo35bo$240b
oboo32boo3bo$225bobo13bo14bo19bo4bo38b3o$224bobbo27bo20bobo43bo$225bob
o27boo19b3obobo38bo$255booboo17b3o$254bo3bo21b3o$227bo25b3obbo17bobboo
$226boboo22boo3bo$226boboo25boo18bobo$225bo3bo24b3o19bo$226b4o30boo$
226b3o$253bo$254bo$253boo$250boo$250bo$250boo36b3o$251boo37bo$249bo39b
o$248b3o$230boo15b3o$230boo15bobo$247boboo$244b6o$243bo4bo$243bobbo$
244boo$$238boo$238boo19$224b3o$226bo$225bo17$53bo$51booboo$51booboo$
51boo$53boobo$54bobbo$54bobbo$55boo12boo$69boo5$160b3o$39bo122bo$34bo
bbobobbo3bo30boo82bo$34bo4boob5o30boo$34bo3bo4bobo$$36b3o33boo$37bo$
74bo$69boobboo$69boo4$14b3o46boobboo$15bo47boboboo$15bobbo43bobb4o$15b
obbo34boo7bo4bo$16bobo33bobboo5bo3bo$31boo8boboo7bo4bo8bo$31boo4b3oboo
bo8boo3bo3bobbo$38bo3bobo9bo5boobbo$39bo3bo11bobobo4bo$15bo41bo6bo$14b
obo41boo3bo$15bo$$39boo3boo$13b4o22boo3boo$13boo3bo$14bo4bo35bo$16bob
oo32boo3bo$bobo13bo14bo19bo4bo38b3o$obbo27bo20bobo43bo$bobo27boo19b3ob
obo38bo$31booboo17b3o$30bo3bo21b3o$3bo25b3obbo17bobboo$bboboo22boo3bo$
bboboo25boo18bobo$bo3bo24b3o19bo$bb4o30boo$bb3o$29bo$30bo$29boo$26boo$
26bo$26boo$27boo$25bo$24b3o$6boo15b3o$6boo15bobo$23boboo$20b6o$19bo4bo
$19bobbo$20boo$$14boo$14boo!

BCNU,
-dbell

[dbell]

I think this is now the smallest period 96 Cordership sideways rake.

Code: Select all

#C A diagonal c/12 period 96 sideways rake.
#C This is shown here at its minimum population of 186 cells.
#C This uses a three-engine Cordership and two attached
#C switch engines.  The leftmost attached switch engines is
#C stabilized by destroying a block from the three-engine
#C Cordership, thereby releasing a glider.  The glider reacts
#C with the rightmost attached switch engine to stabilize it
#C and release the output glider.  The two attached engines
#C stabilize their common interface.
#C David I. Bell, 19 July 2025
x = 88, y = 71, rule = B3/S23
70bo$69bobo$$69bobbo$71boo$72bo4$85b3o$69boo$71bo$69boo6$52bobo6bobo$
22boobbo24bo9bobo$25bobo24bobbo6bo$24bo16bo12b3o$41bo$14bo11boo13bo$
12booboo$12booboo10boo12boo23boo$12boo12bo13bobbo21bobo$14boobo6booboo
11bobo6boo16bo$15bobbo8boo10boo8boo$15bobbo6bo13bo$16boo24boo$42boo$
42boo$22boo15boobo$13boo7boo16b3o$13boo26bo$46bo$46bobo$48boo$$42boo$
oobbo10boo24bobbo$3bobo9boo25boo$bbo12boo$16boo$4boo12bo3boo$15boobbo
bboo$5boo11boo$4bo$bbooboo$5boo$3bo15bo$21bo$16bo4bo$16bo4boo$18bobbo
3boo$18b3o4boo$19bo4$7boo$7boo3$18bo$17bo$17b3o$$15boo$15boo!

This rake happens to also be a back edge-shooter so that closely packed convoys of sideways gliders can be built using multiple rakes.

I found other similar rakes using the same mechanism, but they have a larger population.

The previous smallest sideways rake is the population 212 one based on the interaction of a pair of two-engine Corderships from January 2018.

By the way, the idea of using attached switch engines to a Cordership to release a glider which stabilizes it is not new (but I had forgotten about it). This is one of two rakes shown in jslife's "velocity-c12d/rakes-c12d.lif" file:

Code: Select all

#C A diagonal c/12 period 96 sideways rake.
#C This is shown here at its minimum population of 253 cells.
#C This uses a large Cordership with an attached switch engine.
#C The switch engine is stabilized on one side by destroying a block
#C from the Cordership.  This releases a glider which is used to
#C stabilize the other side of the switch engine and create an
#C output glider.
#C David I. Bell, June 2005
x = 115, y = 74, rule = B3/S23
71bo37bo$71bo7bo28b3o$71bo5b3o27booboo$70boo3bobo28boobobo$76bobbo25b
3obb3o$75bobboo26bo6bo$90boo15b5obo$90boo16b4oboo$113bo$112bo4$78bo$
77bobo18boo$77bobbo17boo$78boo$$58bo15boo$56booboo13boo$58bo$$66boo$
59boo4bobbo$58bobbo4boo$57boo3bo38boo$57bo4bo39boo$40bobo14bo3bo39bo$
40bobobo7bo5bobbo$39bobboobo4b3o6bo$40boo3boboboobo$25bo14boo3boob5o
18bo3bo3bo$24bobo17boboo3boo18bo7bo$43bobo25bobobobobo$24bobbo44bo5bo$
26boo$27bo3$b3o$b3o$bbo21boo43boo$3boo21bo43boo$4bo19boo43bo$3bo14boo
18boo$18boo18boo3$boo20b3o$boo19bo3bo$bbo18bo3bo$bbo15bo3bo$bobo15boo
25boo$o16bobo26boo$bobboo11bo$bbo3bo11boo$4boo14bo$4bo13b3o$17boboo$
19boo$16bo$16bo$14boo$14bobo$6boo5b3o$6boo5bo$14boo$14boo5$14boo$14boo
!

The other rake from the file is similar and happens to have the same minimum population.

The glider producing reaction of the population 253 rake is superior to the one in the population 186 rake since convoys can be made which are a bit more packed.

I can't duplicate that old reaction using a pair of attached switch engines with a three-engine Cordership because the separation of the two switch engines can't be adjusted by a half-diagonal. All three attachments of a switch engine to a block are on the same diagonal, and only full diagonal adjustments of two switch engines seem to leave minimal debris, even if their phases are changed. (If someone knows of a clean half-diagonal switch engine adjustment, please let me know.)

There is one arrangement I found which does change the separation of the switch engines by one half-diagonal. Here is one of the only good results I found from that arrangement.

Code: Select all

#C A diagonal c/12 period 192 weakly sparking spaceship.
#C This uses a three-engine Cordership and two attached switch engines.
#C The two switch engines stabilize their common interface using a
#C beehive-pulling reaction.  Their outside edges are stabilized
#C by a block and a glider released by the three-engine Cordership.
#C David I. Bell, 19 July 2025
x = 87, y = 72, rule = B3/S23
74bo$60boo7boobbobo$60b3o6b4o3bo$60boobobo7bo$63boo10boboo$75bobo$76bo
8boo$85boo$$51bo$51bo$51bo$52boo14bo$52b3o12bobo$52boo13bobo$68bo$$63b
oo$62bobbo$51bo11boo$52bo$51bo$38bo$22booboo6boboobboo$22boo8bob5o$22b
oobobo5bo4boo$25bobo11bobo$26boo$13bo25b3o$13bo$12bobo46bo$13boobbo43b
oo$12bo5bo41bobo$12bo5bo$12bo4bo3boo$16bo4boo$13b3o25boo$$39bo$11boob
oo22booboboo$16bo21b3obbo$11boo$$13boboo3boo$15bo4boo$ooboo6boboobboo$
oo8bob5o$oobobo5bo4boo$3bobo11bobo$4boo$17b3o6$24boo$24boo4$18boo$6boo
10bobbo$6boo11b3o$17bo4bo$19bobo$17bobo4$14boo$14boo!

Those beehives prevent the glider from reaching the appropriate location to recreate the superior glider creating reaction used by the population 253 sideways rake.

EDIT:

The sideways rake has the nice property that its output can be suppressed by sideways gliders.

Code: Select all

#C An in-line inverter reaction for a period 96 sideways rake.
#C This shows three input gliders which suppress the rake's output
#C producing three holes in its output glider stream.
x = 229, y = 154, rule = B3/S23
162bo$162bo$162bob3o$164b3o$165bo13b3o$153bo11boo$152bobo11bo$151boob
oo10boo13bo$152bobbo24boo$154b3o6booboo11b3o6boo$154bobo7b3o12bo8boo$
155boo7bo12bo$155boo20bo3boo$181boo$178bo$161boo16bobbo$152boo7boo16b
3o$152boo$185bo$185b3o$187bo$187bo$140bo40boo$140bo13boo24bobbo$140bob
3o9boo25boo$142b3o$143bo11bo$143boo10boo4boo$144bo8bob3o3boo$144boo11b
oo$$141booboo$142b3o$142bo$157b3o67bo$155b6o66boo$155boo3bo65bobo$157b
obbo3boo$157b3o4boo5$146boo$146boo3$158bo$156boo$157boo$195bo$195boo$
194bobo$$137boo11boo$137b3o9bobbo$137boobobo6b3obo$140boo6b6o6$128b3o$
128b3o$129bo$130boo31bo$131bo31boo$130bo31bobo4$128boo$128boo$129bo$
129bo$128bobo$127bo$128bobboo$129bo3bo8bo$131boo7boo$131bo9boo7$135b3o
15$96b3o$98bo$97bo14$64b3o$66bo$65bo30$3o$bbo$bo!

BCNU,
-dbell

[dbell]

In response to a recent question in "Thread for basic questions", here is a glider loop using Corderships using the simplest possible sparks.

Code: Select all

#C A diagonal c/12 convoy which forms a glider loop.
#C This uses four different Corderships which produce a
#C duoplet spark having all four different orientations.
#C The sparks turn a glider by 90 degrees at each corner.
#C The loop size is adjustable and can contain multiple gliders.
#C The example spaceship shown here has period 1344 (96 * 14).
#C David I. Bell, 24 July 2025
x = 251, y = 268, rule = B3/S23
123b3o$123bobo$122bo3bo$122bo3bo$122bo17boo$122bo4boo11boo$122bo6bo$
123bo5bo$110bo12boo$109boo7bo6bo3bo$108bobob3obbobo6bobo10boo$107b3o3b
oo3bo21bo$108boboboobobo21b3o6boo$109booboo9b3o22boo$110bob5obo3bo3bo
13bo$114b4o5bobbo14bo$125boo13boo$141bo$121boo15b3o$112boo7boo14bo3bo$
112boo22b3oboo$136bobob3o$101b3o31b3obb3o$101bobo$100bo3bo$100bo3bo$
100bo$100bo4boo$100bo6bo$101bo5bo$101boo$103bo3bo$104bobo3$101b3o$100b
o3bo$101bobbo11b3o$103boo12boo$115boboo$116bo$115bo5boo$114boo$114boo
3$106boo$106boo8$100bo$97b4o11bo$110boo$111boo$$100bobo$101bo$99boo$
99bobbo$98booboo10$24bo$24bo$24bo$27boo$27boo12boo43b3o$22bo3b3o11boo
46bo$23b3o15bo45bo$24bo15b3o$8b3o12boo15b3o$17bo5b3o16bo180bo$10boo5b
3o5bo14bobbo178boboo$10b4o4bo4bo16b3o5boo176bo$10boob3oboo6bo15bo6boo
170bo3bobbo$15bobo5b3o192bo9bo11b3o$218bo4boobboo$227boo$213b3o4bo5bo$
21boo191bo6bo4b3o$12boo7boo191bobbo4bo4boo12b3o5boo$12boo25boo173bobbo
6b4o12booboo4boo$38bobbo173bobo21boboboo$39bo199bo3bo$bbo36boo199bobbo
$bbo39boo196b3o$bbo38b3o178boo$5boo36bo169boo7boo$5boo34boo170boo$o3b
3o238boo$b3o240bobbo$bbo241bobbo$boo11b3o230bo$b3o10boobo183bo40bo3bo$
3bo13boo181boboo11boo25b3o$bo14boo186bo10boo$3bo194bo3bobbo9boo5bo$b3o
192bo9bo9boo6bo$15bo180bo4boobboo9boo4bobo$14b3o188boo8bobo4boo$14bo3b
oo178bo5bo9b3o$13b4o3bo3boo173bo4b3o7bobbo$14bo5bo3boo174bo4boo8b3o$
14b4obboo180b4o10bo4bo$15bobb3o198bobbo$218bo$218bobbo$6boo210b3o$6boo
217boo$225boo3$223bo$223bo$207boo$207boo$$220bo$218boo$219boo5$199bo$
198b3o$197booboo$196boo3bo$197bobobobo$198boobobbo$201boobo$202boo$$
191b3o$190bobbo$189bo4bo$189bobb3o$189bo5bo$190b7o$196bo$196bo$194boo
4$193bo$192bobo$191boobo$191boo$192b3o9bo$193bo8boo$194bobbo5boo$191bo
6bo$191bo6bo$191bo4b3o57$116bo27bo15boo$115b3o25b3o14boo$104b3o7booboo
23bo14b4obo$103bo11b3o14bo10booboo9boboboo$103bo3bo8bo14b3o10b3oboo11b
3o$101boo3boo8bobo11bo3bo11b4o11b3o$100bobbobobbo7b4o9boobb3o$100bobbo
bobboo9bo10bo3bo$102booboobbo20bobbo$103bo4bo6booboo11bobo6boo$106boob
oo3bo5bo19boo$105b4o6bo3bo$106boo8bo$$131boboo$113boo15b5o$104boo7boo
15b4o$104boo$131b3o$131b3o$132bo$$94bo11bo26boo$93b3o8bobbo24bobbo$92b
ooboo11bo24boo$93b3o12boo$94bo9boo5b3o$94bobo10b4o3bo$94b4o10bo5bo$97b
o12boobo$110bo$93booboo$92bo5bo$93bo3bo13bo$94bo17bo$112bo$$106b3o7boo
$107bobbo5boo$108boboo$110bo3$98boo$98boo!

It's nice to have glider turners for all the corners using the same simple reaction.

Because of this, it should be easy to make loops having complex patterns.

Note: The rightmost spaceship is new, one of a dozen or so sparking spaceships which I intend to post when they are organized.

EDIT:

Here is an ad-hoc complicated glider loop. I just added turning spaceships as I pleased, and only had to adjust the spacing of the final glider path to complete the loop.

