熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

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GUYTU6J
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » February 26th, 2022, 9:30 am

If you download this, make sure to leave a comment!
immigration-figure-eight.mc
(64.96 KiB) Downloaded 23 times
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

Naszvadi
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by Naszvadi » February 27th, 2022, 7:13 am

GUYTU6J wrote:
February 26th, 2022, 9:30 am
If you download this, make sure to leave a comment!
immigration-figure-eight.mc
Question: is this a multicolour CGoL unit cell? How many alive states have been implemented?

Great work!

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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by yujh » February 27th, 2022, 12:36 pm

GUYTU6J wrote:
February 26th, 2022, 9:30 am
If you download this, make sure to leave a comment!
immigration-figure-eight.mc
Very smart. That uses streams from two different sides with one that is 99% capped. I still haven't got to see how it work, but it's definitely worth some OCA DOTY.
Nothing to apgsearch? Try b38s23/C1!

B34kz5e7c8/S23-a4ityz5k!!!

b2n3-q5y6cn7s23-k4c8

B3-kq6cn8/S2-i3-a4ciyz8

B3-kq4z5e7c8/S2-ci3-a4ciq5ek6eik7

Rule modifier

If you need someone to apgsearch, or if you want to search for an explosive rule, contact me on discord!

Bored of Conway's Game of Life? Try Pedestrian Life -- not pedestrian at all!

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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by dvgrn » March 4th, 2022, 9:12 pm

Naszvadi wrote:
February 27th, 2022, 7:13 am
Question: is this a multicolour CGoL unit cell? How many alive states have been implemented?

Great work!
Immigration is three-state, two colors of live cells, shown here by sparse horizontal lines or (what looks at a distance like) completely filled metacells.

The figure-eight pattern runs great at any step range around 2^20 - 2^24, once Golly works its way through a full cycle and gets its hash tables populated. The period is 16777216 = 2^24, and the size is an equally gargantuan 327680x327680 -- a very nice piece of work!

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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » March 13th, 2022, 8:48 am

Finally, some appreciation to my stable circuitry! For a different taste, I seeked for moving technology.
GUYTU6J wrote:
August 28th, 2021, 2:39 am
It has been two years since invention of this rule, but activity on my side may be decreasing due to real life.
Looking back at the 3c/20o realm, FWKnightship's 6c/40o on the first page can be turned to a compact p20 siderake...
A class of p40+20n forerake will be possible if there is a suitable p20 dot sparker for the following T-to-T+blinker reaction. A single 3c/20o ship does not work for me.

Code: Select all

x = 105, y = 30, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
94bo$93b3o$93b3o5$54bo$5bo17bo21bo7b3o7bo21bo17bo$5bo17bo20b3o6b3o6b3o
19b3o15b3o$4b3o15b3o19bobo15bobo19b3o15b3o$5bo17bo21bo17bo$4b3o15b3o
19b3o15b3o19b3o15b3o$5bo17bo20bobo15bobo19bobo15bobo$14bo30bo17bo21bo
17bo$5bo7b3o7bo60bobo15bobo$3b2ob2o5b3o5b2ob2o$43b5o13b5o$43bo3bo13bo
3bo$2b3ob3o11b3ob3o16bobobo13bobobo$3ob3ob3o7b3ob3ob3o15b3o15b3o$o2bo
3bo2bo7bo2bo3bo2bo$o3bobo3bo7bo3bobo3bo$b3o3b3o9b3o3b3o2$13b3o37b3o37b
3o3$14b3o37b3o37b3o$14b3o37b3o37b3o!
Slight adjustion to the back-to-side reflector brings trailing pair of 3c/20o in the rake in phase, benefiting population at the cost of one-cell wider bounding box:

Code: Select all

x = 26, y = 74, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
5bo13bo$4b3o11b3o$4b3o11b3o2$4b3o11b3o$4bobo11bobo$5bo13bo$4bobo11bobo
2$12bo2$12bo$11b3o2$3bo$2b3o$b2ob2o$3bo2$3bo16b3o$2bobo15bobo$3bo17bo$
3bo8bo8bo$bo3bo15bo$o2bo2bo5bo6bo3bo$o2bo2bo4b3o6bobo$2obob2o$20bobo$
2b3o14b5o$20b3o$21bo11$5bo13bo$4b3o11b3o$4b3o11b3o2$4b3o11b3o$4bobo11b
obo$5bo13bo$4bobo11bobo2$12bo2$12bo$11b3o2$3bo$2b3o$b2ob2o$3bo$22bo$3b
o17b3o$2bobo15b2ob2o$3bo18bo$3bo8bo$bo3bo16bo$o2bo2bo5bo8bobo$o2bo2bo
4b3o8bo$2obob2o15bo$20bo3bo$2b3o14bo2bo2bo$19bo2bo2bo$19b2obob2o2$21b
3o!
The forerake mechanism above has not seen a completion, but another 3c/20o can be added to the back to convert the blinker to a sideways T-ship. If the blinker is deleted instead, it becomes a simple 5-tick delayer to change parity.

Code: Select all

x = 93, y = 34, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
b3o15b3o29b3o15b3o$2bo17bo31bo17bo2$2bo17bo31bo17bo$b3o15b3o29b3o15b3o
$2bo17bo31bo17bo$2bo17bo31bo17bo$o3bo13bo3bo27bo3bo13bo3bo2$o3bo13bo3b
o27bo3bo13bo3bo2$2bo17bo31bo17bo2$2bo$b3o$bobo$2bo$b3o47b3o$bobo48bo$
2bo$51b3o$51b3o$5o46bobo$o3bo46b3o$obobo47bo$b3o6$11bo49bo29bo$10b3o
47b3o27b3o$10b3o47b3o27b3o!
In CGoL, the c/10 technology often starts with converting a glider to an active region like Herschel. Likewise, converting a T-ship to a cloverleaf would be useful. It can be done with three engines at p80+:

Code: Select all

x = 74, y = 30, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
5bo13bo$4b3o11b3o$4b3o11b3o2$4b3o11b3o$4bobo11bobo$5bo13bo$4bobo11bobo
2$12bo$70bo$12bo57b2obo$11b3o56bo2$3b3o$2bo3bo$2bo3bo$4bo2$4bo$3bobo$
4bo$3bobo24bo$3bobo24b2obo$bobobobo22bo$2o2bo2b2o$b2o3b2o$2b5o$4bo$4bo!
With some useful 3c/20o + cloverleaf reactions, long-period forerakes are possible; here are glide-symmetric one-signal p2880 and nine-signal p320 rakes. Now I feel like Christoph Reinthaler

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 593, y = 217, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
43bo319bo$42b3o317b3o$42b3o317b3o2$42b3o317b3o$42bobo317bobo$43bo319bo
$42bobo317bobo8$35bo17bo165bo17bo117bo17bo165bo17bo$33bo3bo13bo3bo161b
o3bo13bo3bo113bo3bo13bo3bo161bo3bo13bo3bo2$35bo17bo165bo17bo117bo17bo
165bo17bo$33bo3bo13bo3bo161bo3bo13bo3bo113bo3bo13bo3bo161bo3bo13bo3bo$
34bobo15bobo163bobo15bobo115bobo15bobo163bobo15bobo$35bo17bo165bo17bo
117bo17bo165bo17bo$33bo3bo13bo3bo161bo3bo13bo3bo113bo3bo13bo3bo161bo3b
o13bo3bo$35bo17bo165bo17bo117bo17bo165bo17bo$35bo17bo165bo17bo117bo17b
o165bo17bo$30bo4bo4bo7bo4bo4bo155bo4bo4bo7bo4bo4bo107bo4bo4bo7bo4bo4bo
155bo4bo4bo7bo4bo4bo$33bo3bo13bo3bo161bo3bo13bo3bo113bo3bo13bo3bo161bo
3bo13bo3bo$28bobo9bobo3bobo9bobo151bobo9bobo3bobo9bobo103bobo9bobo3bob
o9bobo151bobo9bobo3bobo9bobo$34b3o15b3o163b3o15b3o115b3o15b3o163b3o15b
3o2$548bo$32bo5bo11bo5bo159bo5bo11bo5bo111bo5bo11bo5bo159bo5bo4b3o4bo
5bo$547b3o$35bo201bo117bo201bo$34b3o199b3o115b3o199b3o$34b3o199b3o115b
3o199b3o$35bo201bo117bo201bo2$33bo3bo197bo3bo113bo3bo197bo3bo$33b5o
197b5o113b5o197b5o$34bobo199bobo115bobo199bobo$34b3o199b3o115b3o199b3o
7$387bo$384bob2o$387bo22$445bo$445b2obo$20bo13bo203bo13bo87bo13bo90bo
112bo13bo$19b3o11b3o201b3o11b3o85b3o11b3o201b3o11b3o$19b3o11b3o201b3o
11b3o85b3o11b3o201b3o11b3o2$19b3o11b3o201b3o11b3o85b3o11b3o201b3o11b3o
$19bobo11bobo201bobo11bobo85bobo11bobo201bobo11bobo$20bo13bo203bo13bo
87bo13bo203bo13bo$19bobo11bobo201bobo11bobo85bobo11bobo201bobo11bobo2$
27bo217bo101bo217bo2$27bo217bo101bo217bo$26b3o215b3o99b3o15bo199b3o$
363b3o$18b3o231b3o83b3o22b3o206b3o$17bo3bo229bo3bo81bo3bo229bo3bo$17bo
3bo229bo3bo81bo3bo229bo3bo$19bo233bo85bo233bo2$19bo233bo85bo233bo$18bo
bo231bobo83bobo231bobo$19bo233bo85bo233bo$18bobo6bo199bo17bo6bobo83bob
o6bo199bo17bo6bobo$18bobo203bob2o24bobo83bobo203bob2o24bobo$16bobobobo
4bo199bo17bo4bobobobo79bobobobo4bo199bo17bo4bobobobo$15b2o2bo2b2o2b3o
215b3o2b2o2bo2b2o77b2o2bo2b2o2b3o215b3o2b2o2bo2b2o$16b2o3b2o227b2o3b2o
79b2o3b2o227b2o3b2o$17b5o229b5o81b5o229b5o$19bo233bo85bo233bo$19bo233b
o85bo233bo22$3bo265bo53bo265bo$2b3o263b3o51b3o263b3o$b2ob2o261b2ob2o
49b2ob2o261b2ob2o$3bo265bo53bo265bo2$3bo265bo53bo265bo$2bobo263bobo51b
obo263bobo$3bo265bo53bo265bo$3bo265bo53bo265bo$bo3bo261bo3bo49bo3bo
261bo3bo$o2bo2bo259bo2bo2bo47bo2bo2bo259bo2bo2bo$o2bo2bo259bo2bo2bo47b
o2bo2bo259bo2bo2bo$2obob2o259b2obob2o47b2obob2o259b2obob2o$334b3o$2b3o
263b3o51b3o9bo2bo250b3o$337bo$330bo4b3o$329b3o2bobo211bo$330bo2bob2o
210b3o$331b3o2b2o209b3o$332b3obo$335bo2$6bo259bo59bo259bo$5bobo257bobo
57bobo257bobo$5bobo27bo17bo165bo17bo27bobo57bobo27bo17bo165bo17bo27bob
o$5bobo26b3o15b3o163b3o15b3o26bobo57bobo26b3o15b3o163b3o15b3o26bobo$5b
3o26b3o15b3o163b3o15b3o26b3o57b3o26b3o15b3o163b3o15b3o26b3o$35bo17bo
165bo17bo117bo17bo165bo17bo$6bo259bo59bo259bo$5b3o25bo3bo13bo3bo161bo
3bo13bo3bo25b3o57b3o25bo3bo13bo3bo161bo3bo13bo3bo25b3o$33b5o13b5o161b
5o13b5o113b5o13b5o161b5o13b5o$4bo3bo25bobo15bobo163bobo15bobo25bo3bo
55bo3bo25bobo15bobo163bobo15bobo25bo3bo$3b7o24b3o15b3o163b3o15b3o24b7o
53b7o24b3o15b3o163b3o15b3o24b7o$bo4bo4bo249bo4bo4bo49bo4bo4bo249bo4bo
4bo$2o2bo3bo2b2o247b2o2bo3bo2b2o47b2o2bo3bo2b2o247b2o2bo3bo2b2o$bo3bob
o3bo249bo3bobo3bo49bo3bobo3bo249bo3bobo3bo$2b3o3b3o251b3o3b3o51b3o3b3o
251b3o3b3o$3bo5bo253bo5bo53bo5bo253bo5bo4$53bo165bo153bo165bo$52b3o
163b3o151b3o163b3o6b3o$53bo165bo153bo165bo$53bo165bo153bo165bo$52b3o
163b3o151b3o163b3o$52b3o163b3o151b3o163b3o$52bobo163bobo151bobo163bobo
$53bo165bo153bo165bo$9bo42b3o163b3o42bo65bo42b3o163b3o42bo$8b3o41bobo
163bobo41b3o63b3o41bobo163bobo41b3o$8b3o41b3o163b3o41b3o63b3o41b3o163b
3o41b3o2$7b5o249b5o61b5o249b5o$9bo253bo65bo253bo$570b3o$7b5o249b5o61b
5o238bo2bo7b5o$8b3o251b3o63b3o238bo3bo8b3o$8b3o251b3o63b3o238bo3bo8b3o
$8b3o251b3o63b3o238bo2bo9b3o11$363b3o$364bo2$364bo8$50b3o167b3o147b3o
167b3o$51bo169bo149bo169bo$51bo169bo149bo169bo$50b3o167b3o147b3o167b3o
2$49bobobo165bobobo145bobobo165bobobo$49bobobo165bobobo145bobobo165bob
obo$51bo169bo149bo169bo$50b3o167b3o147b3o167b3o$51bo169bo149bo169bo!
The collection of said reactions is still very small. Out of the 20 possible phase combinations, I have only tried the one with smallest population, and even this is very likely incomplete. Not shown are large amounts of cloverleaf-removing interactions.