Code: Select all

#C A Cordership convoy which supports a complicated glider loop.
x = 2138, y = 2456, rule = B3/S23
846bo$845bobo$844bo3bo13b3o$844bo3bo8bo$844bobob3o4boob3o$845boobobbo
5boboo$849bobo8bo$835b3o11boo11bobbo5boo$835bobbo23b3o6boo$838bo$835b
oo$834bobo$835bobb3o$836boobbo3boo$836bo3bo3boo$837bobo$839bo22bo$837b
oo22boboobo$860bo4bobo$861bo5bo$838bo23booboo$838boo$824bo13boo$823bob
o17bo$822bo3bo11bobob3o$822bo3bo6b5obobobo$822bobob3o4booboo$823boobo
bbo5boboo$827bobo8bo$827boo11bobbo$840b3o5$847boo$847boo5$829boo9bo3b
3o$829boo8bobbo3bo$843boboo$840bo3bo$842b3o4$837boo$837boo252$1353bo7b
o$1352b3o5bobo$1351boob4obbobbo$1352b3obbo$1353bobboobbo$1357boobobo$
1361bo10boo$1372boo$1335boo$1334bo$1334bobbo$1332boob4o$1331bo13boo5bo
bbo$1331bo3b3obbo4boo8bo$1331bobbobbob3o9bo14bo$1333boo4b3o10bo3bo9boo
$1335boobobo12booboo8bobo$1336boobo14bobo$1339bo16boboo7b3o$1355bobbo
3bo5bo$1355bo7boo$1344boo9bobbo$1331bo7bo4boo10boo$1330b3o5bobo$1329b
oob4obbobbo24boo$1330b3obbo30boo$1331bobboobbo$1335boobobo$1339bo9$
1335bo$1334b4o6boo$1333bo4bo4b3oboo$1332boo10boob3obbo$1333boboboo4b3o
boobbobo$1334b3o6boo6bobo$1335bo16bo5$1338boo$1338boo$1331bo$1330bobo$
1329booboo$1330bobbo$1332b3o$1332bobo$1333boo$1333boo8$1331boo$1331bo$
1331boo$1329b3o$1329boob3o$1331b4o$1333boo478$301bo$299booboo$$302boo$
303bo$297bo3bo15boo$301bo3bo11boo3$286boo11bo$289boo4bo4b3o$286boob4o
3bo$283b5o4b4o22bo$286b3o6bo4b3o13bobo6boo$287bo12b3o13bobo6boo$286b3o
11booboo12bo$293bo10bo12b3o$293bo8b3o12bobo$$298boo16boboo$289boo7boo
15bobbo$289boo$279bo32bobbo$277booboo30b7o$312b3obboo$280boo$281bo$
275bo3bo$279bo3bo3$277bo$278b3o3$278b3o$278b3o$278booboo11bo$282bo11b
oo$280b3o11b3o$293b3o$291bobbo$291bo$293bo$292bo3$283boo$283boo18$
1204bo$1204bo$1204bob3o$1206b3o$1207bo13b3o$1195bo11boo$1194bobo11bo$
1193booboo10boo13bo$1194bobbo24boo$1196b3o6booboo11b3o6boo$1196bobo7b
3o12bo8boo$1197boo7bo12bo$1197boo20bo3boo$1223boo$1220bo$1203boo16bobb
o$1194boo7boo16b3o$1194boo$1227bo$1227b3o$1229bo$1229bo$1182bo40boo$
1182bo13boo24bobbo$1182bob3o9boo25boo$1184b3o$1185bo11bo$1185boo10boo
4boo$1186bo8bob3o3boo$1186boo11boo$$1183booboo$1184b3o$1184bo$1199b3o$
1197b6o$1197boo3bo$1199bobbo3boo$1199b3o4boo5$1188boo$1188boo3$1200bo$
1198boo$1199boo3$1185bo$$1181bo7bo$1181bo8bo$1180bo4boo3bo$1181bobo6bo
$1181boboo$$1186bo53$469boo$469bobo$469bo14$485boo1631boo3b4o$485bobo
1625b3obobbo6bo$485bo1631bobbobb5o$2117bobbo$2119bo$2116bobo17boo$
2117bo18boo$$2102bo$2099b4o$$2109boo$2109boo$2102bobo16boo4boo3boo$
2103bo16bobbobbo6bo$2101boo18boobobboobbo$501boo1598bobbo16booboobbobb
o$501bobo1596booboo17bobo$501bo1621bo7bobbo$2130boo$2108boo21b3o$2108b
oo$2096boo3b4o$2091b3obobbo6bo24boo$2095bobbobb5o24boo$2095bobbo$2097b
o$2094bobo$2095bo4$517boo$517bobo$517bo3$2111b3o$2100b3o7bo3bo$2095boo
3b4o7b4o$2094boo3bo4bo9bo$2099booboo11boo$2099b4o12boo$2100bo14bo$909b
o$908b3o$897boo8bobobo$906b3ob3o12bo1176boo$533boo361bo3bo23bobo1175b
oo$533bobo365bo6bob3o13boo$533bo360bo7bo5b5o9bo3bo1164b3o6bo$893bo4bo
9boobboo11bobboo1160bo4bo3bobo$894bobobo4bo6boboo14bo1161bo4boo3bo$
894bo8bo8boo9bobboo1162bo6bo$895bo4boobo4bobobbo11bo7boo1156b3obobbobo
$896boboob3o3bobobbo20boo1160b5o$897b3oboo5bo1191bo4$906boo15boo$897b
oo7boo$897boo24boo$$549boo373bobo1152bo$549bobo373boo1151b3o$549bo337b
o1189bobobo$886b3o36b3o1148b3ob3o15bo$885bobobo10bo24bobbo1167boo$884b
3ob3o9bobo23boo1150bob3o14boo$902b5o1171b5o$886bob3o9bo1177boobboo$
886b5o8bobbo4bo1172boboo$886boobboo8bo5boo1174boo$888boboo9boo1175bobo
bbo$890boo10bobo1172bobobbo$886bobobbo1186bo$885bobobbo$886bo$$565boo$
565bobo331b3o$565bo333bobo7boo$899bobb3o4boo$905bo$902bobo$903bo$$891b
oo$891boo7$581boo$581bobo$581bo14$597boo$597bobo$597bo14$613boo$613bob
o$613bo6$1490bo$1490bo$1490bob3o$1492b3o$1493bo13b3o$1481bo11boo$1480b
obo11bo$1479booboo10boo13bo$629boo849bobbo24boo$629bobo850b3o6booboo
11b3o6boo$629bo852bobo7b3o12bo8boo$1483boo7bo12bo$1483boo20bo3boo$
1509boo$1506bo$1489boo16bobbo$1480boo7boo16b3o$1480boo$1513bo$1513b3o$
1515bo$1515bo$1468bo40boo$1468bo13boo24bobbo$645boo821bob3o9boo25boo$
645bobo822b3o$645bo825bo11bo$1471boo10boo4boo$1472bo8bob3o3boo$1472boo
11boo$$1469booboo$1470b3o$1470bo$1485b3o$1483b6o$1483boo3bo530bo$1485b
obbo3boo524bobo$1485b3o4boo523booboo$2018bobbo$661boo1324bo7bo24b3o$
661bobo1322b3o5bobo23bobo$661bo1323boob4obbobbo23boo$1474boo510b3obbo
29boo$1474boo511bobboobbo$1991boobobo$1995bo10boo$1486bo519boo$1484boo
483boo$1485boo481bo$1968bobbo$1466bo499boob4o$1465boo498bo13boo5bobbo$
1464b5o496bo3b3obbo4boo8bo$1463bo501bobbobbob3o9bo14bo12bo$1462boo5bo
497boo4b3o10bo3bo9boo11boo$677boo782b3oboo502boobobo12booboo8bobo9bobo
$677bobo782boboboobboo498boobo14bobo$677bo785bobbobboo502bo16boboo7b3o
$1465boo522bobbo3bo5bo$1458b3o6boobo518bo7boo$1457bo12bo507boo9bobbo$
1457bo3bo503bo7bo4boo10boo$1455boo3boo502b3o5bobo$1454bobbobobbo500boo
b4obbobbo24boo$1454bobbobobboo500b3obbo30boo$1456booboobbo501bobboobbo
$1457bo4bo506boobobo$1460booboo508bo$1459b4o$1460boo$$693boo$693bobo$
693bo766bo$1461bo$1460bo$1969bo$1968b4o6boo$1470bo496bo4bo4b3oboo$
1465booboo496boo10boob3obbo$1458bo5bobb4o496boboboo4b3oboobbobo$1458bo
5bobbo500b3o6boo6bobo$1458bo4booboo501bo16bo$1464boo4$709boo1261boo$
709bobo1260boo$709bo14$725boo$725bobo$725bo14$741boo$741bobo$741bo14$
757boo$757bobo$757bo14$773boo$773bobo$773bo14$789boo$789bobo$789bo14$
805boo$805bobo$805bo14$821boo$821bobo$821bo14$837boo$837bobo$837bo14$
853boo$853bobo$853bo14$869boo$869bobo$869bo14$885boo$885bobo$885bo14$
901boo$901bobo$901bo14$917boo$917bobo$917bo14$933boo$933bobo$933bo14$
949boo$949bobo$949bo14$965boo$965bobo$965bo14$981boo$981bobo$981bo14$
997boo$997bobo$997bo14$1013boo$1013bobo$1013bo14$1029boo$1029bobo$
1029bo6$25bo27bo$24b3o25bobo15bo$13boo8bobobo23bo3bo15bo$22b3ob3o12bo
9bo3bo10bo$12bo3bo23bobo8bobob3o9bo$17bo6bob3o13boo8boobobbo$10bo7bo5b
5o9bo3bo13bobo12bo$9bo4bo9boobboo11bobboo10boo13bo$10bobobo4bo6boboo
14bo1000boo$10bo8bo8boo9bobboo1001bobo$11bo4boobo4bobobbo11bo7boo994bo
$12boboob3o3bobobbo20boo$13b3oboo5bo4$22boo15boo$13boo7boo$13boo24boo
$$40bobo$41boo$3bo$bb3o36b3o$bobobo10bo24bobbo1016boo$3ob3o9bobo23boo
1017bobo$18b5o1038bo$bbob3o9bo$bb5o8bobbo4bo$bboobboo8bo5boo$4boboo9b
oo$6boo10bobo$bbobobbo$bobobbo$bbo3$15b3o$15bobo7boo$15bobb3o4boo$21bo
1055boo$18bobo1056bobo$19bo1057bo$$7boo$7boo11$1093boo$1093bobo$1093bo
110$1187boo$1160bo25bo$1160bo25bobbo$1160bo23boob4o$1164bo12bo5bo$
1160b3obbo10boo5bo3b3obbo$1159bo4bo11bo6bobbobbob3o$1159bo3bo21boo4b3o
$1160b3o24boobobo$1146bo30b3o8boobo$1146bo7bo20boob3o10bo$1146bo5b3o4b
obo13boobbo$1145boo3bobo6bobo13booboo4boo$1151bobbo4bobo14bobo5boo$
1150bobboo4bobo15bo$1160boo3$1157boo$1148boo7boo$1148boo25bo$1174bobo$
1174bobo$1138bo35bobo$1138bo36b3o$1138bo39b3o$1142bo35boo$1138b3obbo$
1137bo4bo$1137bo3bo$1138b3o10bo$1150boboo$1150bob3o$1137bobo11bo3bo$
1137bobo12b3o$1137bobo13bo$1137bobo11bo$1138boo10bobo$1150boboo$$1156b
o3boo$1152boob3obboo$1150bo6bo$1150boo5bo$1155bo$$1142boo$1142boo64$
1779boo$1778bo$1778bobbo$1776boob4o$1775bo20b3o$1775bo3b3obbo$1770bo4b
obbobbob3o3bobo$1769bobo5boo4b3o4bo$1779boobobo$1769bobbo7boobo14bo6b
oo$1771boo10bo12b4o5boo$1772bo22bo3bo$1795bobbo$1796b3o$$1778boo$1769b
oo7boo$1769boo$$1793bo6b3o$1793bo8bo$1799bobbo$1757boo40bobo$1756bo14b
oo26boo$1756bobbo11boo4bo$1754boob4o16bobo$1753bo26bo$1753bo3b3obbo8b
3o3bobo$1753bobbobbob3o10bo3bo$1755boo4b3o5b3o$1757boobobo9bo$1758boob
o10bobboo$1761bo10bo4bo$1777bo$1773bobbo$1774b3o$$1781boo$1781boo4$
1778b3o$1763boo13boo$1763boo14bobo$1778b3o$1774bobb4o$1775b4o$1776bo3$
1771boo$1770bo$1771boo$1759boobo7boo$1758b3obo6bobo$1757bo4bobo4bo$
1758boo6bobo3bo$1759bo3bobbobboo$1762boboo3bo$1761bobo$1761bobo449$
855bo$854bobo$$854bobbo$856boo$857bo7$857bo$855bobbo$854bo3bo$854bo3bo
$855bobbo$836boo7boo9boo$836b3o6b3o$807bo28boobobo$806b3o14boo14boo$
805bo10bobbo4bo$806booboo6b3obbobbo$807b3oboo5boobbobbo$809b4o9bobbo$
797bo25b3o6boo$796bobo33boo$795booboo45boo$795boo49boo$801boo42bo$795b
3obbo$799boboobboo$797bobbo4boo$800bo$798boo23bo$823bo3bo$798bo23bobob
obo$798bo24boboobo$823bo3bo$799bo$796bob3obbobo$785bo10boobob3obo$784b
3o8boo3booboo$783bo10bobbo4bo$784booboo6b3obbobbo$785b3oboo5boobbobbo$
787b4o9bobbo$801b3o6$808boo$808boo4$802boo$790boo9bo3boo$790boo9bo4bo$
802bo3bo$802boboo$803bo4$798boo$798boo!

More gliders can't be added to this particular loop because of collisions between the gliders on the intersecting paths. Small adjustments could be made to avoid the collisions so as to form a fully populated loop, but I didn't bother to do this since I liked seeing the trail of gliders moving around.

BCNU,
-dbell

[johamwit]

It's nice to have glider turners for all the corners using the same simple reaction.
Because of this, it should be easy to make loops having complex patterns.
Note: The rightmost spaceship is new, one of a dozen or so sparking spaceships which I intend to post when they are organized.

BCNU,
-dbell

Just displaying it.

Code: Select all

x = 251, y = 272, rule = B3/S23
#C [[ AUTOSTART GPS 180 TRACK -0.0833333333 -0.0833333333 ]]
124bo$123b3o$122b2o2bo$121b2o2b2o$122b2o$123b5o$127b2o$125bo2bo$126b2o
12b2o$140b2o3$124b2o$110bo12bo2bo$106b4ob2o10bo2bo$105b2ob3ob2o9bo$
106bob3obo2bo4bo2bo3bo20b2o$107bo3b4obo2bob3o2b2o20b2o$110b2ob3o3bobob
2o2b2o$111b4o8b2o3b2o$112bo10b2o4b2o$122bo5b2o13bo$102bo19bobo16b2ob2o
$101b3o8b2o8b3o17bobo$100b2o2bo7b2o25b2obo$99b2o2b2o35bobo$100b2o32b2o
5bo$101b5o28b2o$105b2o$103bo2bo$104b2o5$102b3o$102bobo$102bo$102bo2bo$
103bobo11bo$104b3o9b3o$106b2o7b5o$100b3o4b2o6b2o$106b2o8b3o$116b3o$
116bo2bo$117b2o4$106b2o$106b2o6$98b3o2$102b2o$104bo$98b4obo$98b5o$108b
o$107bo$98bobo6b3o$98bobo$99bo$98bobo$99b2o$99bo6$23b3o$23b3o$24bo65bo
$25b2o63b2o$26bo62bobo$25bo14b2o$40b2o3$23b2o$12bo10b2o$7bo2bobo2bo3bo
4bo199b3o$7bo4b2ob5o4bo15bo173bo8bo3bo$7bo3bo4bobo4bobo15b2o5b2o163b2o
8bo3bo$22bo16bobo6b2o162bob2o7bo3bo12b3o$9b3o11bo2b2o11bo2bo169bo2b2o
23b3o$10bo13bo3bo10b2obo167b4ob3o6b2ob2o9b2o4bo$26b2o12bobo166bo2bobo
2b2o6bo2bo9b3obobo$26bo13bobo15bo151bobobob3o7bobo10b2o3bo$21b2o17b3o
15b2o151b2ob3obo8b2o10b5o$12b2o7b2o17b3o14bobo151b4o2bobo4bo3bo12bo7b
2o$12b2o200bo3bo4bobobobo19b2o$b3o31bo2bobo81bo91bo3bo5bo$b3o30bo6bo
81b2o89bo2bo$2bo32bo5bo80b2o$3b2o31bo202b2o2bo$4bo217b2o$3bo209b2o7b2o
15bo3bo$213b2o24bo$240bobo2$b2o237b3o$b2o239bo$2bo199b3o37b2o$2bo198bo
3bo10bo24bo2bo$bobo44b2o151bo3bo10b3o23b2o$o46b2o152bo3bo11b2o2bo$bo2b
2o11b2o30bo166bo3b3o$2bo3bo9bo2bo182b2ob2o9b6obo$4b2o13bo183bo2bo9b2o
2bob2o$4bo11bo2bo184bobo11b3o$15b4o186b2o12b2o$15bo186bo3bo$15bo185bob
obobo$202bo$220b2o2$6b2o208bo$6b2o207b3o7b2o$215bo3b2o4b2o$219b2o$64b
2o152b3o$63b2o$65bo$154bo52b2o$155b2o50b2o$154b2o4$216bo$215bo$215b3o$
201bo$198b4o3$80b2o$79b2o120bobo$81bo120bo$200b2o$200bo2bo$199b2ob2o4$
188b3o6bo$189b2o3b2obo$188b2o5bobo$193b3obo$196b2o3$96b2o$95b2o$97bo$
186bo$187b2o$186b2o4$196bo$190b3o2bobo$194b2o5$112b2o$111b2o$113bo14$
128b2o$127b2o$129bo2$176bobo$176b2o$177bo10$144b2o$143b2o$145bo14$160b
2o$159b2o$116bo25b3o16bo$114b2ob2o27bo$117b2o27b2o$114b3o15b2o12bo2bo$
116bo3bo10bo2bo12bobo$115bo3bo27bo$116b3obo25b2o$118b2o25bobo$102bo6b
2o6bobo10b2o15b2o$101bobo3bo3bo6bo11b3o2b2o7b2o$100bo3bobo3b2o5b2o12bo
14bo$101bobo2bobob2o4b3o11b2o5bo2b2o$102bo3bo2b2o5bob2o11bo4bo3b2o$
106bo4bo3b5o11bo$107bo2bo21bobo$109bo23bo2$113b2o$104b2o7b2o15b3o$104b
2o23bo2bo$128bo4bo$128b6o$94bo37bobo$92b2ob2o36b3o$95b2o37b2o$92b3o$
94bo3bo$93bo3bo$94b3obo$96b2o$95bobo8bo4bo$96bo9bo5bo$95b2o$94b3o$94bo
b2o$93b5o9b2o$109bo$107b3o$108bo$113bo$112b2o$106b2o4b2o$106b2o3$98b2o
$98b2o!

[dbell]

Here are Corderships that I have found which use a three-engine Cordership with two adjacent switch engines.

This list does not include ships with larger populations which have identical sparks to the ones either shown here or in my previous sparking spaceships post.

Code: Select all

#C Diagonal c/12 spaceships which display sparks at their edge.
#C These use a three-engine Cordership and two adjacent switch
#C engines which are stabilized on one side by consuming one of
#C the blocks of the three-engine Cordership, stabilized on the
#C other side by gliders released by the three-engine Cordership
#C due to the missing block, and stabilized between the two switch
#C engines due to their clean interaction.  These are sorted in rows
#C by their minimum populations of 176, 183, 186, 187, 188, 192,
#C 197, 199, 202, and 206 cells.  All of these spaceships have a
#C period of 96 except for the last one in the second row and the
#C one in the second to last row which have a period of 192.
#C The spaceships are all shown at their minimum population.
#C David I. Bell, 27 July 2025
x = 356, y = 882, rule = B3/S23
68bo$67b3o$$67b3o$68booboo$70bo13$50bobo$49booboo$50boboo$54bo$38bo14b
o30bo$22booboo6boboobboo12bo30bo$22boo8bob5o44bo$22boobobo5bo4boo$25bo
bo11bobo$26boo$13bo25b3o6boo$13bo34boo$12bobo46bo$13boobbo43boo$12bo5b
o41bobo$12bo5bo$12bo4bo3boo$16bo4boo$13b3o25boo$$39bo$11booboo22boobob
oo$16bo21b3obbo$11boo$$13boboo3boo$15bo4boo$ooboo6boboobboo$oo8bob5o$
oobobo5bo4boo$3bobo11bobo$4boo$17b3o6$24boo$24boo4$18boo$6boo10bobbo$
6boo11b3o$17bo4bo$19bobo$17bobo4$14boo$14boo21$339bo$337booboo$$340boo
$341bo$335bo3bo$339bo3bo$70bo$69bobo$68booboo130bo133bo$69bobbo130bo7b
o126b3o$71b3o129bo5b3o142boo$71bobo128boo3bobo$72boo134bobbo$72boo133b
obboo114bo$$322bo7bo$85b3o234bo8bo$321bo4boo3bo$322bobo6bo$308bo13bob
oo$292booboo6boboobboo$292boo8bob5o18bo$185boobbo102boobobo5bo4boo$23b
3o132b3o27bobo104bobo11bobo$50b3o134bo108boo$27bo21bo3bo108bo120bo25b
3o6boo$23bo3boo12bo8boo106bo3boo12bo12boo92bo34boo$25bobo13boo9booboo
103bobo13boo104bobo46bo$22b3o16bobo10boo12boo87b3o16bobo11boo11boo78b
oobbo43boo$9bo14bo42bobo74bo14bo29bo12bobo77bo5bo41bobo$9bo30boo27bo
74bo30boo10booboo12bo77bo5bo$9bo8bo4boo16boo101bo8bo4boo16boo12boo90bo
4bo3boo$16bobo5boo14bobbo107bobo5boo14bobbo9bo97bo4boo$10b3obbo3bo4bo
15b3o5boo95b3obbo3bo4bo15b3o5boo98b3o25boo$11bob5o6boo22boo96bob5o6boo
22boo$17bo5boo127bo5boo149bo$12boo133boo132booboo22booboboo$286bo21b3o
bbo$281boo$21boo133boo$12boo7boo124boo7boo125boboo3boo$12boo25boo106b
oo25boo109bo4boo$39boo133boo94booboo6boboobboo$39bobbo131bobbo92boo8bo
b5o$40bobo132bobo92boobobo5bo4boo$b3o36bo95b3o36bo97bobo11bobo$42boo
133boo95boo$5bo34bobbo96bo34bobbo108b3o$bo3boo34boo93bo3boo34boo$3bobo
132bobo$3o132b3o$bbo18boo114bo18boo$14boo133boo$boo12bobo118boo12bobo
141boo$bboo12boo119boo12boo141boo$bbo14bo119bo14bo$bboo133boo$boo133b
oo$288boo$14b3o132b3o124boo10bobbo$13bobb3o129bobb3o122boo11b3o$16bob
oo4boo125boboo4boo126bo4bo$13boo4boo3boo122boo4boo3boo128bobo$15b3obbo
129b3obbo131bobo$16bo3bo130bo3bo$17bobo132bobo$$6boo133boo141boo$6boo
133boo141boo19$70bo$69bobo$68booboo$69bobbo$71b3o$71bobo$72boo$72boo
11$50b3o$49bo3bo$22b3o25boo$26bo25booboo$26boo13bo12boo$26bobbo11bo$
14bo12bobo11bo$13bobo11bo$13bobo10boo14bo$13bobbo8bobo13bobo21b3o$14bo
bo10boo11bo8boo16bo$17bo6boo14bobbo5boo15bo$16boo8bo12boobo$16bo21b3o$
39booboo$39bobboo$22boo16b3o$13boo7boo17bo$13boo$$45b3o$48boo$47bo$42b
oo$3o12boo24bobbo$4bo10boo25boo$4boo$4bobbo$5bobo7b3o4boo$5bo7bo4bo3b
oo$4boo7bo5bo$3bobo13bo$5boo$bboo10boo$4bo14bo$19bo$16boobbo$17bobboo$
18b3o4boo$19bo5boo5$7boo$7boo3$18bo$18bobo$18boo$$15boo$15boo26$68bo$
66booboo$68bo15bo$84bo$84bo$69boo$68bobbo$67boo3bo$67bo4bo$67bo3bo$68b
obbo$56bo12bo$56bo5b3o$55bobo3boobbo$56bo3bo5bo$36bo19bo3bo$22boo7boo
bbobo23bobboo$22b3o6b4o3bo23boo$22boobobo7bo$25boo10boboo$37bobo$38bo
8boo$11b3o33boo$$15bo$11bo3boo41b3o$13bobo44bo$10b3o7boo37bo$12bo7boo
$$11boo28b3o$12boo24boboo$12bo24bo3bo$12boo23bo3bo$11boo25b3o$$19boo$
14bo4boo$oo7boobbobo$3o6b4o3bo$oobobo7bo$3boo10boboo$15bobo$16bo6$23bo
$22bobo$25bo$$22bo$14b3o$5boo5bo3b5obo$5boo6boo4boobboo$13bob6o6$13boo
$13boo29$67bo$66bobo5bo$72booboo$66b3obbo3boo$72booboo$72b4o4$85b3o4$
23b3o$23b3o25bobo$24bo26b3o$25boo24boo$26bo$25bo14boo29b3o$40boo12bo
18bo$52bobo17bo$52b3o$23boo30bo$12bo10boo26b5o$7bobbobobbo3bo4bo$7bo4b
oob5o4bo15bo$7bo3bo4bobo4bobo15boo5boo$22bo16bobo6boo$9b3o11bobboo11bo
bbo$10bo13bo3bo10boobo$26boo12bobo$26bo13bobo$21boo17b3o$12boo7boo17b
3o$12boo$b3o31bobbobo$b3o30bo6bo$bbo32bo5bo$3boo31bo$4bo$3bo4$boo$boo$
bbo$bbo$bobo$o$bobboo11boo$bbo3bo9bobbo$4boo13bo$4bo11bobbo$15b4o$15bo
$15bo4$6boo$6boo30$76bo$62boo7boobbobo$62b3o6b4o3bo$62boobobo7bo$65boo
10boboo$77bobo$78bo3$53bo$24bo26booboo$23bobo$23bobo28boo$23bobbo28bo$
24bobo22bo3bo$27bo25bo3bo15boo$26boo44bobo$26bo13boo32bo$40boo9bo$52b
3o$$24bo$11bo11bobo$7b5o8bobobbo$7bo3bobo4bo3bobbo$7b3o3b3o5bo3bo$13b
oobboobboo$13bo7bo4bo$10b3o9boob3o$10boo12b3oboo9b4obo$22bo4bo11boboo$
21boo18boboo$bbo9boo7boo17boo$bobo8boo27boo$bobo$bobbo29boo$bbobo29boo
$5bo$4boo$4bo4$bbo$bobo$3bo$3bo$3bo$$4bo11bobo$oob3o10bobbo$bb3oboo8bo
bo$5bo$17boo$17boo$17boo4$6boo$6boo20$74bo$60boo7boobbobo$60b3o6b4o3bo
$60boobobo7bo$63boo10boboo$75bobo$76bo8boo$85boo$$51bo$49booboo$$52boo
$53bo$47bo3bo$51bo3bo3$49bo$50b3o$$38bo$22booboo6boboobboo$22boo8bob5o
41bo$22boobobo5bo4boo39bobo$25bobo11bobo38bo$26boo$13bo25b3o$13bo$12bo
bo46bo$13boobbo43boo$12bo5bo41bobo$12bo5bo$12bo4bo3boo$16bo4boo$13b3o
25boo$$39bo$11booboo22booboboo$16bo21b3obbo$11boo$$13boboo3boo$15bo4b
oo$ooboo6boboobboo$oo8bob5o$oobobo5bo4boo$3bobo11bobo$4boo$17b3o6$24b
oo$24boo4$18boo$6boo10bobbo$6boo11b3o$17bo4bo$19bobo$17bobo4$14boo$14b
oo21$62b3o$63bo$63bobbo$63bobbo$64bobo$79boo$79boo4$63boo$$80bo$79bo7b
oo$87boo$77bo$80bo$45bo31bo$45b4o6bo23boo$22bo22bo3bo5bo24bo$22bo$22bo
8bo15b3o31boo$29bobo48boo$23b3obbo3bo46boo$24bob5o44bobbo$30bo44b4o$
25boo15boo31bo$42boo5$5b3o7boo10boo$4bo3bo6boo14bo$5boo15boobbo4bo$7b
ooboo10boobbo7bo$9boo15bo7boo$27bo8bo9b3o$28boobboobboo10bo$34b3o10bo$
35bo$o13boo10boo$o13boo10boo$o8bo$7bobo26boo$b3obbo3bo25boo$bbob5o$8bo
$3boo9$11bo$10b4o$8b5obo$bb3obbo6boo6bo$6bo3bob3o6bobo$7bobobboo7bobo$
22bo$18bo$18bo$18bobo$19bo$8boo9bo$8boo19$74bo$60boo7boobbobo$60b3o6b
4o3bo$60boobobo7bo$63boo10boboo$75bobo$76bo8boo$85boo$$51bo$51bo$51bo$
52boo14bo$52b3o12bobo$52boo13bobo$68bo$$63boo$62bobbo$51bo11boo$52bo$
51bo$38bo$22booboo6boboobboo$22boo8bob5o$22boobobo5bo4boo$25bobo11bobo
$26boo$13bo25b3o$13bo$12bobo46bo$13boobbo43boo$12bo5bo41bobo$12bo5bo$
12bo4bo3boo$16bo4boo$13b3o25boo$$39bo$11booboo22booboboo$16bo21b3obbo$
11boo$$13boboo3boo$15bo4boo$ooboo6boboobboo$oo8bob5o$oobobo5bo4boo$3bo
bo11bobo$4boo$17b3o6$24boo$24boo4$18boo$6boo10bobbo$6boo11b3o$17bo4bo$
19bobo$17bobo4$14boo$14boo18$60bo$58booboo$58booboo$58boo$60boobo$61bo
bbo$61bobbo$62boo12boo$76boo7$84boo$84boo$$41b3o$41b3o35boo$40bo3bo$
41boob3o34bo$41boo4bo28boobboo$44bobbo28boo$23b3o19boo27boo$23b3o$24bo
$25boo$26bo$25bo14boo28boo$40boo28b5o$69bo$71b3o$23boo46bo$12bo10boo$
7bobbobobbo3bo4bo$7bo4boob5o4bo15bo$7bo3bo4bobo4bobo15boo$22bo16bobo$
9b3o11bobboo11bobbo$10bo13bo3bo10boobo$26boo12bobo$26bo13bobo$21boo17b
3o$12boo7boo17b3o$12boo$b3o31bobbobo$b3o30bo6bo$bbo32bo5bo$3boo31bo$4b
o$3bo4$boo$boo$bbo$bbo$bobo$o$bobboo11boo$bbo3bo9bobbo$4boo13bo$4bo11b
obbo$15b4o$15bo$15bo4$6boo$6boo!

The period 192 spaceship was discussed in a previous post.

The population 192 spaceship in the sixth row was shown in my previous post about glider loops using duoplet sparks.

EDIT:

I forgot to include another period 192 spaceship. I have added it to the pattern above (as the third ship in the second row).

BCNU,
-dbell

[dbell]

I accidentally discovered that the population 164 sparking Cordership can be used for period multiplying. The basic reaction is shown here.

Code: Select all

#C A diagonal c/12 period 96 sparking spaceship/puffer.
#C Glider impacts into the smoke can convert the spaceship into a
#C boat-and-block puffer and back again.  Some types of impacts
#C can also create a bit of debris as the conversion is done
#C such as blocks, beehives, blinkers, ponds, or gliders.
#C This example shows an impact with no additional debris.
#C The ship at the left is converted into a puffer by a glider and
#C the puffer on the right is converted into a ship by a glider.
#C David I. Bell, 9 August 2025
x = 269, y = 85, rule = B3/S23
99bo159bo$98bo159bo$98b3o157b3o29$64bobo157bobo$50bobo7bobbobbo143bobo
7bobbobbo$49booboo5boboboobo142booboo5boboboobo$50boboo6bo149boboo6bo$
36boo16bo11b3o127boo16bo11b3o$22bo9bo3b3o14bo13boo113bo9bo3b3o14bo13b
oo$22b4o5bobobbo16bo12boo114b4o5bobobbo16bo12boo$22bo3bo5bo3bobbo142bo
3bo5bo3bobbo$40bo159bo$24b3o10bobo144b3o10bobo35boo$12bo25boo7boo123bo
25boo7boo26boo$12bo34boo123bo34boo$12bo159bo$16bo42boo115bo42boo$12b3o
bbo42boo110b3obbo42boo17bo$11bo4bo42bo111bo4bo42bo18bobo$11bo3bo4boo
149bo3bo4boo56boo$12b3o5boo150b3o5boo61boo$41bo159bo41boo$39boo158boo$
11bobo28bo128bobo28bo$11bobo23bobobbo128bobo23bobobbo$11bobo23bobb3o
128bobo23bobb3o44bo$11bobo24b4o129bobo24b4o44bobo$12boo25bo132boo25bo
46boo$19boo18bo139boo18bo51boo$14boo3boo153boo3boo70boo$o9bo3b3o143bo
9bo3b3o$4o5bobobbo145b4o5bobobbo$o3bo5bo3bobbo142bo3bo5bo3bobbo$18bo
159bo76bo$bb3o10bobo144b3o10bobo76bobo$16boo158boo76boo$259boo$259boo
4$23boo158boo78bo$23boo158boo77bobo$262boo$267boo$15boo158boo90boo$18b
ooboo155booboo$5boo5bo4boo146boo5bo4boo$5boo12boobo142boo12boobo$12bo
bbo4boo150bobbo4boo$14bobobo155bobobo$18bo159bo4$13boo158boo$13boo158b
oo!

The most useful impact produces an output glider (and an unwanted block).

Code: Select all

#C One unit of a diagonal c/12 period doubling convoy.
#C This shows a period 192 sideways rake whose output is thinned to
#C become a period 384 sideways rake.  The actual period doubling is
#C performed by a population 164 sparking spaceship.  The fuse output
#C is deleted by a second population 164 sparking spaceship.
#C David I, Bell, 9 August 2025
x = 240, y = 120, rule = B3/S23
142boobbo$145bobo$144bo16bo$161bo$134bo11boo13bo$132booboo$132booboo
10boo12boo$132boo12bo13bobbo$134boobo6booboo11bobo6boo$135bobbo8boo10b
oo8boo$135bobbo6bo13bo$136boo24boo$162boo$162boo$142boo15boobo$133boo
7boo16b3o$133boo26bo75b3o$166bo72bo$166bobo69bo$168boo$$162boo$120boo
bbo10boo24bobbo$123bobo9boo25boo$122bo12boo$136boo$124boo12bo3boo$135b
oobbobboo$125boo11boo$124bo$122booboo$125boo$123bo15bo$141bo$136bo4bo$
136bo4boo$138bobbo3boo$138b3o4boo$139bo4$127boo$127boo$198boo$199bobbo
4bo$138bo57bobb3obobbobo$137bo58bobbo4b4o$137b3o56bobbo$199bo6bo$47bo
72bo77boobo$46boboo67b4o85bo11boo$50bo153boo12boo$44bo3bobbo129boo$42b
o9bo11b3o114b3o$42bo4boobboo67bobo58boobo$51boo68bo63bo$44bo5bo68boo
56bo3boo3bo4boo$45bo4b3o66bobbo64bo3boo19bo$46bo4boo12b3o5boo43booboo
61bobo15bo8boo$48b4o12booboo4boo109bo17boo6bobbo$35b3o25boboboo110bo4b
obo11bobbooboo5boo$35bobbo24bo3bo131b3ob3o7boo$38bo25bobbo115b4o13bo3b
oo6booboo$35boo15boo10b3o116boo14b3o11bobo$34bobo15boo145b3o12bo$35bo
bb3o135boo12boo9b3o$36boobbo136bobbo4bo4boo10boo$36bo3bo133bobb3obobbo
bo$37bobo10bobo121bobbo4b4o26boo$39bo12bo121bobbo34boo$36bobbo16bo120b
o6bo$36bo13b3o123boobo$51boo131bo$35boobbo11boo129boo$36b3o13boo$10bo
42bo$9b3o$8b3obo14bo23bo$7boo3boo6bobbo3bo22bobo$6boobobboo6bo3bobbo
22bo$7booboboo5bo29bo3boo$8b3oboo6boboo26bobboo60bo$10bo4bo34bo64boo
76bo$11b4o20boo3boo72bobo76bo$13bo12boboo5boo3boo7boobboo122bobbo12bob
oboo$26b3o20b6o123b3ob3o9boobobo$27bo24bo125boobobo12boobo$180b3o15bo$
34b3o111boo31boo$39b3o105bobo$5bo27bobbo3boo106bo$obbobobbo3bo21b5obo
bboo3boo$o4boob5o21boobo3boobo3boo134boo$o3bo4bobo23boo4b3o106boo20boo
10boo$35boboboboo107boo23boo4bo$bb3o10boo13boo140boob4o3bo$3bo11boo12b
o29bo4boo3bo99b5o4b4o$29b3o26bobobb3o3boo87boo12b3o6bo$29boo27boo4boo
4bo87boo13bo$29bo40boo100b3o$66boobboo107bo$58bo8bobo109bo$57bobo7b3o$
57bobo$58bo$181b3o$19boo160b3o$18booboo156bo4bo$7boboo7booboo156bo5bo$
3b3oboobo9b3o159bobo$4bo3bobo168b3obo$5bo3bo165bo3boo5bo$175bo3bobo4b
oo$175bo3bobo3bobo$180bobbo$182boo$10boo170bobbo$10boo171b3o$184bo!

It is really lucky that the sparks from the second sparking spaceship can delete all three of the products in the fuse. (A pair of two-engine Corderships can also do the deletion, but the result is a bulkier convoy.)

Here are multiple period doubling convoys joined together.

Code: Select all

#C A diagonal c/12 period 3072 (96 * 32) sideways rake.
#C This uses an input period 192 rake whose output is thinned by
#C passing through four copies of a period doubling convoy.
#C David I. Bell, 9 August 2025
x = 462, y = 251, rule = B3/S23
369bo$368b3o15bo$367booboo14bo$366boo3bo7b4o3bo$367bobobobo5bo3bo$368b
oobobbo4boo3bo$359bo11boobo7b3o$358b3o11boo10boobo6boo$358bobbo23b3o6b
oo$358b3o25bo$358b3o$357boboobo$358bobb3o$358b4oboobboo$359bob3o3boo$
361b3o$360bobo22boo$361bo22b6o$383b3oboobo68b3o$384booboobo70bo$361boo
22bo3bo70bo$360bo$347bo13boo$346b3o12bo3b3o$345booboo7b8obbo$344boo3bo
6bo5b3oboo$345bobobobo4bo$346boobobbo4boobbo$349boobo7b3o$350boo10boob
o$363b3o$364bo4$370boo$370boo$$298b3o$297bobbo$296bo4bo66bo$296bobb3o
50boo14boo$296bo5bo49boo12bo3bo$297b7o62b4o53bo$303bo61bo57bo$303bo62b
oo55bo8bo$301boo12boo49bo63bobo$315boo107b3obbo3bo$425bob5o$431bo$299b
oo41b3o81boo15boo$282b5o11bobbo39bo3bo97boo$280boo5boo8b3o40bo4bo$280b
o7bo8b3o40bobbobo$280boo8bo4boobooboo20boo15boobobo$282boo7bobbobo4bo
21boo17boobobbo$285bo10bo3boobbo39boobbo57b3o7boo10boo$285bo4bo9bobobb
o39b3o57bo3bo6boo14bo$286boo9bobo5bo100boo15boobbo4bo18boo$297bobo3b3o
11b3o88booboo10boobbo7bo15boo$276b3o17boobo16booboo89boo15bo7boo$275bo
bbo8boo8bobo15boboboo107bo8bo9b3o$274bo4bo7boo9bo15boobo111boobboobboo
10bo$274bobb3o34boobo117b3o10bo$274bo5bo28boo5bo119bo$275b7o27boo90bo
13boo10boo$281bo119bo13boo10boo$281bo119bo8bo$279boo127bobo26boo$351b
oo49b3obbo3bo25boo$351boo50bob5o$409bo$278bo78boo45boo$277bobo76bobo$
276boobo77bo$276boo$277b3o$278bo12b3o65boo$279bobbo7bo3bo64boo$276bo6b
o10bo$276bo6bo10bo70boo$276bo4b3o9bo70bobo45bo$290bo3bo70bo45b4o$291bo
bbo114b5obo$292boo109b3obbo6boo6bo$219bo147boo38bo3bob3o6bobo$218b3o
146boo39bobobboo7bobo$217b3obo14bo36bo149bo$216boo3boo6bobbo3bo35b3o6b
oo63bo26boo44bo$215boobobboo6bo3bobbo34booboo5boo63bo25bobo44bo$216boo
boboo5bo41boobobo70bob3o22bo45bobo$209bo7b3oboo6boboo36b3obb3o71b3o69b
o$208bobo8bo4bo45bo6bo71bo13b3o43boo9bo$207booboo8b4o20boo25b5obo59bo
11boo24boo32boo$207booboo10bo12boboo5boo26b4oboo57bobo11bo24boo19b3o$
206b3o26b3o39bo57booboo10boo13bo39bo$206b3o3bo23bo39bo59bobbo24boo32b
oo5b3o$206b3o4bo124b3o6booboo11b3o6boo9boo13b4o4bo$207boo5bo123bobo7b
3o12bo8boo9boo13boob3oboo$207b3o7boo120boo7bo12bo41bobo$208boo7boo55bo
64boo20bo3boo$209bo62boobo89boo$282bobo77bo$233boo4bo35bo6boo61boo16bo
bbo$232b3o4boo31bobbo7bo52boo7boo16b3o$233bob4obo32bo62boo$234b6o129bo
$197bo12bobo22bo42boo89b3o$196b3o11boo4boo53b3o5boo90bo35bo$195b3obo7b
o7b3o60boo91bo34bobo$194boo3boo17bo59bo45bo40boo38boobbo$193boobobboo
5bo3boob5o106bo13boo24bobbo32bo7boo$194booboboo5bobo3b5o107bob3o9boo
25boo33bo7b3o$195b3oboo9bo115b3o71bo7bobbo$197bo4bo7bobo114bo11bo69boo
$198b4o12bo112boo10boo4boo$200bo12boboo63boo46bo8bob3o3boo$213b3o64boo
46boo11boo$214bo$286boo37booboo$285bobo38b3o$220boo64bo39bo$220boo119b
3o$148b3o188b6o$147bo3bo136boo49boo3bo$146bo4bo136boo51bobbo3boo$145bo
3bo67bobo121b3o4boo$145bobbob3o49boo13bobbo73boo$145bo7bo48boo11bo4bo
72bobo$147bo3bobo61bob3o53bo20bo$147bo3boboo59bo58bo$149b3oboo60bobo
57bo5bo48boo$165boo48bobo56bo6bobo12boo32boo$165boo106bo3bobbo15boo$
274bobboboboo$134bo57b3o84boboo19boo38bo$191bo101boo6bobo36boo$130bo7b
o10boo39bo4boo96boo7bo38boo$130bo8bo49bo3bo$129bo4boo3bo10boo37bobbo4b
o121boobbo$130bobo5bo6boo3bo22boo14bo3bo3bo106boo16bobo$130boboo12bobb
obbo20boo15boobob3o58b3o45boo15bo$150boo41bo62b3o7boo$135bo17b4o37b4o
57bo3bo6boo42boo11boo$151bobobbo10b3o26boo58boob3o11b3obbo22boo6bobo$
126b3o17boo3bobobbo10b3o86boo4bo10b4obo6boo14boo7bo13boo$125bo3bo24boo
9bobo91bobbo13bo21boo23bo$124bo4bo7boo7bobboo15bobo91boo15bobo7boo8bob
o21booboo$123bo3bo9boo8boo15boobo110boo3bo4boo9bo12boo10boo$123bobbob
3o34bobo120bo23boo8bo$123bo7bo27boo4boo117b4o$125bo3bobo27boo53boo35bo
13boo10boo7bo31boo$125bo3boboo80bobo35bo13boo10boo38bobo$127b3oboo82bo
37bo5bo58bo$252bo6bobo25boo$201boo48bo3bobbo28boo$201boo49bobboboboo
59boo$257boboo59boo$127boo$127boo80boo$128bo80boo$$128bo12b3o$$141bo3b
o$126bo5b3o10bo$126bo7bo7bo$126bo5bobo7bobbo$132boo11bo114boo3bo$141bo
bbo113b3o4boo$141b3o109b3obo8boo5bo$257bobobb5o5bobo$123bo134bo3b3o7bo
bo$122b3o148bo$121b3obo5boo$120bo3bo6boo66bo68boo$53bo65boobbobbo69b4o
$51booboo62b3obb4o142boo$51booboo64bo3bobbo85b3o43boo9bo$51boo67bo6bo
58b3o70boo$53boobo65bobbo59bo3bo9bobo12boo32bo$54bobbo66booboo55bo3boo
10bo13boo32bo7bo$54bobbo66bo60bo12boo13bobbo31bo5b3o$55boo12boo115b4o
8bobbo11bo8boo23boo3bobo$69boo117boboo5booboo10b3o7boo29bobbo$188bobbo
20boo38bobboo$123boo64boo24boo$125bo88bobbo$123boo8bo$131boo62boo15boo
$39bo92boo52boo7boo15bobbo$34bobbobobbo3bo30boo107boo25b3o$34bo4boob5o
30boo50bo90bo$34bo3bo4bobo83boo90boo$121b3o4boboo88b3o35bo$36b3o33boo
54bobo126bo$37bo90boo85boo40b3o$74bo102bo10boo24bobbo$69boobboo99b4o9b
obbo24boo$69boo$188b3o$188bobbo3boo$177bobo10bobobboo$14b3o46boobboo
109bo12boo56boo$15bo47boboboo107boo71boo$15bobbo43bobb4o107bobbo$15bo
bbo34boo7bo4bo107booboo$16bobo33bobboo5bo3bo$31boo8boboo7bo4bo8bo126bo
$31boo4b3oboobo8boo3bo3bobbo127boo$38bo3bobo9bo5boobbo125bobb3o$39bo3b
o11bobobo4bo125boobboobboo$15bo41bo6bo126bobo4boo$14bobo41boo3bo80boo
45b3o$15bo127bobo$144bo$39boo3boo$13b4o22boo3boo134boo$13boo3bo127boo
32boo$14bo4bo35bo90boo$16boboo32boo3bo$bobo13bo14bo19bo4bo38b3o$obbo
27bo20bobo43bo55boo34bobo$bobo27boo19b3obobo38bo56boo34boo$31booboo17b
3o135bo$30bo3bo21b3o112bobo$3bo25b3obbo17bobboo114b3o$bboboo22boo3bo
137boo$bboboo25boo18bobo$bo3bo24b3o19bo$bb4o30boo136bo$bb3o167bobo$29b
o142b3o$30bo144bo$29boo140b5o$26boo$26bo$26boo$27boo$25bo$24b3o$6boo
15b3o$6boo15bobo$23boboo$20b6o$19bo4bo$19bobbo$20boo$$14boo$14boo!