Code: Select all

x = 284, y = 389, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo99bo59bo49bo$10b3o97b3o57b3o47b3o$10bob2o96bob2o56bob2o46bob2o46$
35bo$34b3o$34b3o2$34b3o$34bobo$35bo$34bobo5$142bo60bo$141b3o58b3o$141b
3o58b3o46bo$250b3o$141b3o58b3o45b3o$141bobo58bobo$142bo60bo46b3o$141bo
bo58bobo45bobo$251bo$250bobo31$11bo69bo59bo48bo50bo39bo$10b3o67b3o57b
3o46b3o48b3o37b3o$10bob2o66bob2o56bob2o45bob2o47bob2o36bob2o49$72bo$
71b3o198bo$71b3o56bo49bo90b3o$129b3o47b3o48bo40b3o$71b3o55b3o47b3o47b
3o$71bobo155b3o39b3o$40bo31bo56b3o47b3o89bobo$39b3o29bobo55bobo47bobo
47b3o40bo$39b3o88bo49bo48bobo39bobo$129bobo47bobo48bo$39b3o187bobo$39b
obo$40bo$39bobo66$11bo$10b3o$10bob2o23$bo$3o$3o2$3o$obo$bo$obo58$11bo
49bo59bo59bo$10b3o47b3o57b3o57b3o$10bob2o46bob2o56bob2o56bob2o51$31bo
111bo$30b3o109b3o$30b3o109b3o2$30b3o109b3o25bo$30bobo109bobo24b3o$31bo
111bo25b3o$30bobo109bobo$91bo77b3o$90b3o76bobo$90b3o77bo$169bobo$90b3o
$90bobo$91bo$90bobo!
EDIT: it took me a while to build a fore-to-side reflector, which got used in the following fixed asymmetric p820 siderake:

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 82, y = 176, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
43bo13bo$42b3o11b3o$41b2ob2o9b2ob2o$43bo13bo2$43bo13bo$42bobo11bobo$
43bo13bo$43bo13bo$41bo3bo9bo3bo$40bo2bo2bo7bo2bo2bo$40bo2bo2bo7bo2bo2b
o$40b2obob2o7b2obob2o2$42b3o11b3o3$50bo2$50bo10bo13bo$49b3o8b3o11b3o$
61bo13bo$60bobo11bobo$60bobo11bobo$60b3o11b3o$60bobo11bobo$55bo11bobo
11bo$60b3o4b3o4b3o$61bo13bo$61bo13bo$50bo$21b3o11b3o$22bo13bo13bo$22bo
13bo12b3o7bo$21b3o11b3o20b3o$59bo$20bobobo9bobobo20bo$20bobobo9bobobo
19b3o7bo$22bo13bo21b3o15b3o$21b3o11b3o20bobo7bo8bo$22bo13bo22bo7b3o$
58b3o15b3o$58bobo15b3o$50bo7b3o15bobo$21bo6b3o45b3o$21bo6b3o19bo26bo$
20b3o6bo19b3o$21bo$20b3o43b2o$21bo43b3o$45b3o18b2o$21bo24bo9b2o$19b2ob
2o31b3o$46bo9b2o2$18b3ob3o$16b3ob3ob3o$16bo2bo3bo2bob3o$16bo3bobo3bob
3o$17b3o3b3o3bo23$4b3o2$3bo3bo$4b3o3$5bo31bo17bo$4bobo28bo3bo13bo3bo$
3b2ob2o$3b5o29bo17bo$4bobo28bo3bo13bo3bo$b2obobob2o26bobo15bobo$2obo3b
ob2o26bo17bo$b2o5b2o25bo3bo13bo3bo$2b2obob2o28bo17bo$37bo17bo$32bo4bo
4bo7bo4bo4bo$35bo3bo13bo3bo$30bobo9bobo3bobo9bobo$36b3o15b3o3$34bo5bo
11bo5bo2$37bo$36b3o$36b3o$37bo$8bo$7b3o25bo3bo$8bo26b5o$7bobo26bobo$7b
obo26b3o$7b3o$7bobo$2bo11bo$7b3o$8bo$8bo12$10b3o$11bo2$10b3o$10b3o$10b
obo$10b3o$11bo24$53bo$52b3o$52bobo$53bo$52b3o$52bobo$53bo3$51b5o$51bo
3bo$51bobobo$52b3o!
EDIT2 on March 15:
GUYTU6J wrote:
March 1st, 2020, 12:22 am
alternative 3-engine 6c/40

Code: Select all

x = 21, y = 45, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
bo13bo$3o11b3o$3o11b3o2$3o11b3o$obo11bobo$bo13bo$obo11bobo2$8bo2$8bo$
7b3o10$8bo2$8bo$7b3o5$17bo$16b3o$15b2ob2o$17bo2$17bo$16bobo$17bo$17bo$
15bo3bo$14bo2bo2bo$14bo2bo2bo$14b2obob2o2$16b3o!
This back-to-fore reflector, when combined with cloverleaf-to-back converter, happens to give the output on the same lane as the single cloverleaf-to-fore converter. Surely it can be put on the other side, allowing for finer adjustment of output timing at the cost of increased repeat time:

Code: Select all

x = 128, y = 134, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
71bo49bo$70bobo47bobo$20bo48b5o45b5o$19bobo47b2ob2o45b2ob2o$18b5o47b3o
47b3o$18b2ob2o48bo49bo$19b3o48b3o47b3o$8b2o10bo37b2o10b3o35b2o10b3o$8b
4o7b3o36b4o8b3o35b4o8b3o$7bo2b3o6b3o35bo2b3o5b2obob2o32bo2b3o5b2obob2o
$b3o6bob2o5b3o29b3o6bob2o4b2obob2o26b3o6bob2o4b2obob2o$b3o6b3o4b2obob
2o27b3o6b3o2b3ob5ob3o23b3o6b3o2b3ob5ob3o$11bo5b2obob2o37bo3b3o3bo3b3o
33bo3b3o3bo3b3o$14b3ob5ob3o38b2o3bobo3b2o37b2o3bobo3b2o$14b3o3bo3b3o
40b3o3b3o41b3o3b3o$14b2o3bobo3b2o40b3o3b3o41b3o3b3o$16b3o3b3o$16b3o3b
3o7$69b3o$70bo2$69b3o$69b3o$69bobo$69b3o$70bo48b3o$119bobo$119bobo2$
119bobo$119bobo$120bo2$119b3o$118b5o$117b2obob2o$118bobobo$119b3o$120b
o23$8b2o48b2o48b2o$8b4o46b4o46b4o$7bo2b3o44bo2b3o44bo2b3o$b3o6bob2o37b
3o6bob2o37b3o6bob2o$b3o6b3o38b3o6b3o38b3o6b3o$11bo49bo49bo24$21bo49bo
49bo$20bobo47bobo47bobo$19b5o45b5o45b5o$19b2ob2o45b2ob2o45b2ob2o$20b3o
47b3o47b3o$21bo49bo49bo$20b3o47b3o47b3o$20b3o47b3o47b3o$20b3o47b3o47b
3o$18b2obob2o43b2obob2o43b2obob2o$18b2obob2o43b2obob2o43b2obob2o$15b3o
b5ob3o37b3ob5ob3o37b3ob5ob3o$15b3o3bo3b3o37b3o3bo3b3o37b3o3bo3b3o$15b
2o3bobo3b2o37b2o3bobo3b2o37b2o3bobo3b2o$17b3o3b3o41b3o3b3o41b3o3b3o$
17b3o3b3o41b3o3b3o41b3o3b3o7$b3o$2bo$2bo48b3o$b3o48bo$101b3o$obobo46b
3o48bo$obobo46b3o$2bo48bobo48bo$b3o47b3o47b3o$2bo49bo49bo$102bo$100bo
3bo2$100bo3bo2$102bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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GUYTU6J
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Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » March 19th, 2022, 12:54 am

1700th post milestone
There is another way to emit T-ships sideways with 3c/20o technology, namely by using a reverse-Heisenburp to retrieve data stored in cloverleaves with passing spaceships. (I call it reverse since in a normal Heisenburp you detect a moving signal with a static device, but here you detect a static signal with a moving device.) Two signals that can be read in this manner have a separation of at least 400 ticks.

Code: Select all

x = 140, y = 233, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
136bo$25bo13bo96b2obo$24b3o11b3o95bo$23b2ob2o9b2ob2o$25bo13bo2$25bo13b
o$24bobo11bobo$25bo13bo$25bo13bo$23bo3bo9bo3bo$22bo2bo2bo7bo2bo2bo$22b
o2bo2bo7bo2bo2bo$22b2obob2o7b2obob2o2$24b3o11b3o3$32bo2$32bo$31b3o$23b
3o$23bobo2$23bobo$22b2ob2o$22b2ob2o$23b3o$28b2o$23b3o2b2o6bo$24bo11b2o
bo$31b2o3bo$32b2o35$7bo$6b3o$7bo$6bobo$6bobo$6b3o$6bobo$bo11bo$6b3o$7b
o$7bo4$2bo$b3o$b3o$2bo2$o3bo$5o$bobo$b3o14$7bo$6b3o$7bo$6bobo$6bobo$6b
3o$6bobo$bo11bo$6b3o$7bo$7bo4$2bo$b3o$b3o$2bo2$o3bo$5o$bobo$b3o41$8bo$
7b3o$8bo$7bobo$7bobo$7b3o$7bobo$2bo11bo$7b3o$8bo$8bo12$10b3o$11bo2$10b
3o$10b3o$10bobo$10b3o$11bo24$53bo$52b3o$52bobo$53bo$52b3o$52bobo$53bo
3$51b5o$51bo3bo$51bobobo$52b3o!
Consequently the following class of siderakes can be constructed.