The period doubling convoy still works with a period 96 input stream, but that is pointless since the result is larger than a simple period 192 rake.

Unlike my previous period doubling convoy, this one is in-line so that the output gliders travel in the same direction as the input gliders. In addition, the convoys do not need to be spaced further apart as more doubling stages are added.

BCNU,
-dbell

[dbell]

When building backward glider convoys using Corderships, the sideways to backward glider turning reactions using sparking spaceships have been useful. However, a big flaw in those reactions is that gliders have to cross through the backward glider stream.

Because of this I could not construct a packed convoy such as this one.

Code: Select all

#C A difficult convoy to construct using Corderships.
#C The easy method to create such a convoy of backward gliders
#C won't work since each rear glider is in the way of a sideways
#C glider which would otherwise create the other rear glider.
x = 11, y = 10, rule = B3/S23
8bo$9boo$8boo4$o$boo5bo$oo7bo$7b3o!

Obviously what is wanted on these cases is a true edge-shooting backward rake. But that has been difficult to make.

To find a solution I have been investigating reactions which create objects on the edge of Cordership convoys, and have found many useful results which I intend to post. (A few of these are used in the edge rakes shown below.)

Here is a near solution based on a pair of blinkers which is useful in some cases, but not good enough to build the difficult convoy shown above.

Code: Select all

#C A diagonal c/12 period 96 backwards almost edge-shooting rake.
#C This uses a blinker puffer, a loaf puffer, a sparking spaceship
#C to convert loafs into blinkers, and a sideways glider rake.
#C (The loaf conversion is needed since two blinker puffers would
#C interfere with each other.)  The output gliders are on a lane
#C which is only 1.5 diagonals away from being on the edge.
#C David I. Bell, 9 August 2025
x = 205, y = 156, rule = B3/S23
50b3o$$54bo$50bo3boo$52bobo12bo$23b3o23b3o15bo$51bo15bo$27bo$23bo3boo
12bo8boo$25bobo13boo8boo$22b3o16bobo7bo$9bo14bo26boo$9bo30boo8boo23bo$
9bo8bo4boo16boo32bo$16bobo5boo14bobbo31bo$10b3obbo3bo4bo15b3o5boo$11bo
b5o6boo22boo$17bo5boo$12boo$$83bo$21boo60bo$12boo7boo60bo$12boo25boo$
39boo$39bobbo$40bobo$b3o36bo$42boo47bo$5bo34bobbo47bo$bo3boo34boo48bo$
3bobo$3o$bbo18boo53bo$14boo59b3o$boo12bobo56bobobo$bboo12boo55b3ob3o
12bo6bo$bbo14bo73bobo5bo$bboo71bob3o10bo3bo4bo$boo45bo26b5o10b4o$46boo
boo24boobboo8boo3boo$14b3o20bo10bo28boboo13boo$13bobb3o17b3o24boo14boo
12bobbo$16boboo4boo9booboo22bobbo9bobobbo14bo$13boo4boo3boo8boobobo9b
oo11booboo7bobobbo11boo7bo6bo$15b3obbo12b3obb3o7bobbo11bo11bo12boo9bob
o5bo$16bo3bo13bo6bo5boo3bo10b3o21bobobobo5bobbo4bo$17bobo15b5obo5bo4bo
19boo13bobobbo7boo$36b4oboo4bo3bo20boo13b3obo$6boo33bo6bobbo36bobbo$6b
oo32bo8bo39boo$$65bo42bo6bo$45boo14bo3bo41bobo5bo$36boo7boo15bobbo41bo
bbo4bo$36boo24booboo41boo$63bobo$64bo$71boo$$65boo49bo6bo$26bo11boo24b
obbo47bobo5bo$24booboo8bobbo24boo48bobbo4bo$26bo9boobbo61boo12boo$37b
ooboo63boo4bo$37boo3bobboo26bo28boob4o3bo10b3o$27boo11bobobboo52b5o4b
4o$26bobbo11boo26bo7bo24b3o6bo$25boo3bo38bo8bobb3o19bo27bo$25bo4bo37bo
4boo3bobb3o18b3o26bo$25bo3bo39bobo6bobboobbo23bo21bo$26bobbo39boboo10b
obo23bo$27bo15boo38b3o$41boobo13bo15bo18boo36b3o$43bo14bo34boo19boo$
39boo7boo8bo55boo$40boo6boo5bob3obo77bo$41b3o11bob5o42boo33bo$59bobo
43boo32bo$56boo8boo36bo$56boo8boo$30boo25bo29boo50b3o$30boo25boo31bo$
58bo3boo22bobbo29bo$58bo24b5o29booboo25bo$56boboo24b3o32bo27bo$57bo27b
o48boo11bo$51bo81bobbo$65boo53boo11booboo$47bo7bo9boo52bobbo11bo12b3o$
47bo8bobb3o44bo11boo3bo10b3o$46bo4boo3bobb3o43b3o10bo4bo19boo$47bobo6b
obboobbo54bo3bo20boo10bo$47boboo10bobo41b3o11bobbo32bo$61b3o42booboo9b
o34bo$52bo55bo$122boo12bo$122boo8bo3bo18b3o$133bobbo$133booboo$106bo
27bobo26bo$105bobo27bo27bo$68b3o35bo56bo$69boo$69boo34boo$66boboo34bob
o56b3o$59boo4bo3bo53bo$51boo8b3o5boo33b3obobo11bo$51boo5b3obobboobboo
37b3o13boo$62boobo42boo14boo$125bo$122bobbo45bo$122bobo47bo$120boo48b
3o$89b3o27bo$59boo26b7o6bo20bo$59boo25b9o4bo10boo5b4o$85bo7b3obboo10b
oo4bobbo$86b3o6bo3bobbo13bobbo$87boo11b3o14b3o$90bo10bo$91bo18boo$92bo
17boo$$118boo$118boo19bo$139boo$77bo60bobo$77bo$77bo8bo23b3o5boo$84bob
o20boobobo5boo$78b3obbo3bo19bobbobo$79bob5o10boboo5b3o$85bo4boo4bobo3b
ooboo$80boo8boo6boob3obbo9$88bo114bo$87b4o113bo$85b5obo110b3o$79b3obbo
6boo$83bo3bob3o$84bobobboo6$85boo$85boo!

Here is a larger solution that is closer to a true edge shooting rake.

Code: Select all

#C A diagonal c/12 period 96 backwards edge-shooting rake.
#C This uses two blinker puffers, several object conversions using
#C sparking spaceships, two sideways rakes, and a block puffer to
#C create two loafs and a block which turn a sideways glider into a
#C backward glider.  The backward gliders are on a lane which extends
#C one full diagonal past the edge of the Cordership convoy.
#C David I. Bell, 9 August 2025
x = 353, y = 284, rule = B3/S23
51bo$50b3o14boo$49bo10bobbo4bo$50booboo6b3obbobbo$51b3oboo5boobbobbo$
24bo28b4o9bobbo$23b3o14boo25b3o$22bo10bobbo4bo$23booboo6b3obbobbo$24b
3oboo5boobbobbo32b3o$26b4o9bobbo$14bo25b3o6boo$13bobo33boo$12booboo45b
oo$12boo49boo$18boo42bo$12b3obbo$16boboobboo59b3o$14bobbo4boo$17bo$15b
oo23bo$40bo3bo$15bo23bobobobo$15bo24boboobo$40bo3bo46boo$16bo74boo$13b
ob3obbobo$bbo10boobob3obo$b3o8boo3booboo$o10bobbo4bo$booboo6b3obbobbo
72bobo$bb3oboo5boobbobbo30bo27bobo10bobboo$4b4o9bobbo28booboo24booboo
9boo4bo$18b3o19bo10bo27boboo9boo$39b3o24boo15bo15bo$38booboo22bobbo13b
o5bobo7bo3boo$37boobobo9boo11booboo12bo5bobo10bobbo$36b3obb3o7bobbo11b
o23bo10bobo$37bo6bo5boo3bo10b3o33bo$25boo11b5obo5bo4bo19boo$25boo12b4o
boo4bo3bo20boo$44bo6bobbo$43bo8bo$110boo$19boo47bo40bobbo$7boo9bo3boo
24boo14bo3bo40bobo$7boo9bo4bo15boo7boo15bobbo41bo$19bo3bo15boo24booboo
$19boboo43bobo$20bo46bo$74boo$102b3o13boo$68boo32bobo12bobbo$15boo12bo
11boo24bobbo30bo3bo11bobo$15boo10booboo8bobbo24boo31bo3bo12bo$29bo9boo
bbo57bo$40booboo30b3o23bo4boo$40boo3bobboo25bobo23bo6bo$30boo11bobobb
oo24bo3bo23bo5bo9b3o$29bobbo11boo28bo3bo23boo22boo$28boo3bo40bo17boo
10bo3bo16bobbo$28bo4bo40bo4boo11boo11bobo17bobo$28bo3bo41bo6bo44bo$29b
obbo42bo5bo$30bo15boo14bo12boo$44boobo13boo7bo6bo3bo$46bo13bobob3obbob
o6bobo10boo33b3o$42boo7boo6b3o3boo3bo21bo41boo$43boo6boo7boboboobobo
21b3o39bobbo$44b3o14booboo9b3o55bobo$62bob5obo3bo3bo13bo41bo$66b4o5bo
bbo14bo$77boo13boo$33boo58bo$33boo38boo15b3o41b3o$64boo7boo14bo3bo48b
oo$64boo22b3oboo47bobbo$88bobob3o46bobo$53b3o31b3obb3o47bo$53bobo66boo
$52bo3bo65b3o$52bo3bo65boobo17bo$52bo73bo15bobo$52bo4boo59bo3boo3bo14b
obo5boo$52bo6bo35boo31bo14bo5bobbo$53bo5bo34bo30bobo21bobo$53boo39bobb
o27bo24bo$55bo3bo32boob4o21bo4bobo13bo$56bobo32bo20b3o24booboo$91bo3b
3obbo23b4o23bo$86bo4bobbobbob3o3bobo16boo12bobo9bobo$53b3o29bobo5boo4b
3o4bo31bo3bo7bobo5boo$52bo3bo38boobobo36bobobbo8bo5bobbo$53bobbo11b3o
14bobbo7boobo14bo6boo13boob3o15bobo$55boo12boo16boo10bo12b4o5boo14bobb
o17bo$67boboo17bo22bo3bo20bo$68bo42bobbo$67bo5boo37b3o44bo$66boo90bobo
$66boo26boo62bobo5boo$85boo7boo63bo5bobbo$85boo78bobo$58boo106bo$58boo
49bo6b3o$109bo8bo$115bobbo48bo$73boo40bobo48bobo$72bo14boo26boo40bo8bo
bo5boo$72bobbo11boo4bo49boo7boobbobo8bo5bobbo$70boob4o16bobo47b3o6b4o
3bo13bobo$69bo26bo46boobobo7bo17bo$69bo3b3obbo8b3o3bobo50boo10boboo$
69bobbobbob3o10bo3bo63bobo$71boo4b3o5b3o71bo8boo6bo$73boobobo9bo79boo
5bobo$74boobo10bobboo82bobbo3boo$77bo10bo4bo40bo41boo3bobbo$93bo38boob
oo44bobo$89bobbo89bo$90b3o42boo$136bo$97boo31bo3bo49bo$97boo35bo3bo44b
obo$183bobbo3boo$184boo3bobbo$132bo56bobo$94b3o36b3o54bo$79boo13boo$
79boo14bobo23bo$94b3o8booboo6boboobboo68bo$90bobb4o8boo8bob5o41bo27bob
o$91b4o10boobobo5bo4boo39bobo26bobbo3boo$92bo15bobo11bobo38bo28boo3bo
bbo$109boo86bobo$96bo25b3o46bo26bo$87boo7bo73bobo$87boo6bobo46bo25bobb
oo$96boobbo43boo22b7o14bo10bo$95bo5bo41bobo21bobbo3bo14bo9bobo$95bo5bo
64b3obb7o11bo9bobbo3boo$95bo4bo3boo62b3obbo8bo17boo3bobbo$99bo4boo63b
ooboo8bo22bobo$96b3o25boo44b3obobbo28bo$171b3oboo13boo5boo$122bo51bo
13boobo5boo$94booboo22booboboo32bo26bo3bo16bo$99bo21b3obbo31booboo24bo
bboo15bobo$94boo65boo25b3o16bobbo3boo$158b3o15boo11bo18boo3bobbo$96bob
oo3boo55bo3bo10bobbo34bobo$98bo4boo54bo3bo50bo$83booboo6boboobboo58b3o
bo$83boo8bob5o62boo$83boobobo5bo4boo60bobo10boo40bo$86bobo11bobo59bo
11b3obboo34bobo$87boo72boo12bo39bobbo3boo$100b3o57b3o11boo5bo34boo3bo
bbo$160boboo11bo4bo40bobo$159b5o11bo46bo$176bobo$177bo$224boo$107boo
114bobbo$107boo65b3o47bobo3boo$174b3o48bo3bobbo$177boo50bobo$173b3obbo
51bo$101boo$89boo10bobbo37bo3boobboobo10boo12bo$89boo11b3o37bo3boo4bob
oo8boo7boo3bo53boo$100bo4bo36bo3boobbooboo19bobbo53bobbo$102bobo41boo
27bobo54bobo3boo$100bobo41bobbo85bo3bobbo$144bobo17boo48bo22bobo$145bo
18boo48bo23bo$216bo5bo$97boo73boo41bo6bobo$97boo73boo40bo3bobbo18boo$
135bo79bobboboboo15bobbo$134b3o83boboo16bobo3boo$133boobbo52boo42boo5b
o3bobbo$132boobboo34boo17boo41boo9bobo$133boo26boo9boo16bo55bo$134b5o
22b3o$138boo20bob3o$136bobbo5boobb5o7bob3o82boo$137boo6bo7bo7b4o82bobb
o$145bo4boboo8boo84bobo3boo$149b3o90boo5bo3bobbo$242boo9bobo$206b3o45b
o$135b3o68bobbo$135bobo71bo6b3o$135bo70boo13bo34boo$135bobbo66bobo12bo
bo32bobbo$136bobo67bobb3o9bo34bobo3boo$137b3o67boobbo38boo5bo3bobbo$
139boo43bo22bo3bo38boo9bobo$133b3o4boo40booboo21bobo51bo$139boo44boo
23bo$182b3o15boo5bobbo$184bo3bo10bobbo3bo57boo$183bo3bo18bo56bobbo$
184b3obo15boobbobo53bobo3boo$186boo17boobbo48boo5bo3bobbo$185bobo10boo
36bobo19boo9bobo$139boo45bo11b3obboo30bobbo31bo$139boo44boo12bo36bobo$
184b3o11boo5bo46boo$184boboo11bo4bo47bobo17boo$149b3o31b5o11bo38bo13b
3o16bobbo$151bo48bobo34boboo11bobbo16bobo3boo$201bo35boboo12bo12boo5bo
3bobbo$149b4o70b3o10bo3bo12bo7boo3boo9bobo$151b3o70bo12b4o20boo15bo$
153bo44b3o23bobbo9b3o15bo$198b3o23bobbo24bo$201boo22bobo24bobbo24boo$
197b3obbo37boo9b3o25bobbo$240boo9b3o26bobo3boo$188boo12bo48bobbo19boo
5bo3bobbo$188boo7boo3bo49bobo19boo9bobo$198bobbo22bo27b3o31bo$199bobo
21bobo$224bo$241bo46boo$241bo45bobbo$222b4o62bobo3boo$196boo24boo3bo
13bo40boo5bo3bobbo$196boo25bo4bo11bobo39boo9bobo$225boboo11bo53bo$226b
o15boo$243bo44b3o$240b3o47bo$241boo46bo$238bo$238boo$206b5o7bo19boo$
204boo5boo4bobo8boo6boo$204bo7bo4bo10boo4boo$204boo7bo3bobbo13boobo$
206boo6bo3b3o15boo$209bo$209bo4bo13boo$210boobo14boo$$236boo$236boo$
256b3o$195bo62bo60bo$194bobo60bo62bo$225bo3bo6boo80b3o$194bobbo3bob3o
17bobbob3o5boo$196bo4bo24bobobo$197boboobobo9bobo7bo$198boo3bo4boo4b3o
bobooboo$199bo8boo6bobboo3bobo3bo$224bobo8$206bo$206b3o$198bo6bo3bo$
198bo3b3o4bo$198bo3b3oboboo$202boo3bo6$203boo$203boo4$351bo$352bo$350b
3o!