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 1282, y = 462, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
441b3o11b3o$441bobo11bobo$442bo13bo$442bo13bo$442bo13bo$440bo3bo9bo3bo
$441bobo11bobo2$441bobo11bobo$440b5o9b5o$441b3o11b3o$442bo13bo2$460bo
13bo$459bobo11bobo$448b3o8bobo11bobo$448b3o8bobo11bobo$449bo9b3o11b3o
2$460bo13bo$459b3o11b3o2$458bo3bo9bo3bo$457b7o7b7o365bo13bo385bo13bo$
42bo13bo398bo4bo4bo3bo4bo4bo362b3o11b3o183bo13bo185b3o11b3o$41b3o11b3o
183bo13bo198b2o2bo3bo2b2ob2o2bo3bo2b2o361bobo11bobo182b3o11b3o184bobo
11bobo$42bo13bo183b3o11b3o198bo3bobo3bo3bo3bobo3bo160bo13bo188bo13bo
184bo13bo186bo13bo$42bo13bo183b3o11b3o199b3o3b3o5b3o3b3o160b3o11b3o
186b3o11b3o183bo13bo185b3o11b3o$41b3o11b3o183bo13bo192b3o6bo5bo7bo5bo
161b3o11b3o186bobo11bobo182b3o11b3o184bobo11bobo$41b3o11b3o364bo13bo
11b3o392bo13bo183b3o11b3o185bo13bo$41bobo11bobo181bo3bo9bo3bo163b3o11b
3o11bo189b3o11b3o385bobo11bobo$42bo13bo182b5o9b5o163b3o11b3o201bobo11b
obo386bo13bo$41b3o11b3o182bobo11bobo165bo13bo203bo13bo186b5o9b5o181b3o
11b3o183b5o9b5o$41bobo11bobo182b3o11b3o200b3o179bobo11bobo185bo3bo9bo
3bo181bobo11bobo183bo3bo9bo3bo$41b3o11b3o362bo3bo9bo3bo19bo382bobobo9b
obobo181b3o11b3o183bobobo9bobobo$420b5o9b5o27b3o178bo194b3o11b3o383b3o
11b3o$60bo13bo173bo172bobo11bobo19b3o6b3o591bo13bo$49bo10bo13bo184bo
13bo147b3o11b3o19b3o7bo8bo170bo213bo13bo173bo10bo13bo186bo13bo$59b3o
11b3o172bo9b3o11b3o182bobo15b3o168b3o9bo13bo177bo9bobo11bobo182b3o11b
3o174bo9bobo11bobo$49bo10bo13bo172b3o7bobobo9bobobo181b3o15b3o179b3o
11b3o185b5o9b5o171bo10bo13bo184b5o9b5o$48b3o8b3o11b3o182bobo11bobo154b
o28bo197b2ob2o9b2ob2o175bo8b2ob2o9b2ob2o170b3o8b3o11b3o174bo8b2ob2o9b
2ob2o$60bo13bo373b3o23b5o179bo13bo176b3o8b3o11b3o183bo13bo174b3o8b3o
11b3o$429bo18b3o25bo384bo13bo385bo13bo$60bo13bo184bo13bo146b3o5b3o18bo
208bo13bo187b3o11b3o183bo13bo185b3o11b3o$58b2ob2o9b2ob2o181bobo11bobo
199b5o178bobo11bobo186b3o11b3o181b2ob2o9b2ob2o183b3o11b3o$258b3o11b3o
144bo3bo51b3o180bo13bo187b3o11b3o383b3o11b3o$258bobo11bobo145b3o43bo8b
3o180bo13bo185b2obob2o7b2obob2o379b2obob2o7b2obob2o$57b3ob3o7b3ob3o
180b3o11b3o191b2obo5b3o178bo3bo9bo3bo183b2obob2o7b2obob2o178b3ob3o7b3o
b3o180b2obob2o7b2obob2o$55b3ob3ob3o3b3ob3ob3o175b2obobob2o5b2obobob2o
188bo180bo7bo2bo2bo7bo2bo2bo179b3ob5ob3ob3ob5ob3o173b3ob3ob3o3b3ob3ob
3o175b3ob5ob3ob3ob5ob3o$55bo2bo3bo2bo3bo2bo3bo2bo168bo6bobobobobo5bobo
bobobo143bo34bo198bo2bo2bo7bo2bo2bo179b3o3bo3b3ob3o3bo3b3o173bo2bo3bo
2bo3bo2bo3bo2bo175b3o3bo3b3ob3o3bo3b3o$49bo5bo3bobo3bo3bo3bobo3bo175bo
2b3o2bo5bo2b3o2bo142bobo33b2obo187bo7b2obob2o7b2obob2o179b2o3bobo3b2ob
2o3bobo3b2o167bo5bo3bobo3bo3bo3bobo3bo175b2o3bobo3b2ob2o3bobo3b2o$24b
3o11b3o15b3o3b3o5b3o3b3o145b3o11b3o7bo7b2obob2o7b2obob2o142b2ob2o32bo
167b3o11b3o5b3o175b3o11b3o9bo6b3o3b3o5b3o3b3o144b3o11b3o15b3o3b3o5b3o
3b3o145b3o11b3o9bo6b3o3b3o5b3o3b3o$24bobo11bobo8bo174bobo11bobo6b3o9bo
13bo145b5o200bobo11bobo16b3o11b3o150bobo11bobo16b3o3b3o5b3o3b3o144bobo
11bobo8bo174bobo11bobo16b3o3b3o5b3o3b3o$24bobo11bobo7b3o173bobo11bobo
179bobo6bo194bobo11bobo183bobo11bobo9bo173bobo11bobo7b3o173bobo11bobo
9bo$417b2obobob2o423b3o397b3o$24bobo11bobo183bobo11bobo175b2obo3bob2o
2bo194bobo11bobo24bo158bobo11bobo183bobo11bobo183bobo11bobo$24bobo11bo
bo183bobo11bobo25bo150b2o5b2o2b3o193bobo11bobo183bobo11bobo18bo164bobo
11bobo183bobo11bobo18bo$25bo13bo18bo8bo157bo13bo178b2obob2o200bo13bo
25bo159bo13bo18b3o164bo13bo18bo8bo157bo13bo18b3o$57b3o197bo8bo8bo388b
3o7bo183b3o7bo188b3o198b3o7bo$24b3o11b3o16b3o7bo156b3o11b3o15b3o6b3o5b
o3bo346b3o11b3o15bo16bobo148b3o11b3o18bo164b3o11b3o16b3o7bo156b3o11b3o
18bo$23b5o9b5o24b3o154b5o9b5o14b3o364b5o9b5o13b3o15bobo147b5o9b5o26bo
154b5o9b5o24b3o154b5o9b5o26bo$22b2obob2o7b2obob2o14b3o162b2obob2o7b2ob
ob2o32bo346b2obob2o7b2obob2o4bo8bo16bobo146b2obob2o7b2obob2o14bo3bo5b
3o6b3o143b2obob2o7b2obob2o14b3o162b2obob2o7b2obob2o14bo3bo5b3o6b3o$23b
obobo9bobobo15bobo15b3o145bobobo9bobobo6bo6b5o13bo3bo345bobobo9bobobo
13bobo15b3o147bobobo9bobobo15b5o15bo145bobobo9bobobo15bobo15b3o145bobo
bo9bobobo15b5o15bo$24b3o11b3o8bo8bo16bobo146b3o11b3o16bo16bobo347b3o
11b3o6bo7bobo166b3o11b3o17bobo163b3o11b3o8bo8bo16bobo146b3o11b3o17bobo
$25bo13bo17bobo165bo13bo8bo26bo349bo13bo6b3o6b3o16bo150bo13bo10bo7b3o
16bo147bo13bo17bobo165bo13bo10bo7b3o16bo$49bo25bobo169b3o5b5o13bo3bo
377bobo15b3o200b3o170bo25bobo198b3o$48b3o23b2ob2o177b3o16bo374bo199bo
26bo170b3o23b2ob2o171bo26bo$74b2ob2o177b3o16bo379b3o14bo3bo172b3o25bo
196b2ob2o170b3o25bo$31b3o41b3o153b3o22b3o11bo4bo4bo350b3o22bo6b2o6b7o
153b3o41bo3bo151b3o41b3o153b3o41bo3bo$31b3o197b3o39bo3bo353b3o22bo5bo
6bo4bo4bo151b3o197b3o197b3o$32bo34b2o6b3o154bo35bobo9bobo349bo35b2o2bo
3bo2b2o151bo34b2o6bo3bo152bo34b2o6b3o154bo34b2o6bo3bo$24bo41b3o7bo147b
o40b3o6b3o347bo39b3o2bo3bobo3bo144bo41b3o155bo41b3o7bo147bo41b3o$23b3o
41b2o154b3o397b3o44b3o3b3o144b3o41b2o8bo145b3o41b2o154b3o41b2o8bo$24bo
32b2o165bo32b2o365bo32b2o12bo5bo146bo32b2o165bo32b2o165bo32b2o$23bobo
30b3o164bobo30b3o13bo5bo344bobo30b3o164bobo30b3o164bobo30b3o164bobo30b
3o$23bobo31b2o164bobo31b2o364bobo31b2o164bobo31b2o164bobo31b2o164bobo
31b2o$23b3o197b3o397b3o197b3o197b3o197b3o$23bobo197bobo397bobo197bobo
197bobo197bobo$18bo9b2o188bo9b2o388bo9b2o188bo9b2o188bo9b2o188bo9b2o$
23b3o2bo194b3o2bo394b3o2bo194b3o2bo194b3o2bo194b3o2bo$24bo199bo399bo
199bo199bo199bo$24bo6b2o191bo6b2o391bo6b2o191bo6b2o191bo6b2o191bo6b2o$
32bo199bo399bo199bo199bo199bo$32bo199bo399bo199bo199bo199bo6$404bo$
403b3o$402bobobo$403bobo3$404bo$403bobo$403b3o$403bobo$403b3o$400b2obo
bob2o$400bobobobobo$400bo2b3o2bo$401b2obob2o$404bo6$399bo$398b3o$399bo
$7bo199bo190bobo206bo199bo199bo199bo$5bo3bo195bo3bo188bobo204bo3bo195b
o3bo195bo3bo195bo3bo$398b3o$7bo199bo190bobo206bo199bo199bo199bo$5bo3bo
195bo3bo183bo11bo199bo3bo195bo3bo195bo3bo195bo3bo$6bobo197bobo189b3o
205bobo197bobo197bobo197bobo$7bo199bo191bo207bo199bo199bo199bo$5bo3bo
195bo3bo189bo205bo3bo195bo3bo195bo3bo195bo3bo$7bo199bo399bo199bo199bo
199bo$7bo199bo399bo199bo199bo199bo$2bo4bo4bo189bo4bo4bo389bo4bo4bo189b
o4bo4bo189bo4bo4bo189bo4bo4bo$5bo3bo195bo3bo395bo3bo195bo3bo195bo3bo
195bo3bo$obo9bobo185bobo9bobo189bo195bobo9bobo185bobo9bobo185bobo9bobo
185bobo9bobo$6b3o197b3o194b3o200b3o197b3o197b3o197b3o$402bobobo68bo$
403bobo68b3o$4bo5bo193bo5bo264bo128bo5bo193bo5bo193bo5bo193bo5bo$474bo
bo$404bo69bobo$b3o197b3o199bobo68b3o124b3o197b3o197b3o197b3o$2bo199bo
200b3o68bobo125bo199bo199bo199bo$403bobo63bo11bo$b3o197b3o199b3o68b3o
124b3o197b3o197b3o197b3o$b3o197b3o196b2obobob2o66bo125b3o197b3o197b3o
197b3o$bobo197bobo196bobobobobo66bo125bobo197bobo197bobo197bobo$b3o
197b3o196bo2b3o2bo192b3o197b3o197b3o197b3o$2bo199bo198b2obob2o194bo
199bo199bo199bo$404bo6$399bo$398b3o$399bo$77b3o127bo69b3o118bobo206bo
69b3o127bo69b3o127bo69b3o127bo69b3o$78bo126bo3bo68bo119bobo204bo3bo68b
o126bo3bo68bo126bo3bo68bo126bo3bo68bo$398b3o$77b3o127bo69b3o118bobo
206bo69b3o127bo69b3o127bo69b3o127bo69b3o$77b3o125bo3bo67b3o113bo11bo
199bo3bo67b3o125bo3bo67b3o125bo3bo67b3o125bo3bo67b3o$77bobo126bobo68bo
bo118b3o205bobo68bobo126bobo68bobo126bobo68bobo126bobo68bobo$77b3o127b
o69b3o119bo207bo69b3o127bo69b3o127bo69b3o127bo69b3o$78bo126bo3bo68bo
120bo205bo3bo68bo126bo3bo68bo126bo3bo68bo126bo3bo68bo$207bo399bo199bo
199bo199bo$207bo399bo199bo199bo199bo$202bo4bo4bo389bo4bo4bo189bo4bo4bo
189bo4bo4bo189bo4bo4bo$205bo3bo395bo3bo195bo3bo195bo3bo195bo3bo$200bob
o9bobo189bo195bobo9bobo185bobo9bobo185bobo9bobo185bobo9bobo$206b3o194b
3o200b3o197b3o197b3o197b3o$402bobobo68bo$403bobo68b3o$204bo5bo264bo
128bo5bo193bo5bo193bo5bo193bo5bo$474bobo$45b3o356bo69bobo$46bo154b3o
199bobo68b3o124b3o197b3o197b3o197b3o$202bo200b3o68bobo125bo199bo199bo
199bo$46bo356bobo63bo11bo$201b3o199b3o68b3o124b3o197b3o197b3o197b3o$
201b3o196b2obobob2o66bo125b3o197b3o197b3o197b3o$201bobo196bobobobobo
66bo125bobo197bobo197bobo197bobo$201b3o196bo2b3o2bo192b3o197b3o197b3o
197b3o$202bo198b2obob2o194bo199bo199bo199bo$8bo395bo$6bo3bo2$8bo$6bo3b
o$7bobo$8bo390bo$6bo3bo387b3o$8bo390bo$8bo268b3o118bobo206bo69b3o127bo
69b3o127bo69b3o127bo69b3o$3bo4bo4bo264bo119bobo204bo3bo68bo126bo3bo68b
o126bo3bo68bo126bo3bo68bo$6bo3bo387b3o$bobo9bobo261b3o118bobo206bo69b
3o127bo69b3o127bo69b3o127bo69b3o$7b3o267b3o113bo11bo199bo3bo67b3o125bo
3bo67b3o125bo3bo67b3o125bo3bo67b3o$277bobo118b3o205bobo68bobo126bobo
68bobo126bobo68bobo126bobo68bobo$277b3o119bo207bo69b3o127bo69b3o127bo
69b3o127bo69b3o$5bo5bo266bo120bo205bo3bo68bo126bo3bo68bo126bo3bo68bo
126bo3bo68bo$607bo199bo199bo199bo$607bo199bo199bo199bo$602bo4bo4bo189b
o4bo4bo189bo4bo4bo189bo4bo4bo$605bo3bo195bo3bo195bo3bo195bo3bo$600bobo
9bobo185bobo9bobo185bobo9bobo185bobo9bobo$606b3o197b3o197b3o197b3o$
475bo$474b3o$475bo128bo5bo193bo5bo193bo5bo193bo5bo$11bo462bobo$10b3o
232b3o226bobo$10b3o233bo227b3o124b3o197b3o197b3o197b3o$474bobo125bo
199bo199bo199bo$10b3o233bo222bo11bo$10bobo461b3o124b3o197b3o197b3o197b
3o$11bo463bo125b3o197b3o197b3o197b3o$10bobo462bo125bobo197bobo197bobo
197bobo$601b3o197b3o197b3o197b3o$602bo199bo199bo199bo$208bo$206bo3bo2$
208bo$206bo3bo$207bobo$208bo$206bo3bo$208bo$208bo398bo69b3o127bo69b3o
127bo69b3o127bo69b3o$203bo4bo4bo391bo3bo68bo126bo3bo68bo126bo3bo68bo
126bo3bo68bo$206bo3bo$201bobo9bobo189bo201bo69b3o127bo69b3o127bo69b3o
127bo69b3o$207b3o194b3o198bo3bo67b3o125bo3bo67b3o125bo3bo67b3o125bo3bo
67b3o$403bobobo198bobo68bobo126bobo68bobo126bobo68bobo126bobo68bobo$
404bobo200bo69b3o127bo69b3o127bo69b3o127bo69b3o$205bo5bo393bo3bo68bo
126bo3bo68bo126bo3bo68bo126bo3bo68bo$607bo199bo199bo199bo$405bo201bo
199bo199bo199bo$404bobo195bo4bo4bo189bo4bo4bo189bo4bo4bo189bo4bo4bo$
404b3o198bo3bo195bo3bo195bo3bo195bo3bo$404bobo193bobo9bobo185bobo9bobo
185bobo9bobo185bobo9bobo$52b3o349b3o199b3o197b3o197b3o197b3o$52bobo
346b2obobob2o$53bo347bobobobobo$45b3o5bo347bo2b3o2bo194bo5bo193bo5bo
193bo5bo193bo5bo$46bo6bo157bo190b2obob2o$51bo3bo154b3o192bo39b3o$46bo
5bobo155b3o233bo154b3o197b3o197b3o197b3o$602bo199bo199bo199bo$52bobo
155b3o233bo$51b5o154bobo388b3o197b3o197b3o197b3o$52b3o156bo389b3o197b
3o197b3o197b3o$53bo156bobo388bobo197bobo197bobo197bobo$601b3o197b3o
197b3o197b3o$602bo199bo199bo199bo$408bo$406bo3bo2$408bo$406bo3bo$407bo
bo$408bo$406bo3bo$408bo$408bo268b3o127bo69b3o127bo69b3o127bo69b3o$403b
o4bo4bo264bo126bo3bo68bo126bo3bo68bo126bo3bo68bo$406bo3bo$401bobo9bobo
261b3o127bo69b3o127bo69b3o127bo69b3o$407b3o267b3o125bo3bo67b3o125bo3bo
67b3o125bo3bo67b3o$677bobo126bobo68bobo126bobo68bobo126bobo68bobo$677b
3o127bo69b3o127bo69b3o127bo69b3o$405bo5bo266bo126bo3bo68bo126bo3bo68bo
126bo3bo68bo$807bo199bo199bo$807bo199bo199bo$802bo4bo4bo189bo4bo4bo
189bo4bo4bo$805bo3bo195bo3bo195bo3bo$800bobo9bobo185bobo9bobo185bobo9b
obo$252b3o551b3o197b3o197b3o$252bobo$253bo$245b3o5bo550bo5bo193bo5bo
193bo5bo$246bo6bo157bo$251bo3bo154b3o232b3o$246bo5bobo155b3o233bo154b
3o197b3o197b3o$802bo199bo199bo$252bobo155b3o233bo$251b5o154bobo388b3o
197b3o197b3o$252b3o156bo389b3o197b3o197b3o$253bo156bobo388bobo197bobo
197bobo$801b3o197b3o197b3o$802bo199bo199bo$608bo$606bo3bo2$608bo$606bo
3bo$607bobo$608bo$606bo3bo$608bo$608bo268b3o127bo69b3o127bo69b3o$603bo
4bo4bo264bo126bo3bo68bo126bo3bo68bo$606bo3bo$601bobo9bobo261b3o127bo
69b3o127bo69b3o$607b3o267b3o125bo3bo67b3o125bo3bo67b3o$877bobo126bobo
68bobo126bobo68bobo$877b3o127bo69b3o127bo69b3o$605bo5bo266bo126bo3bo
68bo126bo3bo68bo$1007bo199bo$1007bo199bo$1002bo4bo4bo189bo4bo4bo$1005b
o3bo195bo3bo$1000bobo9bobo185bobo9bobo$452b3o551b3o197b3o$452bobo$453b
o$445b3o5bo550bo5bo193bo5bo$446bo6bo157bo$451bo3bo154b3o232b3o$446bo5b
obo155b3o233bo154b3o197b3o$1002bo199bo$452bobo155b3o233bo$451b5o154bob
o388b3o197b3o$452b3o156bo389b3o197b3o$453bo156bobo388bobo197bobo$1001b
3o197b3o$1002bo199bo$808bo$806bo3bo2$808bo$806bo3bo$807bobo$808bo$806b
o3bo$808bo$808bo268b3o127bo69b3o$803bo4bo4bo264bo126bo3bo68bo$806bo3bo
$801bobo9bobo261b3o127bo69b3o$807b3o267b3o125bo3bo67b3o$1077bobo126bob
o68bobo$1077b3o127bo69b3o$805bo5bo266bo126bo3bo68bo$1207bo$1207bo$
1202bo4bo4bo$1205bo3bo$1200bobo9bobo$652b3o551b3o$652bobo$653bo$645b3o
5bo550bo5bo$646bo6bo157bo$651bo3bo154b3o232b3o$646bo5bobo155b3o233bo
154b3o$1202bo$652bobo155b3o233bo$651b5o154bobo388b3o$652b3o156bo389b3o
$653bo156bobo388bobo$1201b3o$1202bo$1008bo$1006bo3bo2$1008bo$1006bo3bo
$1007bobo$1008bo$1006bo3bo$1008bo$1008bo268b3o$1003bo4bo4bo264bo$1006b
o3bo$1001bobo9bobo261b3o$1007b3o267b3o$1277bobo$1277b3o$1005bo5bo266bo
6$852b3o$852bobo$853bo$845b3o5bo$846bo6bo157bo$851bo3bo154b3o232b3o$
846bo5bobo155b3o233bo2$852bobo155b3o233bo$851b5o154bobo$852b3o156bo$
853bo156bobo3$1208bo$1206bo3bo2$1208bo$1206bo3bo$1207bobo$1208bo$1206b
o3bo$1208bo$1208bo$1203bo4bo4bo$1206bo3bo$1201bobo9bobo$1207b3o3$1205b
o5bo6$1052b3o$1052bobo$1053bo$1045b3o5bo$1046bo6bo157bo$1051bo3bo154b
3o$1046bo5bobo155b3o2$1052bobo155b3o$1051b5o154bobo$1052b3o156bo$1053b
o156bobo25$1252b3o$1252bobo$1253bo$1245b3o5bo$1246bo6bo$1251bo3bo$
1246bo5bobo2$1252bobo$1251b5o$1252b3o$1253bo!
However, the fore-to-side reflector on the top is not easy to adjust. To read a cloverleaf one more time, it needs to wait another 240 ticks, and the resulting T-ship delay is 240*(3/20) = 36 ticks; but the distance between a forward 3c/20o and a chasing T-ship shrinks at a speed of c/2-3c/20 = (10-3)c/20 = 7c/20, and 7 is not a factor of 36. Also, there seems to be a possible plus-or-minus-20-tick discrepancy inside the reflector.
There is another issue in the design that can lead to conflicts between signals in the same loop, and it can be solved by flipping the cloverleaf(s) so they rotate in the other direction.

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 126, y = 439, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
84b3o11b3o$85bo13bo$85bo13bo$84b3o11b3o2$83bobobo9bobobo$83bobobo9bobo
bo$85bo13bo$84b3o11b3o$85bo13bo3$102b3o11b3o$91b3o$91b3o7bo3bo9bo3bo$
92bo9b3o11b3o3$103bo13bo$102bobo11bobo$101b2ob2o9b2ob2o$101b5o9b5o$
102bobo11bobo$99b2obobob2o5b2obobob2o$98b2obo3bob2o3b2obo3bob2o$99b2o
5b2o5b2o5b2o$91b3o6b2obob2o7b2obob2o$91b3o$92bo3$49bo13bo$48b3o11b3o$
47b2ob2o9b2ob2o34b3o6b3o$49bo13bo37bo7b3o$110bo$49bo13bo37bo$48bobo11b
obo35b3o16bo$49bo13bo37bo16b3o$49bo13bo27b3o7bo17bo$47bo3bo9bo3bo25b3o
5bo3bo14bobo$46bo2bo2bo7bo2bo2bo25bo25bobo$46bo2bo2bo7bo2bo2bo32bo3bo
14b3o$46b2obob2o7b2obob2o51bobo$101bo11bo11bo$48b3o11b3o45bo7b3o$110b
2o7bo$110bo8bo$56bo43bo$100b2obo$56bo43bo$55b3o32bo$47b3o40b2obo$47bob
o40bo2$47bobo$46b2ob2o$46b2ob2o$47b3o$52b2o$47b3o2b2o$48bo$55b2o$56b2o
31$70bo$69b3o$70bo$69bobo$69bobo$69b3o$69bobo$64bo11bo$69b3o$70bo$70bo
31$72bo$71b3o$71b3o2$70b5o$72bo2$70b5o$71b3o$71b3o$71b3o4$77bo$76b3o$
77bo$77bo$76b3o$76b3o$76bobo$77bo$76b3o$76bobo$76b3o9$bo$3o$3o2$3o$obo
$bo$obo28$33bo$32b3o$32b3o2$31b5o$33bo2$31b5o$32b3o$32b3o$32b3o22$32bo
$31b3o$31b3o2$31b3o$31bobo$32bo$31bobo15$34b3o$34bobo$35bo$35bo$35bo$
33bo3bo$34bobo2$34bobo$33b5o$34b3o$35bo10$38bo$37b3o$36bobobo$37bobo3$
38bo$37bobo$37b3o$37bobo$37b3o$34b2obobob2o$34bobobobobo$34bo2b3o2bo$
35b2obob2o$38bo9$41bo$39bo3bo2$41bo$39bo3bo$40bobo$41bo$39bo3bo$41bo$
41bo$36bo4bo4bo$39bo3bo$34bobo9bobo$40b3o3$38bo5bo10$44bo$43b3o$43b3o
2$43b3o$43bobo$44bo$43bobo15$46b3o$46bobo$47bo$47bo$47bo$45bo3bo$46bob
o2$46bobo$45b5o$46b3o$47bo10$50bo$49b3o$48bobobo$49bobo3$50bo$49bobo$
49b3o$49bobo$49b3o$46b2obobob2o$46bobobobobo$46bo2b3o2bo$47b2obob2o$
50bo9$53bo$51bo3bo2$53bo$51bo3bo$52bobo$53bo$51bo3bo$53bo$53bo$48bo4bo
4bo$51bo3bo$46bobo9bobo$52b3o3$50bo5bo20$95bo$94b3o$94b3o2$94b3o$94bob
o$95bo$94bobo!
Side-to-side 180-degree reflector chained to delay a T-ship by 98 ticks:

Code: Select all

x = 57, y = 25, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
3bo$ob2o$3bo49bo$52b3o$51b2ob2o$53bo2$53bo$52bobo$53bo$53bo$51bo3bo$
50bo2bo2bo$14b3o33bo2bo2bo$15bo34b2obob2o2$15bo36b3o$14b3o$15bo$15bo$
13bo3bo2$13bo3bo2$15bo!
Accidental 3T synthesis for xs12_4aala6.

Code: Select all

x = 10, y = 12, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
b3o$b3o$2bo3$6bo$6b2obo$6bo$3o$bo2$bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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GUYTU6J
Posts: 1850
Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » March 28th, 2022, 12:48 am

Nine days makes a new post reasonable, and there is an essentially different idea. Side-to-fore+back splitter/duplicator working at periods 120+40n:

Code: Select all

x = 114, y = 59, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
71bo13bo$70b3o11b3o$70b3o11b3o2$70b3o11b3o$70bobo11bobo$71bo13bo$70bob
o11bobo2$78bo2$78bo$77b3o11bo13bo$90b3o11b3o$89b2ob2o9b2ob2o$91bo13bo
2$91bo13bo$90bobo11bobo$91bo13bo$91bo13bo$89bo3bo9bo3bo$78bo9bo2bo2bo
7bo2bo2bo$88bo2bo2bo7bo2bo2bo$78bo9b2obob2o7b2obob2o$77b3o$90b3o11b3o
3$98bo2$98bo$97b3o7bo$89bo16bobo$2o86b3o15bobo$3o75bo10bo16bobo$2o86bo
bo15b3o$78bo9bobo$77b3o8b3o16bo$88bobo15b3o$83bo$88b3o14bo3bo$89bo6b2o
6b7o$89bo5bo6bo4bo4bo$101b2o2bo3bo2b2o$97b3o2bo3bobo3bo$103b3o3b3o$90b
2o12bo5bo$89b3o$90b2o2$106b3o$60b2o45bo$60b3o6bo$60b2o6b4o34b3o$69bo
36b3o$106bobo$106b3o$107bo!
It uses a 6-engine p40 siderake with the output suppressed by another trailing 3c/20, involving no cloverleaf. Therefore we start to have simpler moving memory loops: shown below are backrakes with periods 400, 400/2, 440, 480, 480/4 respectively.

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 487, y = 139, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
304bo13bo85bo13bo$303b3o11b3o83b3o11b3o$302bobobo9bobobo81bobobo9bobob
o$303bobo11bobo83bobo11bobo3$304bo13bo85bo13bo$303bobo11bobo83bobo11bo
bo$303b3o11b3o83b3o11b3o$303bobo11bobo83bobo11bobo$303b3o11b3o83b3o11b
3o$300b2obobob2o5b2obobob2o77b2obobob2o5b2obobob2o$300bobobobobo5bobob
obobo77bobobobobo5bobobobobo$300bo2b3o2bo5bo2b3o2bo77bo2b3o2bo5bo2b3o
2bo$204bo13bo82b2obob2o7b2obob2o79b2obob2o7b2obob2o$203b3o11b3o84bo13b
o85bo13bo$204bo13bo$203bobo11bobo$203bobo11bobo$203b3o11b3o91bo10bo13b
o74bo10bo13bo$203bobo11bobo101b3o11b3o83b3o11b3o$4bo13bo85bo13bo79bo
11bobo11bo86bo9b3o11b3o73bo9b3o11b3o$3b3o11b3o83b3o11b3o83b3o4b3o4b3o
90b3o97b3o$3b3o11b3o83b3o11b3o84bo13bo101b5o9b5o81b5o9b5o$4bo13bo85bo
13bo85bo13bo103bo13bo85bo13bo2$2bo3bo9bo3bo81bo3bo9bo3bo101bo13bo83b5o
4bo4b5o81b5o4bo4b5o$2b5o9b5o81b5o9b5o100b3o11b3o83b3o11b3o83b3o11b3o$
3bobo11bobo83bobo11bobo102bo13bo84b3o5bo5b3o83b3o5bo5b3o$3b3o11b3o83b
3o11b3o102bo13bo84b3o4b3o4b3o83b3o4b3o4b3o$221b3o11b3o$221b3o11b3o$11b
o99bo99bo9bobo11bobo73bo99bo$22bo13bo85bo13bo85bo13bo83bo99bo$11bo9b3o
11b3o73bo9b3o11b3o73bo9b3o11b3o73bo7b3o89bo7b3o$10b3o7bobobo9bobobo71b
3o7bobobo9bobobo71b3o8bobo11bobo72b3o6bobo88b3o6bobo$21bobo11bobo83bob
o11bobo83b3o11b3o82bo99bo$319b3o97b3o$319bobo15b3o79bobo15b3o$22bo13bo
85bo13bo92bo90bo8bo8bo81bo8bo8bo$21bobo11bobo83bobo11bobo82bo117bo99bo
$21b3o11b3o83b3o11b3o82bo8bo99bo7b3o89bo7b3o$21bobo11bobo83bobo11bobo
81b3o6b3o87b5o5b3o87b5o5b3o$21b3o11b3o83b3o11b3o82bo97bo3bo13bobobo77b
o3bo13bobobo$18b2obobob2o5b2obobob2o77b2obobob2o5b2obobob2o78b3o96bobo
bo13bobobo77bobobo13bobobo$11bo6bobobobobo5bobobobobo70bo6bobobobobo5b
obobobobo70bo8bo16b3o71bo7b3o16bo72bo7b3o16bo$18bo2b3o2bo5bo2b3o2bo77b
o2b3o2bo5bo2b3o2bo95bo3bo96b3o97b3o$11bo7b2obob2o7b2obob2o71bo7b2obob
2o7b2obob2o71bo8bo15bo3bo70bo26bo72bo26bo$10b3o9bo13bo73b3o9bo13bo73b
3o5b2ob2o15bo71b3o97b3o$326b2o$238bo86b3o$217b3ob3o13bobo86b2o$29bo99b
o85b3ob3ob3o3bo8bo77b2o98b2o$215bo2bo3bo2bo11bobo75b3o97b3o$20bo8bo8bo
81bo8bo8bo76bo3bobo3bo3bo7bobo76b2o98b2o$19b3o6b3o5bo3bo78b3o6b3o5bo3b
o75b3o3b3o3b3o4bobobobo$19b3o97b3o112b2o2bo2b2o$38bo99bo96b2o3b2o$11bo
6b5o13bo3bo70bo6b5o13bo3bo70bo24b5o$20bo16bobo80bo16bobo83b2o13bo$11bo
26bo72bo26bo72bo10b3o13bo$10b3o5b5o13bo3bo69b3o5b5o13bo3bo69b2o11b2o$
19b3o16bo80b3o16bo73b3o$19b3o16bo80b3o16bo73b3o$19b3o11bo4bo4bo75b3o
11bo4bo4bo69b2o$36bo3bo95bo3bo$31bobo9bobo85bobo9bobo$28b3o6b3o88b3o6b
3o3$35bo5bo93bo5bo4$44bo13bo85bo13bo85bo13bo85bo13bo85bo13bo$43b3o11b
3o83b3o11b3o83b3o11b3o83b3o11b3o83b3o11b3o$43b3o11b3o83b3o11b3o83b3o
11b3o83b3o11b3o83b3o11b3o2$43b3o11b3o83b3o11b3o83b3o11b3o83b3o11b3o83b
3o11b3o$43bobo11bobo83bobo11bobo83bobo11bobo83bobo11bobo83bobo11bobo$
44bo13bo85bo13bo85bo13bo85bo13bo85bo13bo$43bobo11bobo83bobo11bobo83bob
o11bobo83bobo11bobo83bobo11bobo2$51bo99bo99bo99bo99bo2$51bo99bo99bo99b
o99bo$50b3o11bo13bo71b3o11bo13bo71b3o11bo13bo71b3o11bo13bo71b3o11bo13b
o$63b3o11b3o83b3o11b3o83b3o11b3o83b3o11b3o83b3o11b3o$62b2ob2o9b2ob2o
81b2ob2o9b2ob2o81b2ob2o9b2ob2o81b2ob2o9b2ob2o81b2ob2o9b2ob2o$64bo13bo
85bo13bo85bo13bo85bo13bo51bo33bo13bo$429b3o$64bo13bo85bo13bo85bo13bo
85bo13bo50b3o32bo13bo$63bobo11bobo83bobo11bobo83bobo11bobo83bobo11bobo
83bobo11bobo$64bo13bo85bo13bo85bo13bo85bo13bo85bo13bo$64bo13bo85bo13bo
85bo13bo85bo13bo85bo13bo$62bo3bo9bo3bo81bo3bo9bo3bo81bo3bo9bo3bo81bo3b
o9bo3bo81bo3bo9bo3bo$51bo9bo2bo2bo7bo2bo2bo69bo9bo2bo2bo7bo2bo2bo69bo
9bo2bo2bo7bo2bo2bo69bo9bo2bo2bo7bo2bo2bo69bo9bo2bo2bo7bo2bo2bo$61bo2bo
2bo7bo2bo2bo79bo2bo2bo7bo2bo2bo79bo2bo2bo7bo2bo2bo79bo2bo2bo7bo2bo2bo
79bo2bo2bo7bo2bo2bo$51bo9b2obob2o7b2obob2o69bo9b2obob2o7b2obob2o69bo9b
2obob2o7b2obob2o69bo9b2obob2o7b2obob2o69bo9b2obob2o7b2obob2o$50b3o97b
3o97b3o97b3o97b3o$63b3o11b3o83b3o11b3o83b3o11b3o83b3o11b3o83b3o11b3o3$
71bo99bo99bo99bo99bo$20bo99bo99bo99bo99bo$19b3o49bo47b3o49bo47b3o49bo
47b3o49bo47b3o49bo$19bobo48b3o7bo38bobo48b3o7bo38bobo48b3o7bo38bobo48b
3o7bo38bobo48b3o7bo$20bo41bo16bobo38bo41bo16bobo38bo41bo16bobo38bo41bo
16bobo38bo41bo16bobo$19b3o39b3o15bobo37b3o39b3o15bobo37b3o39b3o15bobo
37b3o39b3o15bobo37b3o39b3o15bobo$b3o15bobo29bo10bo16bobo19b3o15bobo29b
o10bo16bobo19b3o15bobo29bo10bo16bobo19b3o15bobo29bo10bo16bobo19b3o15bo
bo29bo10bo16bobo$2bo17bo40bobo15b3o20bo17bo40bobo15b3o20bo17bo40bobo
15b3o20bo17bo40bobo15b3o20bo8bo8bo40bobo15b3o$2bo48bo9bobo38bo48bo9bob
o38bo48bo9bobo38bo48bo9bobo38bo48bo9bobo$b3o46b3o8b3o16bo20b3o46b3o8b
3o16bo20b3o46b3o8b3o16bo20b3o46b3o8b3o16bo20b3o7bo38b3o8b3o16bo$18b5o
38bobo15b3o36b5o38bobo15b3o36b5o38bobo15b3o36b5o38bobo15b3o28b3o5b5o
38bobo15b3o$obobo13bo3bo33bo43bobobo13bo3bo33bo43bobobo13bo3bo33bo43bo
bobo13bo3bo33bo43bobobo13bo3bo33bo$obobo13bobobo38b3o14bo3bo17bobobo
13bobobo38b3o14bo3bo17bobobo13bobobo38b3o14bo3bo17bobobo13bobobo38b3o
14bo3bo17bobobo13bobobo38b3o14bo3bo$2bo16b3o40bo6b2o6b7o18bo16b3o40bo
6b2o6b7o18bo16b3o40bo6b2o6b7o18bo16b3o40bo6b2o6b7o18bo16b3o40bo6b2o6b
7o$b3o58bo5bo6bo4bo4bo15b3o58bo5bo6bo4bo4bo15b3o58bo5bo6bo4bo4bo15b3o
58bo5bo6bo4bo4bo15b3o58bo5bo6bo4bo4bo$2bo71b2o2bo3bo2b2o15bo71b2o2bo3b
o2b2o15bo71b2o2bo3bo2b2o15bo71b2o2bo3bo2b2o15bo71b2o2bo3bo2b2o$70b3o2b
o3bobo3bo84b3o2bo3bobo3bo84b3o2bo3bobo3bo84b3o2bo3bobo3bo84b3o2bo3bobo
3bo$76b3o3b3o91b3o3b3o91b3o3b3o91b3o3b3o91b3o3b3o$63b2o12bo5bo79b2o12b
o5bo79b2o12bo5bo79b2o12bo5bo79b2o12bo5bo$52b2o8b3o87b2o8b3o87b2o8b3o
87b2o8b3o87b2o8b3o$53bo9b2o88bo9b2o88bo9b2o88bo9b2o88bo9b2o$53bo99bo
99bo99bo99bo$50b3o26b3o68b3o26b3o68b3o26b3o68b3o26b3o68b3o26b3o$80bo
99bo99bo99bo99bo$39bo$79b3o97b3o97b3o97b3o97b3o$39bo39b3o97b3o97b3o97b
3o97b3o$49bo29bobo97bobo97bobo97bobo97bobo$35bobo3bobo2bob2o29b3o48bo
48b3o48bo48b3o48bo48b3o48bo48b3o$49bo30bo48b3o48bo48b3o48bo48b3o48bo
48b3o48bo$39bo89b3o97b3o97b3o97b3o2$39bo$69bo$66bob2o$69bo!
Advance only the fore-to-back reflector at the top by 14 ticks and shift it 7 cells upward, and another 40 ticks will add to the loop period. When inserting signals, remember that two consecutive T-ships have to be separated by at least 120 ticks, or equivalently, (20-6)*3=42 cells upward or (20+6)*3=78 cells downward considering Doppler effect. Another minor modification is to advance the fore-to-back reflector by 2 ticks and shift the back-to-side reflector 1 cell upward.
Other cloverleaf-producing interactions: (the rightmost two differ by one cell vertically)