Here is how that difficult convoy can be made using the new edge rake along with the previous lane crossing glider turning method.

Code: Select all

#C A difficult convoy being constructed using Corderships.
x = 458, y = 426, rule = B3/S23
59b3o$58bo3bo$58bo3bo$58bo3bo12b3o$75b3o$59booboo9boo4bo$60bobbo9b3obo
bo$61bobo10boo3bo$62boo10b5o$59bo3bo12bo7boo$58bobobobo19boo$59bo3$74b
oobbo$$74bo3bo$74bo$75bobo13bo$92boo$75b3obbobo3b3obbobo$64boo13bo3bo
4boboobo$53bo10boobboo8boo10b3o$52b3o12bobbo6bo$51bobobo12boobboo5bobo
3bo$50b3ob3o14boob3obbo3boo$71boobb3obbo$52bob3o14bo6b3o$52b5o22bo$52b
oobboo11boobo$54boboo12bobo$56boo13bo$52bobobbo$51bobobbo$30boobbo17bo
$33bobo$32bo16bo$49bo98b3o$34boo13bo97bobbo$146bo4bo$35boo12boo95bobb
3o$34bo13bobbo94bo5bo$32booboo11bobo96b7o$35boo10boo104bo$33bo13bo105b
o$50boo99boo12boo$41bo8boo113boo$24bo15bobo7boo$23bobo14bobo4boobo$41b
o6b3o98boo$23bobbo3bob3o14bo82b5o11bobbo$4bo20bo4bo99boo5boo8b3o$26bob
oobobo96bo7bo8b3o$8bo18boo3bo97boo8bo4boobooboo20boo$28bo20bo82boo7bo
bbobo4bo21boo$3obo43bobo84bo10bo3boobbo$3obo43bobo84bo4bo9bobobbo$bo8b
oo37bo86boo9bobo5bo$bbo3b3oboo135bobo3b3o11b3o$3bo6bo115b3o17boobo16b
ooboo$4bobobobo114bobbo8boo8bobo15boboboo$5bo15boo101bo4bo7boo9bo15boo
bo$21boo101bobb3o34boobo$124bo5bo28boo5bo$125b7o27boo$22boo5b3o99bo$
20boo9bo99bo$20bo4bo103boo$20booboboobboo$22bobbo$23bo52bo$11b3o63boo
49bo$9bo3boo61boo49bobo$3b3o3bobobboo6bobo101boobo$8bo5bo7bobbo100boo$
9bobboo7bo3bo101b3o$9bo12bobbo102bo12b3o$22b3o104bobbo7bo3bo$126bo6bo
10bo$15b3o108bo6bo10bo$17bo108bo4b3o9bo$9boo129bo3bo$9boo4b3o123bobbo$
16boo124boo$14boboo$13bobb5o$13bobbob3o44b3o$19boo43bo3bo62boo$63bo4bo
8boo3b3o46boo$63bobbobo7b4o$63boobobo6bo3boo$65boobobbo4boobobo$67boo
bbo133boo$68b3o13bo6boo31bo81bobbo4bo$81bobbo6boo31bo78bobb3obobbobo$
54bo27b3o39bo78bobbo4b4o$54bo73bo74bobbo$54bo69b3obbo76bo6bo$58bo12bo
51bo4bo76boobo$54b3obbo10boo51bo3bo85bo11boo$53bo4bo11bo53b3o84boo12b
oo$53bo3bo74bobo53boo$54b3o51bo23boo54b3o$71b3o35boo12bobo7bo54boobo$
69boob3o19boobbo9boo13bobo66bo$53bobo13boobbo21boo26bobo58bo3boo3bo4b
oo$53bobo13booboo23bo25bobo68bo3boo19bo$53bobo14bobo25b3o23boo65bobo
15bo8boo$53bobo15bo119bo17boo6bobbo$54boo130bo4bobo11bobbooboo5boo$
206b3ob3o7boo$190b4o13bo3boo6booboo$190boo14b3o11bobo$206b3o12bo$68b3o
112boo12boo9b3o$67bo3boo42boo67bobbo4bo4boo10boo$39bo74bobo64bobb3obo
bbobo$38boo7bo19bo48bo64bobbo4b4o26boo$37bobob3obbobo9boo8bo3bo108bobb
o34boo$36b3o3boo3bo10boo9b3o112bo6bo50boo$37boboboobobo136boobo41bo9bo
3b3o$38booboo148bo36b4o5bobobbo$39bob5obo141boo37bo3bo5bo3bobbo$43b4o
11boo186bo$58boo170b3o10bobo$218bo25boo7boo$66boo150bo34boo$66boo150bo
$222bo$218b3obbo$28b3o186bo4bo$28b3o35boo15boo115bo16bo3bo4boo$42bo23b
oo14bobo115bo17b3o5boo$28boboo13bo6bobo29bo99bobbo12boboboo41bo$28bo3b
o7bo11bobobo83bo44b3ob3o9boobobo38boo$30b3o6bo3bobbo10boo82boo5bo36boo
bobo12boobo10bobo28bo$40b3obbo10bo83boo7bo37b3o15bo11bobo23bobobbo$41b
o3bo101b3o38boo27bobo23bobb3o$43boo172bobo24b4o$43bo174boo25bo$29bo
195boo18bo$28bobo147boo11boo27boo3boo$29bo149bobbo4bo3boo13bo9bo3b3o
32boobbo$28boo146bobb3obobbobo17b4o5bobobbo37bobo$28boo146bobbo4b4o18b
o3bo5bo3bobbo33bo16bo$29bo146bobbo44bo49bo$27boboo148bo6bo21b3o10bobo
23bo11boo13bo$28boboobo144boobo40boo21booboo$28bo4bo152bo58booboo10boo
12boo$31bobo150boo59boo12bo13bobbo$247boobo6booboo11bobo6boo$248bobbo
8boo10boo8boo$248bobbo6bo13bo$229boo18boo24boo$229boo44boo$275boo$33b
oo220boo15boobo$33boo186boo23boo7boo16b3o$224booboo17boo26bo$47b3o161b
oo5bo4boo54bo$45booboo130b3o28boo12boobo50bobo$45b5o168bobbo4boo53boo$
45bo174bobobo$45boob3o173bo50boo$47b3o183boobbo10boo24bobbo$236bobo9b
oo25boo12bo$172bo62bo12boo35b5o7boo$173boo5bo38boo28boo34bo3bobo4b3o$
172boo7bo6b3o28boo16boo12bo3boo28b3o3b3o3b3o$179b3o66boobbobboo34boobb
3o$209bo7bo20boo11boo38bo$208b3o5bobo18bo50b3o16boo$207boob4obbobbo15b
ooboo48boo17boo$208b3obbo24boo$209bobboobbo19bo15bo19bo$213boobobo35bo
15booboo53b3o6bo$196b3o18bo31bo4bo17bo54bo4bo3bobo$249bo4boo24boo45bo
4boo3bo$251bobbo3boo20boo45bo6bo$251b3o4boo13boo17b3o8boo23b3obobbobo$
252bo19bobbo20bobo4boo27b5o$271boo3bo15bob3obboo36bo10boo$271bo4bo16b
4obo49boo$204boo65bo3bo16booboo14bo$204boo34boo30bobbo17b4o4bo8bobo$
208boo30boo31bo20bo5bobbo6bobboo$207bobbo68boo21b3o3b7o$207bobo57bo11b
oo22boobbobbo3bo6boo$208bo42bo11b5o7boo24b3obb3obb7o3boo$250bo12bo3bob
o4b3o26bo4b3obbo28boo$250b3o10b3o3b3o3b3o23boo6booboo14boob3o7boo$228b
oobbo36boobb3o34b3obobbo11booboo8bo$231bobo35bo41b3oboo12boobobo10bo$
216boo12bo35b3o45bo17boboo7b3o$215bobbo47boo63b5o3bo3b3o$215bobo14boo
96b3o6bo$216bo103boo9bobo$233boo71b3o6bo4boo10boo$204bo27bo72bo4bo3bob
o$205boo5bo17booboo70bo4boo3bo26boo$204boo7bo19boo70bo6bo29boo$211b3o
10boo5bo51bo22b3obobbobo$223bobbo55bobo25b5o$223bobo55bo33bo$224bo41bo
3b3obo6bo4bo$265bobo3bobobo5bobo$265bob7oboo5boobo$266b3oboo3bo9bo$
272b3o10bo$232boo39bo12bo$231bobbo$231bobo3b3o$232bo77boo$273bo36b4o5b
oboo$261bo8bo37boob3o5bo3bobo$257boobobo10bo34boo3boo10bobbo$257bobboo
boobboo3bo35boobobo9bob3obo$240boo15bo5bobo47bo5bobo5bobo$239bobbo15b
oobbo8bo38b3o15bo$239bobo3b3o14bobb3obbo$240bo21b3o97bo$362bo$296bobo
63bo$296b3o66boo$296boo67boo12boo$248boo110bo3b3o11boo$247bobbo110b3o
15bo$247bobo3b3o43bo48b3o11bo15b3o$248bo48bobo47bo3bo9boo15b3o$297b3o
46bo4bo9b3o16bo$236bo63bo44bo3bo13bo14bobbo$237boo5bo51b5o44bobbob3o8b
o16b3o5boo$236boo7bo99bo7bo9bo15bo6boo$243b3o10boo89bo3bobo7b3o$255bo
bbo3boo22bo60bo3boboo$255bobo3bobbo20bobo5bo55b3oboo$256bo5boo27booboo
69boo$285b3obbo3boo69boo$291booboo$291b4o81bobo$349boo25bobbo$264boo
45bo37boo25bobbo$263bobbo3boo38bo39bo25bo3bo$263bobo3bobbo37b3o64bobo$
264bo5boo78bo27bo3$322bobo23bo5b3o$321bo26bo7bo$272boo48bobbo22bo5bobo
10boo$271bobbo3boo18b3o23bobo27boo10bobbo$271bobo3bobbo7b4o4b4oboo24bo
11b3o23bo3bo$272bo5boo8boboboo4boobbo23b3o38boo$289boo9b3o23bo$291bo3b
obo13bo12boo35bo$310bobo13bo13b3o16boo$311bo12bobbo12b3o5boo3boobboo5b
o$280boo42bobo13boo6boo3boo4boo$279bobbo3boo36bo14bo23bo$279bobo3bobbo
48boobbo18b4o$280bo5boo5boo43bo3bo9bo6bobo$293boo43bobbo10bo5bobboobo$
268bo70b3o7bo9bo4bo$269boo5bo37boobo27boo6bo6bo$268boo7bo35b3obo6bobo
19b4o11bobbo$275b3o10boo22bo4bobo4bo25bo3bo6boo$287bobbo22boo6bobo3bo
23bo$287bobo4boo18bo3bobbobboo26bobo$288bo4bobbo20boboo3boboobo11b3o9b
o$294bobo19bobo8bobo11b4o$295bo20bobo21boobboo$341boobo29bobo$341b3o
29bo$296boo44bo31bobbo$295bobbo77bobo$295bobo4boo75bo11b3o$296bo4bobbo
73b3o$302bobo73bo$303bo30boo40boo$321bo9bob4o41bo13b3o$316bo3b5o5boobo
3boo37bobbo12b3o5boo$304boo9bobo7boo4bobbooboo37bobo13boo6boo$303bobbo
8bo7boboo5b6o38bo14bo$303bobo4boo4bo8boo6bo55boobbo38bo$304bo4bobbo4bo
3b4o65bo3bo9bo26b3o$310bobo9b3o65bobbo10bo26bobbo$311bo79b3o7bo29b3o$
397boo6bo25b3o14boo$354bo43b4o28boboobo12boo$312boo9boo29bobo45bo3bo
24bobb3o$311bobbo8boo29boo30bo16bo27b4oboo$311bobo4boo65bobo16bobo25bo
b3o$312bo4bobbo59boobbooboo4b3o9bo28b3o10bo$318bobo59boobb5o4b4o18bo
19boo10bo$300bo18bo68bo3boobboo17bo32bo$301boo5bo57b3o17bo6boobo20bo5b
o22bobo7boo$300boo7bo60bo15b3o4b3o20bo6bobo5boo16bo6boo$307b3o10boo48b
oo14b3o5bo20bo3bobbo8boobboo$319bobbo47bobbo42bobboboboo6b3obboo9bobo$
319bobo4boo43bobo47boboo8bo14boo$320bo4bobbo42bo63bo$326bobo27bo13boo
11boobo60bo$327bo26booboo10bobo12boo60bo$371boo72b3obo$357boo9boo75boo
bboo$328boo28bo11bo74boobboo$327bobbo21bo3bo$327bobo4boo20bo3bo84boo$
328bo4bobbo108bo4bo$334bobo34b3o71bo4bo$335bo18bo69boo3bo16bobo$355b3o
36bo27b3o4boo$374bo18bobo21b3obo8boo$336boo35bobo16bo3bo24bobobb5o9bo$
335bobbo16b3o16bo18bobo26bo3b3o10boo$335bobo4bo12b3o36bo14b3o$336bo4bo
bo11booboo48bo3bo23bobbo$341bobbo14bo34b4o10b3obbo22bobbo$342boo13b3o
33bo4bo9bo3bo23b3o$395bo13b3o$392bo3bobbo9boo7boo3boo$344boo46bob3obo
19boo3boo8boo$343bobbo46b3obo34b3o$343bobo4bo81b3o$344bo4bobo81bobo$
349bobbo58bo21bobo$332bo17boo8boo46b5o20b3o$333boo5bo19boo45bo$332boo
7bo81bo$339b3o10boo25b3o7bobo4boo10bo3bo9boboo$351bobbo27b3o5bo18b3o
12b3o$351bobo4bo23b3o30boo4b3o3bo$352bo4bobo23bo30bobbo4b5o$357bobbo
52bo5bo5bo$358boo8boo42bobboo$368boo41booboob3o$411bobbo$360boo49boboo
$359bobbo49boo$359bobo4bo39bo$360bo4bobo38boo$365bobbo35boobbo$366boo
8boo24bo4boo$376boo25boo$403bo$368boo15boo6bobboobo$367bobbo14boo5bo3b
o3boo$367bobo4bo17bo3b3obo$368bo4bobo22boo$373bobbo$374boo8boo$384boo
$$376boo15boo$375bobbo14boo28bo$375bobo4bo38boo$376bo4bobo38boo$381bo
bbo$364bo17boo8boo$365boo5bo19boo$364boo7bo$371b3o10boo$383bobbo$383bo
bo4bo$384bo4bobo$389bobbo$390boo8boo$400boo$$392boo$391bobbo$391bobo4b
o$392bo4bobo$397bobbo$398boo3$400boo$399bobbo$399bobo$400bo4$404bo$
405boo$404boo4$396bo$397boo5bo$396boo7bo$403b3o23$436bo$437boo$436boo
4$428bo$429boo5bo$428boo7bo$435b3o!

There are still limitations on the edge rake. It could not be used for the other outside glider on the difficult convoy, for example.

Perhaps better (and smaller) edge rakes exist with better clearance.

EDIT:

Here is an improved backward edge rake which has better clearance and is much smaller.

Code: Select all

#C A diagonal c/12 period 96 backward edge rake.
#C This uses an edge blinker puffer, an edge blinker-to-block
#C converter, and two sideways rakes.  The backward gliders are
#C on a path which extends 1.5 diagonal cells beyond the edge
#C of the blocks.
#C David I. Bell, 10 August 2025
x = 257, y = 202, rule = B3/S23
102bo$100booboo$103boo$100b3o$102bo3bo$75bo25bo3bo12bo$73booboo24b3obo
11bo$76boo26boo12bo$73b3o15boo10bobo$75bo3bo10bobbo10bo$74bo3bo24boo$
75b3obo22b3o$77boo23boboo$61bo6boo6bobo10boo10b5o20bo$60bobo3bo3bo6bo
11b3obboo4b3o23bo$59bo3bobo3boo5boo12bo8boboo23bo$60bobobboboboo4b3o
11boo5bo$61bo3bobboo5boboo11bo4bo3boo$65bo4bo3b5o11bo$66bobbo21bobo$
68bo23bo$134bo$72boo60bo$63boo7boo15b3o42bo$63boo23bobbo$87bo4bo$87b6o
$53bo37bobo$51booboo36b3o6b3o$54boo37boo6bobbo37bo$51b3o50bo37bo$53bo
3bo43boo15boo22bo$52bo3bo43bobo15boo$53b3obo43bobb3o$55boo45boobbo$54b
obo8bo4bo31bo3bo$55bo9bo5bo31bobo10bobo$54boo49bo12bo31bo$53b3o46bobbo
16bo27bo$53boboo45bo13b3o7boo22bo$52b5o9boo49boo7boo$68bo32boobbo11boo
$66b3o33b3o13boo$67bo51bo$72bo$71boo44bo40bo$65boo4boo42bobo40bo$65boo
47bo43bo$113boo$112b3o$57boo36bo17bobbo$57boo35b3o10bo6boo$94bobbo6bo
bbo$94b3o6bo3bo9boo47bo$94b3o7bobo11boo46bo$93boboobo7bo10bo48bo$94bo
bb3o$94b4oboo$95bob3o$97b3o$98boo$174bo$174bo$94boo78bo$94boobo$94b4o$
96bo3$182bo$89boo3b4o84bo$84b3obobbo6bo7boo74bo$88bobbobb5o7boo$88bobb
o73bo$90bo70b4oboo5b3o$87bobo70boob3oboo4b3o$88bo54bobo15bob3obo7boo$
134bob3o4bobo16bo3b4o4boo$132boobo4bo5bo18boob3o20boo$114boo18boo4bobb
obbo19b5o20boo$114boo24bobbobbo20bo$139bo4bo$135bobbo16boo$136boo17boo
$104bobo$103bo3bo11bobo$74bo28bo4bo9bobbo77boo$74bo28bo4bo10bobo77boo$
74bob3o12b4o9bo3bo19boo34boo$76b3o10bobo12bobbo20boo35boo$77bo9bo3b3o
27bo18boo9boo11bo$77boo7b3o31boboo15bobooboobo4bo44boo$78bo6bo4b3o27bo
boo18boo3bo48bobo$63bo14boo6bob4o27bo3bo16bo6bo50bo$88bo31b4o17bobboo$
67bo7booboo8bobo29b3o18b3o5boo$76b3o10bo58bo$59b3obo12bo50boo20boboo
45bo$59b3obo57bobo3boo22bo46boo$60bo8boo14boo25bob3o4bobo26bo46bobo$
61bo3b3oboo13bobbo22boobo4bo5bo24boo$62bo6bo15boo25boo4bobbobbo24boo$
63bobobobo48bobbobbo$64bo52bo4bo$113bobbo$114boo$223bo$80boo83boo57bo$
80boo82bobo55b3o$166bo$76boo$75bobbo$76bobo14bo$37bo32b3o4bo14bo37b3o
33bo$36b3o29bo3boo18b3o35b3o33boo$25b3o7booboo22b3o3bobobboo39bo4bobo
7bo3boo30bobo$24bo11b3o14bo13bo5bo39bobobboobboo6booboo$24bo3bo8bo14b
3o13bobboo40bob4obbobo6boobo$22boo3boo8bobo11bo3bo12bo45bo6bobo9bo$21b
obbobobbo7b4o9boobb3o61bob3o10bobo$21bobbobobboo9bo10bo3bo78bo$23boob
oobbo20bobbo$24bo4bo6booboo11bobo6boo$27booboo3bo5bo19boo5boo63boo$26b
4o6bo3bo27boo51boo9bobo$27boo8bo83boo11bo$$52boboo$34boo15b5o$25boo7b
oo15b4o79bo$25boo107boo$52b3o12bo8boo55bobo$52b3o11bobo7boo$53bo11boob
oo$66bobbo$15bo11bo26boo12b3o$14b3o8bobbo24bobbo11bobo$13booboo11bo24b
oo13boo$14b3o12boo38boo184bo$15bo9boo5b3o66boo153bo$15bobo10b4o3bo64bo
bo151b3o$15b4o10bo5bo66bo$18bo12boobo32bo$31bo36bo$14booboo49boo7bo$
13bo5bo47b3o6bo25bo$14bo3bo13bo43b3o23boo$15bo17bo67bobo$33bo34b3o$66b
o4bo$27b3o7boo27boo3bo$28bobbo5boo29b4o$29boboo$31bo3$19boo$19boo4$70b
o$29bo40boo$27boo40bobo$28boo$$9b3o$9b3o$8bo3bo$9boob3o$9boo4bo$12bobb
o$13boo$$bbo$ooboo$ooboo$oo36bo$bboobo32boo$3bobbo30bobo$3bobbo$4boo5$
bb3o$$bbobo$3bo$4bo$4boo$boboobo$b4oboo$bb5o6bo$4boo5boo$12boo5$8b3o!

BCNU,
-dbell

[dbell]

I finally found a reaction to make a backward edge rake with total clearance.

Code: Select all

#C A diagonal c/12 period 96 backward edge rake with large clearance.
#C This uses several edge puffers, sideways rakes, and a two-engine
#C Cordership.  Backward gliders are created whose path is separated
#C from the edge of the convoy by 5.5 diagonal cells.
#C David I. Bell, 13 August 2025
x = 303, y = 243, rule = B3/S23
52bo$51boo7bo$50bobob3obbobo$49b3o3boo3bo$50boboboobobo$25bo25booboo$
24boo7bo18bob5obo$23bobob3obbobo21b4o$22b3o3boo3bo$23boboboobobo$24boo
boo41b3o$25bob5obo$29b4o11boo$44boo$7bo$6boboo$10bo$4bo3bobbo$bbo9bo4b
oo59b3o$bbo4boobboo4boo$11boo15bo8b3o11boo$4bo5bo13boobobo7bo14boo$5bo
4b3o17bo6boo12bo$6bo4boo12booboboo7bobo$8b4o14bo12bobbo$26bo4bo7bobo$
26bo13bo35bo9b3o$3bo12boo8bobbo45b3o$bboo7bo4boo10boo$bobob3obbobo62b
3o$3o3boo3bo26boo36booboo$boboboobobo27boo9bo28bo$bbooboo41bobo$3bob5o
bo83bo$7b4o37bobbo42bobo$50boo42bobo$51bo43bo$65boo$65boo3$48boo53bo$
36bo13bo51bobo$6bo30boboobobo4boo51bobo$9bo6bobo12b3o3b4o3bo3b3o15bo
36bo$4bo11bobobo16bobbooboo3boo16boo$3bo3bobbo10boboo11bo10b3obo14bo$
4b3obbo10boobobo8b3o11bo3bo10boobbo$5bo3bo13bobo8b3o13bobbo10booboo$7b
oo15bo25b3o12boboo42bo$7bo43boo11booboo41bobo$46boo16bo3bo41bobo$37boo
7boo17bobo43bo$27bo9boo25boo$10boo14bobo$10boo47boo4boo$26bobbo30bo$
28boo70bo18bo$29bo69bobo16bobo$98booboo15bobo$98boo19bo$104boo$73bo24b
3obbo$26boo44bobo27boboo9b3o$28bo42booboo24bobbo$27boo42boo16boo12bo
23bo$26b3o48boo9bobbo9boo23bobo$26boo43b3obbo12bobbo33bobo$25b3obo45bo
boo22bo25bo$26bo3bo11boo29bobbo22booboo$28bobbo10bobo21bo9bo11bo13bo$
28b3o12b3o12b3o3b4o6boo11boo3bo6bo23b3o$29boo9boobbo13bobo3booboo19bo
3boo4boobo$40boboo14b3obbo10bo13boboboo3boo36bo$39boobo20boo3bo3booboo
11bo3boo3boo35bobo$64b4o7bo13b3o42bobo$65b3o4bo16b3o43bo$74bo$$31boo
37boo59b3o$31boo28boo7boo16bo$61boo24b3o53bo$86boobbo51bobo$85boobboo
51bobo$51bo37bo53bo$50bobo38boo$49booboo37boo$49boo88b3o$55boo$49b3obb
o96bo$53boboo66bo7bo18bobo$51bobbo67b3o5bobo17bobo$54bo9bobboo52boob4o
bbobbo17bo$52boo8boo5bo52b3obbo$69bo23b3o6bo20bobboobbo$52bo41boo3boob
o24boobobo16boo$50booboo9bo3bo24boo5bobo28bo17boo$53bo10bo33b3obo56bo$
50bo14bo35boo55bobo$52bo11b3o46boo43bobo$113boo44bo$69bobo$70bo3bo$63b
oo4bo3bo3bo79boo$63boo4bo6b3o78boo$75booboo6boo79bo$74boo3bo6boo78bobo
$55boo18bobobobo11b5o68bobo$55boo19boobobbo10boobo70bo$79boobo12boobo
7boo10b3o$80boo15bobo6boobo10bo23bo$98boo5boo3bo8bo23bobo19boo$104bo3b
oo32booboo18boo$104bo37boo16boo13bo$85boo10boo6bobo40boo9bobbo11bobo$
85boo10boo43b3obbo12bobbo10bobo$71b3o6bo65boboo25bo$72boo3boobo26boo
35bobbo$71boo5bobo26boo28bo9bo11bo$76b3obo48b3o3b4o6boo11boo3bo9boo$
79boo48bobo3booboo19bo3boo8boo$129b3obbo10bo13boboboo3boo13bo$134boo3b
o3booboo11bo3boo3boo12bobo$135b4o7bo13b3o19bobo$136b3o4bo16b3o20bo$
145bo$$141boo38boo$132boo7boo16bo21boo$132boo24b3o30bo$157boobbo28bobo
$81bo3boo69boobboo28bobo$75boboo3boboobo34bo37bo30bo$73boobo3bobo4boo
4bo27bobo38boo$76bobobb3obboo4bobo25booboo37boo$77bo4boo8bobo25boo67b
oo$93bo32boo61boo$120b3obbo73bo$124boboo70bobo$90bo31bobbo72bobo$88bo
bbo33bo9bobboo59bo$79boo8boo32boo8boo5bo$79boo59bo$123bo73boo5b4o$121b
ooboo9bo3bo57boo5b3obo$124bo10bo68bo3bo$121bo14bo69boo$123bo11b3o67b3o
$198boo$140bobo$141bo3bo$134boo4bo3bo$134boo4bo62bo$77bo123booboo$76b
3o123bobbo$65boo8bobobo46boo75boo$74b3ob3o12bo32boo$64bo3bo23bobo85bo$
69bo6bob3o13boo84boo$62bo7bo5b5o9bo3bo84bobo$61bo4bo9boobboo11bobboo$
62bobobo4bo6boboo14bo140bo$62bo8bo8boo9bobboo142bo$63bo4boobo4bobobbo
11bo7boo12b3o118b3o$64boboob3o3bobobbo20boo16bo13bo$65b3oboo5bo42boo
10boo$119bobbo9boo$120bobo$120bo$74boo15boo26boo$65boo7boo42bobo53boo
30bo$65boo24boo27boo53boo25b5o7boo$117boo55bo27bo3bobo4b3o$92bobo10bo
13bo28bo53b3o3b3o3b3o$93boo10bo42boo58boobb3o$55bo49bo8bo32bobo58bo$
54b3o36b3o16bobo90b3o16boo$53bobobo10bo24bobbo9b3obbo3bo89boo17boo$52b
3ob3o9bobo23boo11bob5o$70b5o38bo$54bob3o9bo39boo75boo$54b5o8bobbo4bo
109b3o$54boobboo8bo5boo109boobo$56boboo9boo118bo13bo$58boo10bobo108bo
3boo3bo12bo28boo$54bobobbo131bo11bo28boo$53bobobbo83boo44bobo$54bo88b
oo43bo41boo$142bo40bo4bobo13bo24b3o$116bo85booboo21bob3o$67b3o46boo69b
4o36b3o$67bobo7boo36bobo69boo12bobo21bobo5bo$67bobb3o4boo28b3o91bo3bo
19bo6bo$73bo127boobbo18bo7bo36bo$70bobo129b3o20bo44bo$71bo131bo21bo42b
3o$$59boo56bo$59boo54b3o$115b3o$$191boo$110boo79boo$111boo$67bobo40bo$
67boo$50bo17bo$49b3o$48booboo$47boo3bo146boo$48bobobobo144boo$49boobo
bbo$52boobo$53boo$42bo$41b3o$40boobbo$39boobboo$40boo36boo$41b5o33boo$
45boo31bo$43bobbo$44boo3$301bo$302bo$42b3o255b3o$42bobo$42bo$42bobbo$
43bobo$44b3o$46boo$40b3o4boo$46boo$51bobo$51boo$52bo4$48b3o!

Here is a demonstration on using the rake to interleave gliders.

Code: Select all

#C A diagonal c/12 pseudo-period 48 backward edge rake.
#C This uses two period 96 backward rakes whose output gliders are
#C interleaved on the same path.
#C David I. Bell, 13 August 2025
x = 523, y = 449, rule = B3/S23
50bo$49bobo$$49bobbo3bob3o$51bo4bo$23bo28boboobobo$22bobo28boo3bo$54bo
$22bobbo3bob3o$24bo4bo$25boboobobo36b3o$26boo3bo$27bo15boo$43boo5$6boo
boo5boo11bo47b3o$6boo8boo10b4o$6boobobo11boo3b5o$9bobo11boo3boo3bo$10b
oo16b9o$28b4oboobbo9boo$34bobbo10boo$35b3o9bo$85b3o$bo13boo10boo$obo
12boo11bo$$obbo3bob3o25boo35b3o$bbo4bo29boo35bobo$3boboobobo63bobo$4b
oo3bo64bo4boo13bo$5bo42bo24b3o3boo12bobo$48bo30bo13bobo$48bo26b4o15bo$
52bo12bo10boo$48b3obbo10boo10bo$47bo4bo11bo$47bo3bo25bo$48b3o24bobo24b
o$34bo30b3o6b4o23bobo$12bo21bo7bo20boob3o5b3o24bobo$12b3o19bo5b3o4bobo
13boobbo8bo25bo$4bo6bo3bo17boo3bobo6bobo13booboo4boo$4bo3b3o4bo23bobbo
4bobo14bobo5boo$4bo3b3oboboo6b3o13bobboo4bobo15bo$8boo3bo8b3o23boo$
110bo$18bobo88bobo$18bobbo23boo62bobo$36boo7boo63bo$19b3o14boo25bo$9b
oo51bobo$9boo51bobo$26bo35bobo$26bo36b3o52bo$26bo39b3o48bobo$30bo35boo
31bo17bobo$26b3obbo66b3o17bo$25bo4bo66booboo$25bo3bo68b3o$26b3o10bo59b
o14b3o$38boboo30bo26bobo$38bob3o28b3o25b4o23bo$25bobo11bo3bo16b3o7boob
oo27bo22bobo$25bobo12b3o16bo11b3o14bo36bobo$25bobo13bo17bo3bo8bo14b3o
8booboo23bo$25bobo11bo17boo3boo8bobo11bo3bo6bo5bo$26boo10bobo15bobbobo
bbo7b4o9boobb3o6bo3bo$38boboo14bobbobobboo9bo10bo3bo8bo22b3o$58booboo
bbo20bobbo$44bo3boo9bo4bo6booboo11bobo6boo36bo$40boob3obboo12booboo3bo
5bo19boo35bobo$38bo6bo15b4o6bo3bo57bobo$38boo5bo16boo8bo61bo$43bo$87bo
boo$30boo37boo15b5o39b3o$30boo28boo7boo15b4o$60boo80bo$87b3o51bobo$87b
3o51bobo$88bo53bo$124boo$50bo11bo26boo$49b3o8bobbo24bobbo31bo3bo10b3o$
48booboo11bo24boo37bo$49b3o12boo55bo7bo20bo$50bo9boo5b3o26bo23bo4bo23b
obo$50bobo10b4o3bo24b3o23bobobo4bo18bobo$50b4o10bo5bo23booboo22bo8bo
19bo$53bo12boobo23boobobo23bo4boobo6b3o$66bo25b3obb3o23boboob3o5bo3bo$
49booboo39bo6bo23b3oboo5bo5bo6boo$48bo5bo39b5obo34bo12boo$49bo3bo13bo
27b4oboo33bo22bo$50bo17bo31bo36b4o16bobo$68bo30bo12boo27bobo13bobo$
112boo23bo5bo14bo$62b3o7boo62bo6bo$63bobbo5boo61b3o$64boboo12b3o13boo
36boobo18boo$66bo11b7o9bo39boo20boo$77b9o11bo36boo30bo$76bo7b3o53bo24b
obo$54boo21b3o12boobboboo36bo3bo24bobo$54boo22boo13bobbo40b3o26bo$81bo
10bo4bobo$82bo13boo3boo$83bo12boobboboo11bo48boo$74bo19boboo3boo10boob
oo25bo20boo$73b3o17booboo3bo40b3o29bo$72booboo7boo7boobo14booboboo13b
3o7booboo27bobo$71boobobo7boo9bo18bo15bo11b3o14bo13bobo$70b3obb3o33bo
bbo15bo3bo8bo14b3o13bo$71bo6bo27boo4boo14boo3boo8bobo11bo3bo$72b5obo
27boo19bobbobobbo7b4o9boobb3o$73b4oboo47bobbobobboo9bo10bo3bo10boo$78b
o50booboobbo20bobbo11boo$77bo52bo4bo6booboo11bobo6boo13bo$133booboo3bo
5bo19boo12bobo$132b4o6bo3bo34bobo$133boo8bo38bo$75bo$73boobo81boboo$
140boo15b5o18boo$76bo54boo7boo15b4o19boo$73bobbo12bo41boo57bo$74bo13b
3o67b3o28bobo$88boobo66b3o28bobo$79boo9b3o66bo30bo$72b3o5boo8boo$79boo
9boo29bo11bo26boo$79bo10boo28b3o8bobbo24bobbo25boo$88boobo27booboo11bo
24boo26boo$89boo29b3o12boo61bo$121bo9boo5b3o56bobo$121bobo10b4o3bo55bo
bo$121b4o10bo5bo56bo$78boo44bo12boobo$78boo57bo$120booboo71boo$119bo5b
o70boo7boo$120bo3bo13bo67boo$121bo17bo62bo$139bo61bobobo$200boo4bo$
133b3o7boo56bo5bo$134bobbo5boo56b3obbo$135boboo63bobboo$137bo65b3o$
204bo$74bobo$73bo51boo$74bobbo47boo$76bobo123boo$79bo11b3o109boo28bo$
78b3o121bo31bo$64b3o11bo97bo32bo22b3o$64b3o9boo57bo40boo29boo$78bo13b
3o38boo40bobo29bobo$64boboo8bobbo12b3o5boo32boo$64bo3bo7bobo13boo6boo$
66b3o7bo14bo23b3o$89boobbo21b3o$90bo3bo19bo3bo$90bobbo21boob3o$73boo
16b3o21boo4bo$64boo7boo43bobbo82bo6boo$64boo53boo82bobo3bo3bo$96boo
104bo3bobo3boo$99bo8bo61boo31bobobboboboo$96bobbo6booboo60boo31bo3bobb
oo$97bobo6booboo59bo37bo4bo$52bobo38boo11boo36bo64bobbo10boo$51bo14boo
25boo13boobo32boo65bo11boo$52bobbo10boo25boo14bobbo30bobo$54bobo52bobb
o$57bo52boo$56b3o14bo$56bo8b5o3boo$54boo8b6o131bo$56bo8booboo114b3o8bo
5bo29boo$54bobbo7booboo38b3o72bo3bo6bo7bo28boo$54bobo9bobo115boo9b4obb
oo$54bo12b3o38bobo75booboo9b3o$68b3o38bo78boo11bobo$68bobbo38bo27boo
62bo23b3o$68bobbo38boo27boo61bo22boobbo35bo$69b3o4boo29boboobo25bo89b
oo36bo$76boo29b4oboo110bob3o35b3o$108b5o6bo102bobboo$110boo5boo101bo$
118boo98b3obbo$218boobbo$58boo149bo8booboo$58boo147boobo9boo$205bo9boo
3bo$114b3o88bo6bobboo$69bobo118boo20bo$69boo119boo13boobbobbo$70bo133b
o3b4o$205b3obo$106boo97b3o48bo$53b3o51boo146boo7bo$51b7o48bo147bobob3o
bbobo$50b9o3boo189b3o3boo3bo$49bo7b3obobbo133boo54boboboobobo$50b3o6b
3obobo132boo29bo25booboo$51boo11boo162boo7bo18bob5obo$54bo172bobob3obb
obo21b4o$55bo170b3o3boo3bo$56bo170boboboobobo$228booboo41b3o$229bob5ob
o$41bo191b4o11boo$40bobo205boo$39booboo167bo$39booboo166boboo$38b3o33b
oo138bo$38b3o3bo30boo131bo3bobbo81bo$38b3o4bo28bo131bo9bo4boo59b3o13bo
$39boo5bo159bo4boobboo4boo73b3o$39b3o173boo15bo8b3o11boo$40boo166bo5bo
13boobobo7bo14boo$41boo166bo4b3o17bo6boo12bo$210bo4boo12booboboo7bobo$
212b4o14bo12bobbo$41bo188bo4bo7bobo$40b3o187bo13bo35bo9b3o$39bo3bo163b
o12boo8bobbo45b3o$43boo8bobo150boo7bo4boo10boo$42boo9boo150bobob3obbob
o62b3o$54bo149b3o3boo3bo26boo36booboo$205boboboobobo27boo9bo28bo$206b
ooboo41bobo$207bob5obo83bo$211b4o37bobbo42bobo$254boo42bobo$255bo43bo$
47b3o219boo$269boo3$252boo53bo$240bo13bo51bobo$210bo30boboobobo4boo51b
obo$213bo6bobo12b3o3b4o3bo3b3o15bo36bo$208bo11bobobo16bobbooboo3boo16b
oo$207bo3bobbo10boboo11bo10b3obo14bo$208b3obbo10boobobo8b3o11bo3bo10b
oobbo$209bo3bo13bobo8b3o13bobbo10booboo$211boo15bo25b3o12boboo42bo13bo
$211bo43boo11booboo41bobo13bo$250boo16bo3bo41bobo11b3o$241boo7boo17bob
o43bo$231bo9boo25boo$214boo14bobo$214boo47boo4boo$230bobbo30bo$232boo
70bo18bo$233bo69bobo16bobo$302booboo15bobo$302boo19bo$308boo$277bo24b
3obbo$230boo44bobo27boboo9b3o$232bo42booboo24bobbo$231boo42boo16boo12b
o23bo$230b3o48boo9bobbo9boo23bobo$230boo43b3obbo12bobbo33bobo$229b3obo
45boboo22bo25bo$230bo3bo11boo29bobbo22booboo$232bobbo10bobo21bo9bo11bo
13bo$232b3o12b3o12b3o3b4o6boo11boo3bo6bo23b3o$233boo9boobbo13bobo3boob
oo19bo3boo4boobo$244boboo14b3obbo10bo13boboboo3boo36bo$243boobo20boo3b
o3booboo11bo3boo3boo35bobo$268b4o7bo13b3o42bobo$269b3o4bo16b3o43bo$
278bo$$235boo37boo59b3o$235boo28boo7boo16bo$265boo24b3o53bo13bo$290boo
bbo51bobo13bo$289boobboo51bobo11b3o$255bo37bo53bo$254bobo38boo$253boob
oo37boo$253boo88b3o$259boo$253b3obbo96bo$257boboo66bo7bo18bobo$255bobb
o67b3o5bobo17bobo$258bo9bobboo52boob4obbobbo17bo$256boo8boo5bo52b3obbo
$273bo23b3o6bo20bobboobbo$256bo41boo3boobo24boobobo16boo$254booboo9bo
3bo24boo5bobo28bo17boo$257bo10bo33b3obo56bo$254bo14bo35boo55bobo$256bo
11b3o46boo43bobo$317boo44bo$273bobo$274bo3bo$267boo4bo3bo3bo79boo$267b
oo4bo6b3o78boo$279booboo6boo79bo$278boo3bo6boo78bobo$259boo18bobobobo
11b5o68bobo$259boo19boobobbo10boobo70bo$283boobo12boobo7boo10b3o$284b
oo15bobo6boobo10bo23bo$302boo5boo3bo8bo23bobo19boo$308bo3boo32booboo
18boo$308bo37boo16boo13bo13bo$289boo10boo6bobo40boo9bobbo11bobo13bo$
289boo10boo43b3obbo12bobbo10bobo11b3o$275b3o6bo65boboo25bo$276boo3boob
o26boo35bobbo$275boo5bobo26boo28bo9bo11bo$280b3obo48b3o3b4o6boo11boo3b
o9boo$283boo48bobo3booboo19bo3boo8boo$333b3obbo10bo13boboboo3boo13bo$
338boo3bo3booboo11bo3boo3boo12bobo$339b4o7bo13b3o19bobo$340b3o4bo16b3o
20bo$349bo$$345boo38boo$336boo7boo16bo21boo$336boo24b3o30bo$361boobbo
28bobo$285bo3boo69boobboo28bobo$279boboo3boboobo34bo37bo30bo$277boobo
3bobo4boo4bo27bobo38boo$280bobobb3obboo4bobo25booboo37boo$281bo4boo8bo
bo25boo67boo$297bo32boo61boo$324b3obbo73bo$328boboo70bobo$294bo31bobbo
72bobo$292bobbo33bo9bobboo59bo$283boo8boo32boo8boo5bo$283boo59bo$327bo
73boo5b4o$325booboo9bo3bo57boo5b3obo$328bo10bo68bo3bo12bo$325bo14bo69b
oo14bo$327bo11b3o67b3o12b3o$402boo$344bobo$345bo3bo$338boo4bo3bo$338b
oo4bo62bo$281bo123booboo$280b3o123bobbo$269boo8bobobo46boo75boo$278b3o
b3o12bo32boo$268bo3bo23bobo85bo$273bo6bob3o13boo84boo$266bo7bo5b5o9bo
3bo84bobo$265bo4bo9boobboo11bobboo$266bobobo4bo6boboo14bo140bo$266bo8b
o8boo9bobboo142bo$267bo4boobo4bobobbo11bo7boo12b3o118b3o$268boboob3o3b
obobbo20boo16bo13bo$269b3oboo5bo42boo10boo$323bobbo9boo$324bobo$324bo$
278boo15boo26boo$269boo7boo42bobo53boo30bo$269boo24boo27boo53boo25b5o
7boo$321boo55bo27bo3bobo4b3o$296bobo10bo13bo28bo53b3o3b3o3b3o$297boo
10bo42boo58boobb3o$259bo49bo8bo32bobo58bo$258b3o36b3o16bobo90b3o16boo$
257bobobo10bo24bobbo9b3obbo3bo89boo17boo27bo$256b3ob3o9bobo23boo11bob
5o140bo$274b5o38bo138b3o$258bob3o9bo39boo75boo$258b5o8bobbo4bo109b3o$
258boobboo8bo5boo109boobo$260boboo9boo118bo13bo$262boo10bobo108bo3boo
3bo12bo28boo$258bobobbo131bo11bo28boo$257bobobbo83boo44bobo$258bo88boo
43bo41boo$346bo40bo4bobo13bo24b3o$320bo85booboo21bob3o$271b3o46boo69b
4o36b3o$271bobo7boo36bobo69boo12bobo21bobo5bo$271bobb3o4boo28b3o91bo3b
o19bo6bo$277bo127boobbo18bo7bo36bo$274bobo129b3o20bo44bo$275bo131bo21b
o42b3o$$263boo56bo$263boo54b3o$319b3o$$395boo$314boo79boo$315boo$271bo
bo40bo$271boo$254bo17bo$253b3o$252booboo$251boo3bo146boo84bo$252bobobo
bo144boo85bo$253boobobbo228b3o$256boobo$257boo$246bo$245b3o$244boobbo$
243boobboo$244boo36boo$245b5o33boo$249boo31bo$247bobbo$248boo3$505bo$
506bo$246b3o255b3o$246bobo$246bo$246bobbo$247bobo$248b3o$250boo$244b3o
4boo$250boo$255bobo$255boo$256bo3$521bo$252b3o267bo$520b3o!