Code: Select all

x = 315, y = 59, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
42bo13bo95bo13bo105bo13bo$41b3o11b3o93b3o11b3o103b3o11b3o$41b3o11b3o
93b3o11b3o103b3o11b3o2$41b3o11b3o93b3o11b3o103b3o11b3o$41bobo11bobo93b
obo11bobo103bobo11bobo$42bo13bo95bo13bo105bo13bo$41bobo11bobo93bobo11b
obo103bobo11bobo2$49bo109bo119bo2$49bo109bo119bo$48b3o11bo13bo81b3o11b
o13bo91b3o11bo13bo$61b3o11b3o93b3o11b3o103b3o11b3o$60b2ob2o9b2ob2o91b
2ob2o9b2ob2o101b2ob2o9b2ob2o$62bo13bo95bo13bo105bo13bo2$62bo13bo95bo
13bo105bo13bo$61bobo11bobo93bobo11bobo103bobo11bobo$62bo13bo95bo13bo
105bo13bo$62bo13bo95bo13bo105bo13bo$60bo3bo9bo3bo91bo3bo9bo3bo101bo3bo
9bo3bo$49bo9bo2bo2bo7bo2bo2bo79bo9bo2bo2bo7bo2bo2bo89bo9bo2bo2bo7bo2bo
2bo$59bo2bo2bo7bo2bo2bo89bo2bo2bo7bo2bo2bo99bo2bo2bo7bo2bo2bo$49bo9b2o
bob2o7b2obob2o79bo9b2obob2o7b2obob2o89bo9b2obob2o7b2obob2o$48b3o107b3o
117b3o$61b3o11b3o93b3o11b3o103b3o11b3o3$69bo109bo119bo2$69bo109bo30b2o
87bo$68b3o7bo99b3o7bo21b3o85b3o7bo$60bo16bobo90bo16bobo20b2o78bo16bobo
$59b3o15bobo89b3o15bobo99b3o15bobo$49bo10bo16bobo79bo10bo16bobo89bo10b
o16bobo$59bobo15b3o89bobo15b3o99bobo15b3o$49bo9bobo97bo9bobo107bo9bobo
$48b3o8b3o16bo79b3o8b3o16bo89b3o8b3o16bo$59bobo15b3o89bobo15b3o99bobo
15b3o$54bo109bo119bo$59b3o14bo3bo88b3o14bo3bo98b3o14bo3bo$60bo6b2o6b7o
88bo6b2o6b7o98bo6b2o6b7o$2o58bo5bo6bo4bo4bo86bo5bo6bo4bo4bo96bo5bo6bo
4bo4bo$3o69b2o2bo3bo2b2o97b2o2bo3bo2b2o55b2o50b2o2bo3bo2b2o$2o66b3o2bo
3bobo3bo34bo59b3o2bo3bobo3bo56b3o45b3o2bo3bobo3bo$74b3o3b3o32bob2o65b
3o3b3o57b2o52b3o3b3o$61b2o12bo5bo36bo52b2o12bo5bo99b2o12bo5bo$60b3o
107b3o117b3o$61b2o108b2o118b2o2$77b3o107b3o117b3o$78bo109bo119bo$40bo
109bo119bo$39b4o34b3o69b4o34b3o79b4o34b3o$40bo36b3o70bo36b3o80bo36b3o$
77bobo107bobo117bobo$77b3o107b3o117b3o$78bo109bo119bo!
The last one leads to another p40 side-to-fore reflector. However, my instinct tells me that there should be a p20 equivalent.

Code: Select all

x = 80, y = 91, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
37bo13bo$36b3o11b3o$36b3o11b3o2$36b3o11b3o$36bobo11bobo$37bo13bo$36bob
o11bobo2$44bo2$44bo$43b3o11bo13bo$56b3o11b3o$55b2ob2o9b2ob2o$57bo13bo
2$57bo13bo$56bobo11bobo$57bo13bo$57bo13bo$55bo3bo9bo3bo$44bo9bo2bo2bo
7bo2bo2bo$54bo2bo2bo7bo2bo2bo$44bo9b2obob2o7b2obob2o$43b3o$56b3o11b3o
3$64bo2$64bo$63b3o7bo$55bo16bobo$54b3o15bobo$44bo10bo16bobo$54bobo15b
3o$44bo9bobo$43b3o8b3o16bo$54bobo15b3o$49bo$54b3o14bo3bo$55bo6b2o6b7o$
15b2o38bo5bo6bo4bo4bo$15b3o49b2o2bo3bo2b2o$15b2o46b3o2bo3bobo3bo$69b3o
3b3o$56b2o12bo5bo$55b3o$56b2o2$72b3o$73bo$35bo$34b4o34b3o$35bo36b3o$
72bobo$72b3o$73bo22$6bo$5b3o$6bo$5bobo$5bobo$5b3o$5bobo$o11bo$5b3o$6bo
$6bo!
Now looking for small p40+20n memory loops... If no size limit, the T-to-cloverleaf converter is applicable at p80+20n, but the cloverleaf-pushing part is too long.
I thought there is que when spelling consecutive
EDIT: gun-supported p40 oscillator

Code: Select all

x = 44, y = 44, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
9bo$8bobo$9bo22bo$30b2obo$17b2o11bobo$18bo$12b3o2bobo$14bo3bo$13b2o27b
o$12bo12bo15bobo$3bo20bobo15bo$2bobo20bo$3bo28b3o$3b2o26bo2bo$31bo2bo$
31b4o2$10bo26bobo$9bobo24bob2o$10bo26bo4$16b2o5b2o$6bo9bo5bobo8bo$4b2o
bo9bo5b2o7bobo$4bobo21b3o2bo$28bobo$30bo2$39b2o$40bo$18bo15b3o2bobo$bo
15bobo16bo3bo$obo3b3o9bo16b2o$bo3bo2bo$5bo2bo16bo$5b4o15bobo$25bo$11bo
bo11b2o$10bob2o$11bo22bo$33bobo$34bo!
EDIT2: attempts with another p20 spaceship, including side-to-back, side-to-side, back-to-side reflectors, and some cloverleaf or object-producing collisions:

Code: Select all

x = 917, y = 231, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
7b3o11b3o43b3o11b3o23b3o11b3o103b3o11b3o303b3o11b3o153b3o11b3o53b3o11b
3o33b3o11b3o33b3o11b3o$8bo13bo45bo13bo25bo13bo105bo13bo305bo13bo155bo
13bo55bo13bo35bo13bo35bo13bo$8bo13bo45bo13bo25bo13bo105bo13bo305bo13bo
155bo13bo55bo13bo35bo13bo35bo13bo$7b3o11b3o43b3o11b3o23b3o11b3o103b3o
11b3o303b3o11b3o153b3o11b3o53b3o11b3o33b3o11b3o33b3o11b3o2$6bobobo9bob
obo41bobobo9bobobo21bobobo9bobobo101bobobo9bobobo301bobobo9bobobo151bo
bobo9bobobo51bobobo9bobobo31bobobo9bobobo31bobobo9bobobo$6bobobo9bobob
o41bobobo9bobobo21bobobo9bobobo101bobobo9bobobo301bobobo9bobobo151bobo
bo9bobobo51bobobo9bobobo31bobobo9bobobo31bobobo9bobobo$8bo13bo45bo13bo
25bo13bo105bo13bo305bo13bo155bo13bo55bo13bo35bo13bo35bo13bo$7b3o11b3o
43b3o11b3o23b3o11b3o103b3o11b3o303b3o11b3o153b3o11b3o53b3o11b3o33b3o
11b3o33b3o11b3o$8bo13bo45bo13bo25bo13bo105bo13bo305bo13bo155bo13bo55bo
13bo35bo13bo35bo13bo4$14b3o57b3o37b3o117b3o317b3o167b3o67b3o47b3o47b3o
$14b3o57b3o37b3o117b3o317b3o167b3o67b3o47b3o47b3o$15bo59bo39bo119bo
319bo169bo69bo49bo49bo5$6bo59bo39bo119bo319bo169bo69bo49bo49bo$5b3o57b
3o37b3o117b3o317b3o167b3o67b3o47b3o47b3o$6bo59bo39bo119bo319bo43bo125b
o69bo25b2o22bo49bo$5bobo31b2o24bobo37bobo117bobo317bobo42b2obo121bobo
67bobo23b3o21bobo47bobo$5bobo30b3o24bobo37bobo117bobo33b2o282bobo42bo
124bobo67bobo24b2o21bobo28b2o17bobo27b2o$5b3o6bo24b2o24b3o6bo30b3o6bo
110b3o6bo25b3o282b3o6bo160b3o6bo60b3o6bo40b3o6bo20b3o17b3o6bo19b3o$5bo
bo5b4o48bobo5b4o28bobo5b4o108bobo5b4o24b2o282bobo5b4o158bobo5b4o58bobo
5b4o38bobo5b4o19b2o17bobo5b4o18b2o$o12bob2o43bo12bob2o23bo12bob2o103bo
12bob2o303bo12bob2o153bo12bob2o53bo12bob2o33bo12bob2o33bo12bob2o$5b3o
5bobo49b3o5bobo29b3o5bobo109b3o5bobo309b3o5bobo159b3o5bobo59b3o5bobo
39b3o5bobo39b3o5bobo$6bo59bo39bo119bo319bo169bo27b2o40bo49bo49bo$6bo
59bo39bo119bo319bo169bo26b3o40bo49bo49bo$744b2o17$74bo40bo$73b3o38b3o$
73b3o38b3o110b3o11b3o$228bo13bo$228bo13bo$227b3o11b3o2$226bobobo9bobob
o$226bobobo9bobobo$228bo13bo$227b3o11b3o$228bo13bo4$234b3o$234b3o$235b
o5$226bo$225b3o$226bo21b2o$225bobo19b3o$225bobo20b2o$225b3o6bo$225bobo
5b4o$220bo12bob2o$225b3o5bobo$226bo$226bo320b3o11b3o$548bo13bo$548bo
13bo$547b3o11b3o2$546bobobo9bobobo$546bobobo9bobobo$548bo13bo$547b3o
11b3o$548bo13bo4$554b3o$554b3o$555bo5$227b3o11b3o63b3o11b3o53b3o11b3o
152bo$228bo13bo65bo13bo55bo13bo152b3o$228bo13bo65bo13bo55bo13bo153bo$
227b3o11b3o63b3o11b3o53b3o11b3o151bobo41b2o$545bobo40b3o$226bobobo9bob
obo61bobobo9bobobo51bobobo9bobobo150b3o6bo34b2o$226bobobo9bobobo61bobo
bo9bobobo51bobobo9bobobo150bobo5b4o$228bo13bo65bo13bo55bo13bo147bo12bo
b2o$227b3o11b3o63b3o11b3o53b3o11b3o151b3o5bobo$228bo13bo65bo13bo55bo
13bo153bo$546bo3$234b3o77b3o67b3o$234b3o77b3o67b3o$235bo79bo69bo4$410b
o$226bo79bo33bo35bo33b2obo$225b3o77b3o32b2obo31b3o32bo$226bo33bo45bo
33bo35bo$225bobo32b2obo41bobo67bobo$225bobo32bo44bobo67bobo$225b3o6bo
70b3o6bo60b3o6bo$225bobo5b4o68bobo5b4o58bobo5b4o$220bo12bob2o63bo12bob
2o53bo12bob2o$225b3o5bobo69b3o5bobo59b3o5bobo$226bo79bo69bo$226bo79bo
69bo20$227b3o11b3o$228bo13bo$228bo13bo$227b3o11b3o2$226bobobo9bobobo$
226bobobo9bobobo$228bo13bo$227b3o11b3o$228bo13bo4$234b3o$234b3o$235bo
5$226bo320b3o11b3o$225b3o35b2o283bo13bo$226bo35b3o283bo13bo$225bobo35b
2o282b3o11b3o$225bobo$225b3o6bo311bobobo9bobobo$225bobo5b4o309bobobo9b
obobo$220bo12bob2o311bo13bo$225b3o5bobo311b3o11b3o$226bo321bo13bo$226b
o3$554b3o$554b3o$555bo5$546bo$545b3o$546bo28b2o$545bobo26b3o$545bobo
27b2o$545b3o6bo$545bobo5b4o$540bo12bob2o$545b3o5bobo$546bo$227b3o11b3o
302bo$228bo13bo$228bo13bo$227b3o11b3o2$226bobobo9bobobo$226bobobo9bobo
bo$228bo13bo$227b3o11b3o$228bo13bo4$234b3o$234b3o$235bo5$226bo$225b3o$
226bo$225bobo$225bobo$225b3o6bo$225bobo5b4o33b2o$220bo12bob2o32b3o$
225b3o5bobo34b2o$226bo$226bo!
Why no side-to-fore? Maybe the spark is not exposed enough...
EDIT on April 2: taking inspiration from the almost-strictly-volatile p480, a spark completes the p101 asymmetric oscillator partial. The simpler boat-eating-T reaction would work had the catalyst below not made that domino surface.

Code: Select all

x = 98, y = 49, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
52bo$50b2obo$17bo2bo29bobo36bo$16bob2obo30b2o17bo16bobo$17bo2bo31bo18b
2obo14bo$2bo21bo25b2obo17bo$bobo19bobo24bobo$2bo17bo3bo27bo$2b2o16b3ob
o27b2o$obo17bo3bobo$2obo19bob2o$2bo21bo$17bo2bo55bo$16bob2obo53bobo$
17bo2bo55bo3$75bo$74bobo$75bo2$12bo49bo31bo$11bob2o46bob2o24bo3bobo$
12bobo47bobo23bobo3bo$13bo49bo24b2o2$12bo49bo$11bobo47bobo$12bo49bo$
12bo2bo46bo2bo$11bob2obo44bob2obo$12bo2bo46bo2bo5$7b3o48bo25b3o4b2o$7b
o2bo46b3o25bo5bob2o$10bo48b2o34bo$9b2o46bobo25bo8bobo$8bo49bo36bo$94b
2o$95bobo$94bob2o$95bo$95bo$59bobo29bob2o$59b2obo28b2o$61bo!
p54 T-ship shuttle from the smallest reflector:

Code: Select all

x = 18, y = 18, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11b2o$11bob2o$15bo$15bo$11bo2bob2o$8bob2o3bobo$11bo2b2o$15bo$14bobo$
15bo$11bo$2o8bobo$o10bo$bo$bo2bobobo$2b2ob3obo$4bo3bo$4b2o!
Random p4 oscs that make me hesitate whether they should be added to the collection or not

Code: Select all

x = 35, y = 10, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
19bob2obo4b2o$6b2o11b2o2b2o4bo$5bobo13b2o7bo$4bobo14bo8bob2o$o3bob2o
11bo3bo5bo2bobo$obo5bo10bo3bo6bo2bo$o2bo4bo11bobobo8b2o$2bobo2bo12bo2b
2o7bo$3bo2bo12bobo10b2o$3bo2bo13bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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GUYTU6J
Posts: 1850
Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » April 5th, 2022, 11:34 am

Nowadays this topic has been more of a public research log than a discussion thread. I feel lonely I just reviewed my old questions.
GUYTU6J wrote:
November 13th, 2020, 11:17 am
How do one actually enginner a caber tosser after calculating the ratio (v + u) / (v - u) mentioned in LifeWiki? I cannot make this one from Glimmering Garden work, where v = c/2 and u = 3c/20 :
GUYTU6J wrote:
March 19th, 2022, 12:54 am
... the distance between a forward 3c/20o and a chasing T-ship shrinks at a speed of c/2-3c/20 = (10-3)c/20 = 7c/20
To the past self: if you have calculated a bit more, you would see that (v + u) / (v - u) in this case equals to (10+3)/(10-3) = 13/7. But the intervals and base period p measured in ticks should be finite positive integers, which cannot contain an infinite amount of 7's among prime factors, which is actually required to ensure that every interval of the form p*(13/7)^n is an integer. So without regulators to round up the fractional intervals you are unable to construct a caber tosser with c/2 and 3c/20 and a stationary reflecting&duplicating base.

On the other hand, if the faster spaceship is c/4 instead, then the ratio (5+3)/(5-3) = 4 is a nice round number and a power of 2, suggesting another caber tosser design. Short of knowledge of interactions between xq4_nmkz31 and xq20_dadz373, I beginned with building a backrake. It turns out that the minimum viable period is 120, as shown below. Certainly it can be reduced with a smaller p120 siderake on the left, but this is not the goal at the moment.