It should be possible to create a triggerable version of the rake so that backward gliders are only created on demand. A close call for such an object is to simply delete one of the beehives or blocks, which suppresses the backward glider but lets a sideways glider escape. Perturbing one of the objects or adding a bait object might work for a clean solution.

I didn't add this as an edit to my previous post since this is such an improvement that I thought it deserved its own post.

EDIT:

Here is a triggered edge rake. This was a bit more complicated than I expected, but it does work.

Code: Select all

#C A diagonal c/12 triggered backward edge rake with large clearance.
#C This is based on a period 96 edge rake with additional components to
#C suppress output gliders unless input gliders are present.  This
#C example shows the rake being triggered by a period 288 (96 * 3)
#C sideways rake.  Backward gliders are created whose path is separated
#C from the edge of the convoy by 5.5 diagonal cells.
#C David I. Bell, 14 August 2025
x = 432, y = 398, rule = B3/S23
120bo$119boo$118boboo$118bobboo$116b4ob3o$93bo21bobbobobboo$92boo22bob
obob3o$91boboo22boob3obo$91bobboo21b4obbobo$89b4ob3o23bo3bo$88bobbobo
bboo22bo3bo$89bobobob3o22bobbo$90boob3obo$90b4obbobo37bo$93bo3bo38bo$
93bo3bo38bo$93bobbo12boo$109boo4$144bo$82boo60bo$72b3o7boo11boo47bo$
75b3o11boo4bobo$75b3o11booboobboo$76bo16boobbo$71bo28boo$70boo29boo9b
3o$69boboo24bob3o12bo37bo$69bobboo24b3o10bo40bo$67b4ob3o6boo7booboo13b
o43bo$66bobbobobboo5boo9boo13bo$67bobobob3o16bo15bo3bo28bo$68boob3obo
27boo6bo29bo$68b4obbobo26boo36bo$71bo3bo69bo$71bo3bo65b3obbo13bo$71bo
bbo65bo4bo13bobo$113b3o24bo3bo14bobo$141b3o16bo$117bo$113bo3boo12bo24b
oo$72boo41bobo13boo7bobo$112b3o16bobo6bobo$99bo14bo25bobo25bo$99bo30b
oo8bobo24bobo$99bo8bo4boo16boo8boo24bobo$77boo27bobo5boo14bobbo34bo$
76bobbo20b3obbo3bo4bo15b3o5boo$69b3o4bobboo20bob5o6boo22boo$75bobboo8b
o18bo5boo$75b4o9boo12boo$86boobo86bo$84booboo86bobo$85b3o23boo62bobo$
86bo15boo7boo63bo$102boo25boo$75boo52boo$75boo52bobbo32b3o$130bobo33bo
$91b3o36bo35bobbo14bo$132boo32bobbo13bobo$95bo34bobbo33bobo13bobo$91bo
3boo34boo5b3o43bo$93bobo43bo$90b3o46bobbo$92bo18boo26bobbo38b3o$104boo
34bobo$91boo12bobo47boo9boo24bo$92boo12boo47boo34bobo$92bo14bo83bobo$
92boo98bo$91boo46bo$138bobo$104b3o19boo3b4o4bo49b3o$103bobb3o12b3obobb
o6bo19bobo$106boboo4boo9bobbobb5o64bo$103boo4boo3boo9bobbo8b4o17bo40bo
bo$105b3obbo16bo9boo3bo10bo3bo41bobo$106bo3bo13bobo11bo4bo9bo4bo41bo$
107bobo15bo14boboo11bo$141bo12boobboo19bo$96boo38boo16bobo18boobobo7bo
8b3o$96boo29boo7boo18boo17bobbooboobbooboo$127boo25bobbo17bo5bobo5bo
18bo$116b3o35bobo19boobbo8bo17bobo$117bo31boo29bobb3obbo18bobo$117bobb
o28boo29b3o15boo8bo$117bobbo77boo$118bobo47boo$205b3o$167bo3bo$172bo
43bo$165bo7bo41bobo$117bo46bo4bo45bobo$116bobo46bobobo4bo31boo8bo$117b
o47bo8bo20bo3boo5boo$166bo4boobo8bobbo6boobooboo$167boboob3o11b3o3bo7b
o13boo$115b4o49b3oboo4boo3boob4o3bo6boo12boo$115boo3bo11boo44boo9boo4b
oobboo23bo$116bo4bo12bo60boobboo22bobo$118boboo8bobob3o86bobo$119bo10b
obboo50bo38bo$129bo3boo$131b3o$222boo$222boo$232bo$231bobo$121boo52boo
54bobo$121boo45bo5bobboo53bo$168bo4b3obbo$168bo4bo4bo$173b5o52boo$174b
oo54boo$240bo$239bobo$239bobo$240bo$173boo44bo3boobboobo$173boo44bo3b
oo4boboo$219bo3boobbooboo6boo$223boo13boo$221bobbo23bo$192bo3boobboobo
17bobo23bobo$192bo3boo4boboo16bo24bobo$192bo3boobbooboo36bo6bo$196boo
43bo$194bobbo43bo$194bobo17boo30boo$195bo18boo30boo$256bo$176boobbo74b
obo$179bobo73bobo$178bo70bo6bo$187boo60bo$180boo5boo19bo13b3o24bo$199b
oo4boo3boo12bo29boo$181boo15bobbo3bo5bo11bo30boo$180bo18bobbobboo3bo
53bo$178booboo17bobo4bob3o51bobo$181boo17b3o7boo51bobo$179bo27boboboo
44bo6bo$208boobo45bo$186boo22boo45bo$186boo74boo$170bo3boobboobo80boo$
170bo3boo4boboo24boo62bo$170bo3boobbooboo25boo35bo25bobo$174boo68bobo
5bo18bobo$172bobbo74booboo17bo$172bobo69b3obbo3boo9boo$173bo43bo32boob
oo8bobbo$217bo32b4o10boo4boo$219bo5bo44boo$218bo6bobo52bo$217bo3bobbo
54bobo$218bobboboboo52bobo$223boboo36bo16bo$237boo23bobo8boo$237boo23b
obbo6bobbo$189boo72boo8boo3boo$188boboo86boo$173boobb5o6bobboo95bo$
173bo7bo11bo6b3o84bobo$173bo4boboo13bo4b3o7boo75bobo$177b3o12bobo4bo3b
o6boo76bo$193bo6boob3o11b3obbo58boo$200boo4bo10b4obo6boo49bobbo$203bo
bbo13bo21boo37boo3boo$204boo15bobo7boo8bobo42boo$180boo40boo3bo4boo9bo
52bo$180boo50bo39bo22bobo$228b4o24booboo6boboobboo20bobo$195bo13boo10b
oo7bo25boo8bob5o23bo$195bo13boo10boo33boobobo5bo4boo15boo$197bo5bo55bo
bo11bobo12bobbo$196bo6bobo25boo27boo27boo3boo$195bo3bobbo28boo40b3o6b
oo10boo$196bobboboboo77boo20bo$201boboo98bobo$303bobo$304bo$297boo$
283boo11bobbo$257bo24bobbo11boo3boo$249b3o3b4o23bobboo3boo10boo$249bob
o3booboo22boboo4boo20bo$249b3obbo24bobbobo26bobo$254boo3bo19boo30bobo$
255b4o3boo14bo33bo$204boo3bo46b3o3boo9boobboo26boo$202b3o4boo62boobbo
26bobbo$197b3obo8boo5bo56boboo27boo3boo$201bobobb5o5bobo56boo33boo$
202bo3b3o7bobo101bo$217bo101bobo$65bobo251bobo$65bobobo7bo134boo106bo$
64bobboobo4b3o235boo$65boo3boboboobo135boo49bo47bobbo$65boo3boob5o125b
oo9bo38boo9b3o46boo3boo$69boboo3boo125boo47bobobo7b3o51boo$68bobo16boo
163bo3boo5bo3bo60bo$87boo164boo8b4o60bobo$253b3o7boboo60bobo$328bo3$
326boo$326boo$95boo160boo77bo$85bobbo6boo160boo76bobo$72boobo6boobobb
oo177boo66bobo$72b6o4boobo4bo175bobo67bo$78bo3boo184bo60boo$70b3o6bo4b
o4boo237bobbo$56b3o11boo6bo5booboo240boo3boo$54b7o273boo$53b9o9bo4bo
267bo$52bo7b3o12bo193bo73bobo$53b3o6bo204booboo71bobo$54boo211booboo
72bo$57bo209boo68boo$58bo24bo185boobo63bobbo$59bo22bobo185bobbo63boo3b
oo$82bobo185bobbo68boo$83bo187boo12boo65bo$62boo221boo64bobo$40b3o18bo
bbo286bobo$40bobbo18boo261bo7bo18bo$43bo280b3o5bobo$40boo49bo177b3o51b
oob4obbobbo$39bobo48bobo231b3obbo20boo$40bobb3o44bobo176bobo53bobboobb
o17boo$41boobbo45bo178bo22boo34boobobo25bo$41bo3bo11boo212bo21boo38bo
10boo13bobo$42bobo12boo212boo71boo13bobo$44bo223boboobo33boo51bo$41bo
bbo8boo213b4oboo31bo46boo$41bo10bobbo43bo169b5o32bobbo42bobbo$53bobo
42bobo170boo31boob4o42boo3boo$40boobbo9bo43bobo202bo13boo5bobbo30boo$
41b3o55bo161b3o39bo3b3obbo4boo8bo40bo$90bobo167bo3bo38bobbobbob3o9bo
14bo28bobo$81bob3o4bobo166bo3boo40boo4b3o10bo3bo9boo27bobo$79boobo4bo
5bo166bo46boobobo12booboo8bobo27bo$28bo52boo4bobbobbo167b4o14bobo6bo
19boobo14bobo32boo$27b3o57bobbobbo169boboo21bo22bo16boboo7b3o18bobbo$
26booboo34bo20bo4bo171bobbo12bobo45bobbo3bo5bo20boo3boo$25boobobo33bob
o15bobbo178boo61bo7boo29boo$24b3obb3o32bobo16boo231boo9bobbo45bo$25bo
6bo12boo17bobbo235bo7bo4boo10boo45bobo$26b5obo12boo18bobo234b3o5bobo
62bobo$27b4oboo34bo194bo37boob4obbobbo24boo36bo$32bo34boo194bo38b3obbo
30boo$31bo12boo21bo194bobo38bobboobbo$44boo217bo43boobobo61boo$263boo
46bo62boo$263b3o118bo$29bo23boo211bo116bobo$27boobo22boo116boo88bobobb
o116bobo$170bobo87bo3boo118bo$30bo141bo88boobb3o109boo$27bobbo21boo11b
o200boo108bobbo$28bo17bo5boo323boo3boo$44boo213bo122boo$33boo9b3o19bo
29boo150b3o7bobbo11boo32bo$15bo10b3o37bo29boo153b3o5boboobb3o5boo31b4o
6boo$15bo16bo218b3o6bo3bo40bo4bo4b3oboo$15bob3o10boo220bo11bobbo36boo
10boob3obbo$17b3o11bo233boo38boboboo4b3oboobbobo47bo$18bo41boo19boo
223b3o6boo6bobo47boo$18boo40boo19bobo223bo16bo47bobo$19bo62bo$4bo14boo
260boo$281boo$8bo7booboo254bo$17b3o255boo33boo$3obo12bo255boobbo24bo7b
oo$3obo63boo19boo180bo4boo22booboo$bo8boo14boo40boo19bobo150b3o26b3o
26booboo78b3o$bbo3b3oboo13bobbo61bo180boo27boo$3bo6bo15boo218bo55boobo
$4bobobobo74boo155bo3boo55bobbo60boo$5bo79bobo156bobo56bobbo61boo$61bo
23bo155b3o60boo61bo10boo$61bo181bo97bo37boo$61bo279boo35bo$21boo42bo
176boo96bobo$21boo38b3obbo176boo10bo$60bo4bo177bo186bo$17boo41bo3bo
163bo14boo186bo$16bobbo41b3o163boo7bo5boo185b3o$17bobo206bobob3obbobo$
11b3o4bo206b3o3boo3bo15boo$9bo3boo45bobo163boboboobobo15bobbo53bo$3b3o
3bobobboo44bobo164booboo20boo29b3o20boo$8bo5bo40bo4bobo165bob5obo46b3o
21boo$9bobboo14bo10booboo6boboobboobbobo169b4o46bo3bo$9bo17b3o9boo8bob
5o5boo38boo180boob3o46boo$26booboo8boobobo5bo4boo44bobo179boo4bo46boo$
25boobobo11bobo11bobo42bo184bobbo45bo10boo$24b3obb3o11boo202boo38boo
20bo37boo$25bo6bo23b3o184bo3boo60boo35bo$9boo15b5obo210boo63bobo$9boo
16b4oboo209boo$32bo$31bo199bo9b3o$75boo157bo6b3o$74bobo125bo26bo12bo$
76bo126boboobobo17bo3bobbo$197b3o3b4o3bo18b3obbo21bobo$17boo184bobboob
oo19bo3bo21boo$17boo183bo29boo23bo$41boo157b3o29bo58b3o$41boo157b3o17b
oo81boo$220boo82boo$183bo119bo10boo$183bo51boo78boo$183bob3o47boo77bo$
185b3o$186bo6boo$49boo135boo5boo19bo$49boo136bo17boo5b5o$187boo16boo4b
ooboboo$205bobbo3bobobo$184booboo17b3o7bo13bo12boo$185b3o19bo5bo3bo12b
o12boo$185bo27bo3bo12bo8bo$214b4o19bobo$192boo22bo14b3obbo3bo$180bo11b
oo38bob5o32boo$181boboobobo49bo33boo$175b3o3b4o3bo25boo17boo36bo10boo$
181bobbooboo25boo67boo$180bo101bo$178b3o$178b3o6$238boo$238boo$232b3o
bbooboo$237boboobo$195bo41b3obbo$194boboo$180bobooboo7bobbo52boo$179b
5obboo7bo3bobo49boo$179bobb3obo11boobo48bo$185bo12b3o3$178bo$177b3o$
176b3obo5boo$175bo3bo6boo$174boobbobbo$173b3obb4o$175bo3bobbo$175bo6bo
$177bobbo$179booboo$179bo38boo$219boo$218bo6$160bo$159boo$158b5o$157bo
$156boo5bo17bobo$155b3oboo20boo$156boboboobboo16bo$157bobbobboo$159boo
25boo$161boobo22boo$164bo21bo11$167b3o!

This has a small improvement in an edge block puffer which could be copied back into the base rake. (The two-engine Cordership can create an edge block from a blinker, instead of using a larger sparking spaceship.)

EDIT 2:

I had overlooked a small edge block puffer, so the improvement just above is already obsolete. Here is the newest version.

Code: Select all

#C A diagonal c/12 triggered backward edge rake with large clearance.
#C This is based on a period 96 edge rake with additional components to
#C suppress output gliders unless input gliders are present.  This
#C example shows the rake being triggered by a period 288 (96 * 3)
#C sideways rake.  Backward gliders are created whose path is separated
#C from the edge of the convoy by 5.5 diagonal cells.  This is a small
#C improvement on a previous version.
#C David I. Bell, 14 August 2025
x = 432, y = 365, rule = B3/S23
143b3o$$147boo$149bo$143b4obo11bo$116b3o24b5o12bo$160bo$120boo$122bo
10b3o7bobo$116b4obo11bo9bobo$116b5o23bo$102bo40bobo$102bo30bobbo7boo
22bo$104bo5bo5bobo14boboo7bo23bo$103bo6bobo3bobo14bobbo31bo$102bo3bobb
o7bo15bobo5boo$103bobboboboo4bobo14b3o5boo$108boboo5boo$117bo$$176bo$
114boo60bo$105boo7boo60bo$105boo25boo$131bo$131boo$132boo$94b3o36bobbo
$134bobbo26bo19bo$98boo36bo26bobo18bo$100bo34bo26bo3bo13booboo$94b4obo
62bo3bo8bo$94b5o63bobob3o4boob3o$108bo54boobobbo5boboo$107bobo43bo13bo
bo8bo$94bobo10bobboo24b3o8bo5bo13boo11bobbo$94bobo11bobbo23bo3bo6bo7bo
25b3o9bo$95bo13b3o24boo9b4obboo36bobo$94bobo41booboo9b3o36bobo$95boo
43boo11bobo36bo$95bo11b3o44bo7boo$107bobo16b3o25bo7boo$110bobo13bobo
46boo$106bo6bo3boo7bobo45bobo$110boboo3boo7bo4boo43bo23bo$107bob3obbo
10b3o3boo66bobo$107boob5o16bo3boo62bobo$112bo14b4o4boo63bo$128boo51b3o
$99boo27bo$99boo51b3o24bo5bo$129bo26b3o20b7o12bo$127bobo22bobob3o22bo
17boo7bo$153bo27bo3bo13boo6bobo$126bo53bo17boobo5bobo$128b3o3boo45bo
18b3o5bo$126boobobob3o46bo4bo11boboo$114b3o8bo5bo50bo4bo11boo$113bo3bo
6bo7bo48boobobo12bo6boo$114boo9b4obboo47bobo23boo$116booboo9b3o48bo34b
o$118boo11bobo81bobo$132bo82bobo$132bo83bo3$169booboo12boo26boo$169boo
15boo8b3o15boo$138boo29boobobo23bo25bo$138boo32bobo22b3o23bobo$173boo
48bobo$193bo30bo$161bobo28bobo$132boo13bobo7bobbobbo29bo$120boo10bobbo
10booboo5boboboobo58boo$120boo10b5o10boboo6bo64boo$132boobbo14bo11b3o
66bo$134bo15bo13boo65bobo$132bobo15bo12boo66bobo$232bo3$128boo100boo$
128boo100boo$240bo$171b3o65bobo$169boobbo65bobo$168bo3bo67bo$163bo5bo
bbo46bo3boobboobo$162bobo4bobo47bo3boo4boboo$152boo17bo47bo3boobbooboo
6boo$152boo18bo50boo13boo$172bobo46bobbo23bo$172boo18bo3boobboobo17bob
o23bobo$192bo3boo4boboo16bo24bobo$192bo3boobbooboo36bo6bo$196boo43bo$
194bobbo43bo$160boo32bobo17boo30boo$160boo33bo18boo30boo$256bo$176boo
bbo74bobo$179bobo73bobo$178bo70bo6bo$187boo60bo$180boo5boo19bo13b3o24b
o$199boo4boo3boo12bo29boo$181boo15bobbo3bo5bo11bo30boo$180bo18bobbobb
oo3bo53bo$178booboo17bobo4bob3o51bobo$181boo17b3o7boo51bobo$179bo27bob
oboo44bo6bo$208boobo45bo$186boo22boo45bo$186boo74boo$170bo3boobboobo
80boo$170bo3boo4boboo24boo62bo$170bo3boobbooboo25boo35bo25bobo$174boo
68bobo5bo18bobo$172bobbo74booboo17bo$172bobo69b3obbo3boo9boo$173bo43bo
32booboo8bobbo$217bo32b4o10boo4boo$219bo5bo44boo$218bo6bobo52bo$217bo
3bobbo54bobo$218bobboboboo52bobo$223boboo36bo16bo$237boo23bobo8boo$
237boo23bobbo6bobbo$189boo72boo8boo3boo$188boboo86boo$173boobb5o6bobb
oo95bo$173bo7bo11bo6b3o84bobo$173bo4boboo13bo4b3o7boo75bobo$177b3o12bo
bo4bo3bo6boo76bo$193bo6boob3o11b3obbo58boo$200boo4bo10b4obo6boo49bobbo
$203bobbo13bo21boo37boo3boo$204boo15bobo7boo8bobo42boo$180boo40boo3bo
4boo9bo52bo$180boo50bo39bo22bobo$228b4o24booboo6boboobboo20bobo$195bo
13boo10boo7bo25boo8bob5o23bo$195bo13boo10boo33boobobo5bo4boo15boo$197b
o5bo55bobo11bobo12bobbo$196bo6bobo25boo27boo27boo3boo$195bo3bobbo28boo
40b3o6boo10boo$196bobboboboo77boo20bo$201boboo98bobo$303bobo$304bo$
297boo$283boo11bobbo$257bo24bobbo11boo3boo$249b3o3b4o23bobboo3boo10boo
$249bobo3booboo22boboo4boo20bo$249b3obbo24bobbobo26bobo$254boo3bo19boo
30bobo$255b4o3boo14bo33bo$204boo3bo46b3o3boo9boobboo26boo$202b3o4boo
62boobbo26bobbo$197b3obo8boo5bo56boboo27boo3boo$201bobobb5o5bobo56boo
33boo$202bo3b3o7bobo101bo$217bo101bobo$65bobo251bobo$65bobobo7bo134boo
106bo$64bobboobo4b3o235boo$65boo3boboboobo135boo49bo47bobbo$65boo3boob
5o125boo9bo38boo9b3o46boo3boo$69boboo3boo125boo47bobobo7b3o51boo$68bob
o16boo163bo3boo5bo3bo60bo$87boo164boo8b4o60bobo$253b3o7boboo60bobo$
328bo3$326boo$326boo$95boo160boo77bo$85bobbo6boo160boo76bobo$72boobo6b
oobobboo177boo66bobo$72b6o4boobo4bo175bobo67bo$78bo3boo184bo60boo$70b
3o6bo4bo4boo237bobbo$56b3o11boo6bo5booboo240boo3boo$54b7o273boo$53b9o
9bo4bo267bo$52bo7b3o12bo193bo73bobo$53b3o6bo204booboo71bobo$54boo211b
ooboo72bo$57bo209boo68boo$58bo24bo185boobo63bobbo$59bo22bobo185bobbo
63boo3boo$82bobo185bobbo68boo$83bo187boo12boo65bo$62boo221boo64bobo$
40b3o18bobbo286bobo$40bobbo18boo261bo7bo18bo$43bo280b3o5bobo$40boo49bo
177b3o51boob4obbobbo$39bobo48bobo231b3obbo20boo$40bobb3o44bobo176bobo
53bobboobbo17boo$41boobbo45bo178bo22boo34boobobo25bo$41bo3bo11boo212bo
21boo38bo10boo13bobo$42bobo12boo212boo71boo13bobo$44bo223boboobo33boo
51bo$41bobbo8boo213b4oboo31bo46boo$41bo10bobbo43bo169b5o32bobbo42bobbo
$53bobo42bobo170boo31boob4o42boo3boo$40boobbo9bo43bobo202bo13boo5bobbo
30boo$41b3o55bo161b3o39bo3b3obbo4boo8bo40bo$90bobo167bo3bo38bobbobbob
3o9bo14bo28bobo$81bob3o4bobo166bo3boo40boo4b3o10bo3bo9boo27bobo$79boob
o4bo5bo166bo46boobobo12booboo8bobo27bo$28bo52boo4bobbobbo167b4o14bobo
6bo19boobo14bobo32boo$27b3o57bobbobbo169boboo21bo22bo16boboo7b3o18bobb
o$26booboo34bo20bo4bo171bobbo12bobo45bobbo3bo5bo20boo3boo$25boobobo33b
obo15bobbo178boo61bo7boo29boo$24b3obb3o32bobo16boo231boo9bobbo45bo$25b
o6bo12boo17bobbo235bo7bo4boo10boo45bobo$26b5obo12boo18bobo234b3o5bobo
62bobo$27b4oboo34bo194bo37boob4obbobbo24boo36bo$32bo34boo194bo38b3obbo
30boo$31bo12boo21bo194bobo38bobboobbo$44boo217bo43boobobo61boo$263boo
46bo62boo$263b3o118bo$29bo23boo211bo116bobo$27boobo22boo116boo88bobobb
o116bobo$170bobo87bo3boo118bo$30bo141bo88boobb3o109boo$27bobbo21boo11b
o200boo108bobbo$28bo17bo5boo323boo3boo$44boo213bo122boo$33boo9b3o19bo
29boo150b3o7bobbo11boo32bo$15bo10b3o37bo29boo153b3o5boboobb3o5boo31b4o
6boo$15bo16bo218b3o6bo3bo40bo4bo4b3oboo$15bob3o10boo220bo11bobbo36boo
10boob3obbo$17b3o11bo233boo38boboboo4b3oboobbobo47bo$18bo41boo19boo
223b3o6boo6bobo47boo$18boo40boo19bobo223bo16bo47bobo$19bo62bo$4bo14boo
260boo$281boo$8bo7booboo254bo$17b3o255boo33boo$3obo12bo255boobbo24bo7b
oo$3obo63boo19boo180bo4boo22booboo$bo8boo14boo40boo19bobo150b3o26b3o
26booboo78b3o$bbo3b3oboo13bobbo61bo180boo27boo$3bo6bo15boo218bo55boobo
$4bobobobo74boo155bo3boo55bobbo60boo$5bo79bobo156bobo56bobbo61boo$61bo
23bo155b3o60boo61bo10boo$61bo181bo97bo37boo$61bo279boo35bo$21boo42bo
176boo96bobo$21boo38b3obbo176boo10bo$60bo4bo177bo186bo$17boo41bo3bo
163bo14boo186bo$16bobbo41b3o163boo7bo5boo185b3o$17bobo206bobob3obbobo$
11b3o4bo206b3o3boo3bo15boo$9bo3boo45bobo163boboboobobo15bobbo53bo$3b3o
3bobobboo44bobo164booboo20boo29b3o20boo$8bo5bo40bo4bobo165bob5obo46b3o
21boo$9bobboo14bo10booboo6boboobboobbobo169b4o46bo3bo$9bo17b3o9boo8bob
5o5boo38boo180boob3o46boo$26booboo8boobobo5bo4boo44bobo179boo4bo46boo$
25boobobo11bobo11bobo42bo184bobbo45bo10boo$24b3obb3o11boo202boo38boo
20bo37boo$25bo6bo23b3o184bo3boo60boo35bo$9boo15b5obo210boo63bobo$9boo
16b4oboo209boo$32bo$31bo199bo9b3o$75boo157bo6b3o$74bobo125bo26bo12bo$
76bo126boboobobo17bo3bobbo$197b3o3b4o3bo18b3obbo21bobo$17boo184bobboob
oo19bo3bo21boo$17boo183bo29boo23bo$41boo157b3o29bo58b3o$41boo157b3o17b
oo81boo$220boo82boo$183bo119bo10boo$183bo51boo78boo$183bob3o47boo77bo$
185b3o$186bo6boo$49boo135boo5boo19bo$49boo136bo17boo5b5o$187boo16boo4b
ooboboo$205bobbo3bobobo$184booboo17b3o7bo13bo12boo$185b3o19bo5bo3bo12b
o12boo$185bo27bo3bo12bo8bo$214b4o19bobo$192boo22bo14b3obbo3bo$180bo11b
oo38bob5o32boo$181boboobobo49bo33boo$175b3o3b4o3bo25boo17boo36bo10boo$
181bobbooboo25boo67boo$180bo101bo$178b3o$178b3o6$238boo$238boo$232b3o
bbooboo$237boboobo$195bo41b3obbo$194boboo$180bobooboo7bobbo52boo$179b
5obboo7bo3bobo49boo$179bobb3obo11boobo48bo$185bo12b3o3$178bo$177b3o$
176b3obo5boo$175bo3bo6boo$174boobbobbo$173b3obb4o$175bo3bobbo$175bo6bo
$177bobbo$179booboo$179bo38boo$219boo$218bo6$160bo$159boo$158b5o$157bo
$156boo5bo17bobo$155b3oboo20boo$156boboboobboo16bo$157bobbobboo$159boo
25boo$161boobo22boo$164bo21bo11$167b3o!

EDIT 3:

Here is the smaller edge rake using the simpler block puffer.

Code: Select all

#C A diagonal c/12 period 96 backward edge rake with large clearance.
#C This uses several edge puffers, sideways rakes, and a two-engine
#C Cordership.  Backward gliders are created whose path is separated
#C from the edge of the convoy by 5.5 diagonal cells.  This is a
#C smaller version of a previous rake.
#C David I. Bell, 20 August 2025
x = 239, y = 210, rule = B3/S23
51bo7bo$50b3o5bobo$49boob4obbobbo$50b3obbo$51bobboobbo$24bo7bo22boobob
o$23b3o5bobo25bo$22boob4obbobbo$23b3obbo$24bobboobbo37b3o$28boobobo$
32bo10boo$43boo$6boo$5bo$5bobbo$3boob4o$bbo13boo5bobbo50b3o$bbo3b3obbo
4boo8bo$bbobbobbob3o9bo14bo12bo$4boo4b3o10bo3bo9boo11boo$6boobobo12boo
boo8bobo9bobo$7boobo14bobo$10bo16boboo7b3o$26bobbo3bo5bo$26bo7boo39bo
9b3o$15boo9bobbo45bo$bbo7bo4boo10boo46bo$b3o5bobo64boo$oob4obbobbo24b
oo37b3o$b3obbo30boo37boo$bbobboobbo38bo$6boobobo34booboo43bo$10bo82bob
o$49boo42bobo$50bo24bo18bo$44bo3bo15boo10bo$48bo3bo11boo9bo3$33boo11bo
55bo$36boo4bo4b3o51bobo$6bo26boob4o3bo57bobo$5b4o6boo13b5o4b4o22bo36bo
$4bo4bo4b3oboo13b3o6bo4b3o13bobo$3boo10boob3obbo10bo12b3o13bobo$4bobob
oo4b3oboobbobo8b3o11booboo12bo$5b3o6boo6bobo15bo10bo12b3o$6bo16bo16bo
8b3o12bobo22bo20bo$88bobo5bo12bobo$45boo16boboo27booboo10bobo$36boo7b
oo15bobbo22b3obbo3boo11bo$36boo56booboo$9boo15bo32bobbo31b4o$9boo13boo
boo30b7o42boo$59b3obboo42boo$27boo89bo$28bo88bobo$22bo3bo90bobo$26bo3b
o87bo3$24bo56bo34boo$25b3o52bobo33boo$79booboo42bo$79booboo7bo33bobo$
25b3o50b3o10bo33bobo$25b3o50b3o3bo6bo3bo30bo$25booboo11bo36b3o4bo8bobo
$29bo11boo36boo5bo8bo$27b3o11b3o13b3o19b3o42boo$40b3o14bobo20boo42boo$
38bobbo14bo3bo20boo51bo$38bo17bo3bo72bobo$40bo15bo17boo57bobo$39bo16bo
4boo11boo4bo53bo$56bo6bo15bobo28b3o$57bo5bo14b4o28bobo$30boo25boo18boo
bo28bo3bo18boo$30boo27bo3bo13booboo27bo3bo18boo$60bobo10boo3boo29bo17b
oo13bo$74bo34bo4boo11boo12bobo$73b3o33bo6bo24bobo$57b3o50bo5bo25bo$56b
o3bo13bo22bo12boo$57bobbo14bo20boo7bo6bo3bo$59boo13boo19bobob3obbobo6b
obo10boo12boo$74bo19b3o3boo3bo21bo12boo$95boboboobobo21b3o6boo13bo$71b
obbo21booboo9b3o22boo12bobo$73b4o20bob5obo3bo3bo13bo21bobo$70bo30b4o5b
obbo14bo21bo$71boobboo35boo13boo$128bo$62boo7boo35boo15b3o20boo$62boo
6boo27boo7boo14bo3bo19boo$71boobbo23boo22b3oboo29bo$123bobob3o27bobo$
88b3o31b3obb3o27bobo$88bobo67bo$87bo3bo$87bo3bo$70boo15bo68boo$70boo
15bo4boo62boo$87bo6bo71bo$88bo5bo70bobo$88boo75bobo$90bo3bo71bo$91bobo
$$164boo4bo4bo$88b3o73boo4boo3boo$87bo3bo83b3o$88bobbo11b3o68b3o$90boo
12boo67bobo$102boboo67boo$103bo$102bo5boo60bo$101boo66bobbo$44bo56boo
70bo$44bo123bo4bo$44bo127boo$47boo44boo$47boo12boo30boo53bo20b3o$42bo
3b3o11boo86boo$43b3o15bo85bobo$44bo15b3o$28b3o12boo15b3o$37bo5b3o16bo$
30boo5b3o5bo14bobbo141bo$30b4o4bo4bo16b3o5boo14bobo119bo$30boob3oboo6b
o15bo6boo14b3o117b3o$35bobo5b3o38boo13bo$97boo$98boo$87bo$41boo42bobo
54boo$32boo7boo42b3o55boo27bo$32boo25boo27bo53bo25b4oboo5b3o$58bobbo
22b5o27bo50boob3oboo4b3o$59bo56boo50bob3obo7boo$22bo36boo54bobo51bo3b
4o4boo$22bo39boo8b3o6bo90boob3o$22bo38b3o9boo3boobo91b5o13boo$25boo36b
o8boo5bobo92bo16boo$25boo34boo14b3obo$20bo3b3o53boo$21b3o$22bo128boobb
o$21boo11b3o117bobo$21b3o10boobo115bo16bo$23bo13boo131bo$21bo14boo72b
oo43boo13bo$23bo87boo84bobo$21b3o86bo45boo12boo25bo$35bo48bo70bo13bobb
o21bo4boo$34b3o47boo67booboo11bobo22boo3bo$34bo3boo43bobo70boo10boo24b
o4boo$33b4o3bo3boo108bo13bo26b3oboo$34bo5bo3boo28b3o94boo22boo$34b4obb
oo129boo$35bobb3o130boo64bo$168boobo66bo$169b3o64b3o$26boo56bo85bo$26b
oo55bobo$85bo$84bo$78boo78boo$79boo77boo$78bo$17bo$16boo15bobo$15b5o
13boo$14bo19bo$13boo5bo$12b3oboo148boo$13boboboobboo143boo$14bobbobboo
$9bo6boo$8b3o7boobo$7b3obo9bo$6bo3bo$5boobbobbo$4b3obb4o33boo$6bo3bobb
o33boo$6bo6bo32bo$8bobbo$10booboo$10bo4$9boo$11bo$9boo4$15bo$15boo$7b
3o4boboo$14boboo$14b4o$16boobo$17boo$18bo3$15b3o!
[code]

BCNU,
-dbell