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 194, y = 213, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
61b3o11b3o$61bobo11bobo$62bo13bo$62bo13bo$62bo13bo$60bo3bo9bo3bo$61bob
o11bobo2$61bobo11bobo$60b5o9b5o$61b3o11b3o$62bo13bo2$80bo13bo$79bobo
11bobo$68b3o8bobo11bobo$68b3o8bobo11bobo$69bo9b3o11b3o2$80bo13bo$79b3o
11b3o2$78bo3bo9bo3bo$77b7o7b7o$75bo4bo4bo3bo4bo4bo$74b2o2bo3bo2b2ob2o
2bo3bo2b2o$75bo3bobo3bo3bo3bobo3bo$76b3o3b3o5b3o3b3o$68b3o6bo5bo7bo5bo
$68b3o$69bo3$77b3o$78bo$86b3o$77b3o6b3o$77b3o7bo8bo$77bobo15b3o$77b3o
15b3o$78bo$68b3o23b5o$68b3o25bo$69bo$94b5o$95b3o$95b3o$95b3o2$76bo$76b
2obo$76bo$3b3o11b3o$2bo3bo9bo3bo$2bo3bo9bo3bo$4bo13bo2$4bo13bo$3bobo
11bobo$4bo13bo$3bobo11bobo$3bobo11bobo$bobobobo7bobobobo$2o2bo2b2o5b2o
2bo2b2o$b2o3b2o7b2o3b2o$2b5o9b5o$4bo13bo$4bo13bo2$102bo13bo$100bo3bo9b
o3bo$10b3o8b3o11b3o$10b3o8bobo11bobo64bo13bo$11bo88bo3bo9bo3bo$21bobo
11bobo63bobo11bobo$20b2ob2o9b2ob2o63bo13bo$20b2ob2o9b2ob2o61bo3bo9bo3b
o$21b3o11b3o64bo13bo$28b3o71bo13bo$21b3o4b3o4b3o59bo4bo4bo3bo4bo4bo$
22bo6bo6bo63bo3bo4bo4bo3bo$95bobo9bobobo9bobo$101b3o5bo5b3o2$10b3o$10b
3o6b3o77bo5bo7bo5bo$11bo7bobo99b3o11b3o$20bo101bo13bo$20bo101bo13bo$
20bo17bo48b3o31b3o11b3o$18bo3bo14b3o48bo$19bobo6b3o6b3o80bobobo9bobobo
$28b3o7bo49bo19b3o9bobobo9bobobo$19bobo7bo78b3o11bo13bo$18b5o13bo3bo
68bo11b3o11b3o$19b3o14b5o81bo13bo$20bo16bobo$10b3o24b3o$10b3o$11bo116b
3o$26bo92b3o6b3o$26b2obo99bo$26bo91bo3bo$119b3o$77b3o58bo$78bo29b3o26b
3o$68b3o37b3o9bo15b2ob2o$68b3o6b3o29bo9bobo16bo$60bo8bo7b3o38b2ob2o$
59b3o15bobo38b5o15bo$59b3o15b3o39bobo15bobo$78bo37b2obobob2o13bo$58b5o
52b2obo3bob2o2b3o7bo$60bo55b2o5b2o3b3o5bo3bo$117b2obob2o5bo5bo2bo2bo$
58b5o72bo2bo2bo$59b3o73b2obob2o$59b3o$59b3o46b3o12bo13b3o14bo13bo$108b
3o12b2obo26b3o11b3o$109bo13bo30bo13bo$113bo40bo13bo$113b2obo36b3o11b3o
$113bo39b3o11b3o$153bobo11bobo$154bo13bo$43b3o11b3o93b3o11b3o$44bo13bo
94bobo11bobo$91b2o60b3o11b3o$44bo13bo$43b3o11b3o31b3o$44bo13bo28b3o2b
2o67bo$44bo13bo29bo$42bo3bo9bo3bo100bo8bo13bo$29b3o128b3o6b3o11b3o$30b
o11bo3bo3b3o3bo3bo107bobobo9bobobo$50b3o35bo80bobo11bobo$30bo13bo6bo6b
o28b3o2b2o$63b3o11b3o11b3o$63bobo11bobo63b2o25bo13bo$63bobo11bobo11b2o
50b3o23bobo11bobo$143b2o24b3o11b3o$63bobo11bobo89bobo11bobo$63bobo11bo
bo89b3o11b3o$64bo13bo82bo4b2obobob2o5b2obobob2o$166bobobobobo5bobobobo
bo$63b3o11b3o81bo4bo2b3o2bo5bo2b3o2bo$62b5o9b5o79b3o4b2obob2o7b2obob2o
$50b3o8b2obob2o7b2obob2o88bo13bo$50b3o9bobobo9bobobo$51bo11b3o11b3o$
64bo13bo$177bo2$62bo105bo8bo8bo$60bo3bo5b3o94b3o6b3o5bo3bo$19b3o48b3o
7bo86b3o$19bobo40bo8bo8bo80bo24bo$20bo39bo3bo14b3o84b5o13bo3bo$20bo40b
obo16bo80bo6bo16bobo$2bo17bo41bo16b3o78b3o23bo$b3o14bo3bo27b3o7bo3bo
15bo85b5o13bo3bo$b3o15bobo28b3o9bo104b3o16bo$2bo48bo10bo17bo86b3o16bo$
19bobo35bo4bo4bo10b2ob2o84b3o11bo4bo4bo$o3bo13b5o37bo3bo119bo3bo$5o14b
3o33bobo9bo111bobo9bobo$bobo16bo40b3o5b2o6b3ob3o92b3o6b3o$b3o64b2ob2o
2b3ob3ob3o$70b3o2bo2bo3bo2bo82b2o$59bo5bo5bo3bo3bobo3bo81b3o13bo5bo$
14bo61b3o3b3o83b2o$11bob2o48bo$14bo48b2obo92b2o$63bo95b2o2$29b3o$30bo$
42bo2bo92b2o$30bo11b3o92b3o$42bo95b2o14$88bo$88bo$88bo$29b3o$30bo57bo$
88bo$30bo46bo10bo10bo$29b3o44b3o19b3o$30bo46bo21bo$30bo45bobo19bobo$
28bo3bo43bobo19bobo$76b3o19b3o$28bo3bo43bobo9bo9bobo$71bo11bo9bo11bo$
30bo45b3o9bo9b3o$77bo7b2o3b2o7bo$77bo8bobobo8bo$86bo3bo$88bo!
Next is to engineer a c/4o gun, which is a piece of cake at p60. Base period 60 is chosen for having a variety of oscillators and being a factor of 120.

Code: Select all

x = 72, y = 60, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
26bo$25bobo$21b2o3bo3b2o$21bobo5bobo$20bob2o5b2obo$21bo3b3o3bo$25bobo$
25b3o4$4bo14bo$2b3o12b3o49bo$37bo30bobo$bobobo10bobobo16b2obo28bo$37bo
26b2o$2b3o12b3o42bo2bo$4bo14bo42b4o$63b2o2$42bo$41b3o$24b3o13bo2b2o25b
o$24bo2bo11b3o2bo11b2o11bobo$23bo3bo12bo4bo8bobo13bo$17bo5bo3bo8b2o8b
2o6b2obo$16bobo4bo2bo9bo10bo8bo$17bo10b2o7bo9bob2o$28b2o7bo10bobo5bo$
30bo5bobo9bo5b2obo$37bo9bobo4bobo4bo$48bo7b2o3b2obo$bo54bo4bo$obo6bo
26b2o17bobo$bo5b2ob2o25bo18bo$7bo3bo24bobo17bo$bo5bo3bo25bo17bobo$obo
5b3o45bo$bo6bobo48bo3bo$4bo2bobobo3bobo40bobobobo$3bob2ob3obobob2o41bo
3bo$4bo2bo3bo3bo$10b2o3b2o12b2o3b2o5bo$23bo2bo3bo3bo5bobo$22bob2ob3obo
bob2o4b2o$23bo2bobobo3bobo$20bo$19bobo6bo$20bo5bo3bo$26bobobo$20bo6b3o
15bo$19bobo22b3o$20bo23b3o4$46bo$36bo8bobo$35bobo8bo$36bo!
Combining these two parts gives the following pattern, which as expected is a caber tosser working like a charm. The n-th T-ship is emitted at generations 0, 720, 3600, 15120, 61200, ..., 240*(4^n-1).

Code: Select all

#C [[ STEP 4 ]]
x = 194, y = 388, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
61b3o11b3o$61bobo11bobo$62bo13bo$62bo13bo$62bo13bo$60bo3bo9bo3bo$61bob
o11bobo2$61bobo11bobo$60b5o9b5o$61b3o11b3o$62bo13bo2$80bo13bo$79bobo
11bobo$68b3o8bobo11bobo$68b3o8bobo11bobo$69bo9b3o11b3o2$80bo13bo$79b3o
11b3o2$78bo3bo9bo3bo$77b7o7b7o$75bo4bo4bo3bo4bo4bo$74b2o2bo3bo2b2ob2o
2bo3bo2b2o$75bo3bobo3bo3bo3bobo3bo$76b3o3b3o5b3o3b3o$68b3o6bo5bo7bo5bo
$68b3o$69bo3$77b3o$78bo$86b3o$77b3o6b3o$77b3o7bo8bo$77bobo15b3o$77b3o
15b3o$78bo$68b3o23b5o$68b3o25bo$69bo$94b5o$95b3o$95b3o$95b3o2$76bo$76b
2obo$76bo$3b3o11b3o$2bo3bo9bo3bo$2bo3bo9bo3bo$4bo13bo2$4bo13bo$3bobo
11bobo$4bo13bo$3bobo11bobo$3bobo11bobo$bobobobo7bobobobo$2o2bo2b2o5b2o
2bo2b2o$b2o3b2o7b2o3b2o$2b5o9b5o$4bo13bo$4bo13bo2$102bo13bo$100bo3bo9b
o3bo$10b3o8b3o11b3o$10b3o8bobo11bobo64bo13bo$11bo88bo3bo9bo3bo$21bobo
11bobo63bobo11bobo$20b2ob2o9b2ob2o63bo13bo$20b2ob2o9b2ob2o61bo3bo9bo3b
o$21b3o11b3o64bo13bo$28b3o71bo13bo$21b3o4b3o4b3o59bo4bo4bo3bo4bo4bo$
22bo6bo6bo63bo3bo4bo4bo3bo$95bobo9bobobo9bobo$101b3o5bo5b3o2$10b3o$10b
3o6b3o77bo5bo7bo5bo$11bo7bobo99b3o11b3o$20bo101bo13bo$20bo101bo13bo$
20bo17bo48b3o31b3o11b3o$18bo3bo14b3o48bo$19bobo6b3o6b3o80bobobo9bobobo
$28b3o7bo49bo19b3o9bobobo9bobobo$19bobo7bo78b3o11bo13bo$18b5o13bo3bo
68bo11b3o11b3o$19b3o14b5o81bo13bo$20bo16bobo$10b3o24b3o$10b3o$11bo116b
3o$26bo92b3o6b3o$26b2obo99bo$26bo91bo3bo$119b3o$77b3o58bo$78bo29b3o26b
3o$68b3o37b3o9bo15b2ob2o$68b3o6b3o29bo9bobo16bo$60bo8bo7b3o38b2ob2o$
59b3o15bobo38b5o15bo$59b3o15b3o39bobo15bobo$78bo37b2obobob2o13bo$58b5o
52b2obo3bob2o2b3o7bo$60bo55b2o5b2o3b3o5bo3bo$117b2obob2o5bo5bo2bo2bo$
58b5o72bo2bo2bo$59b3o73b2obob2o$59b3o$59b3o46b3o12bo13b3o14bo13bo$108b
3o12b2obo26b3o11b3o$109bo13bo30bo13bo$113bo40bo13bo$113b2obo36b3o11b3o
$113bo39b3o11b3o$153bobo11bobo$154bo13bo$43b3o11b3o93b3o11b3o$44bo13bo
94bobo11bobo$91b2o60b3o11b3o$44bo13bo$43b3o11b3o31b3o$44bo13bo28b3o2b
2o67bo$44bo13bo29bo$42bo3bo9bo3bo100bo8bo13bo$29b3o128b3o6b3o11b3o$30b
o11bo3bo3b3o3bo3bo107bobobo9bobobo$50b3o35bo80bobo11bobo$30bo13bo6bo6b
o28b3o2b2o$63b3o11b3o11b3o$63bobo11bobo63b2o25bo13bo$63bobo11bobo11b2o
50b3o23bobo11bobo$143b2o24b3o11b3o$63bobo11bobo89bobo11bobo$63bobo11bo
bo89b3o11b3o$64bo13bo82bo4b2obobob2o5b2obobob2o$166bobobobobo5bobobobo
bo$63b3o11b3o81bo4bo2b3o2bo5bo2b3o2bo$62b5o9b5o79b3o4b2obob2o7b2obob2o
$50b3o8b2obob2o7b2obob2o88bo13bo$50b3o9bobobo9bobobo$51bo11b3o11b3o$
64bo13bo$177bo2$62bo105bo8bo8bo$60bo3bo5b3o94b3o6b3o5bo3bo$19b3o48b3o
7bo86b3o$19bobo40bo8bo8bo80bo24bo$20bo39bo3bo14b3o84b5o13bo3bo$20bo40b
obo16bo80bo6bo16bobo$2bo17bo41bo16b3o78b3o23bo$b3o14bo3bo27b3o7bo3bo
15bo85b5o13bo3bo$b3o15bobo28b3o9bo104b3o16bo$2bo48bo10bo17bo86b3o16bo$
19bobo35bo4bo4bo10b2ob2o84b3o11bo4bo4bo$o3bo13b5o37bo3bo119bo3bo$5o14b
3o33bobo9bo111bobo9bobo$bobo16bo40b3o5b2o6b3ob3o92b3o6b3o$b3o64b2ob2o
2b3ob3ob3o$70b3o2bo2bo3bo2bo82b2o$59bo5bo5bo3bo3bobo3bo81b3o13bo5bo$
14bo61b3o3b3o83b2o$11bob2o48bo$14bo48b2obo92b2o$63bo95b2o2$29b3o$30bo$
42bo2bo92b2o$30bo11b3o92b3o$42bo95b2o11$132bo13bo$131b3o11b3o$131b3o
11b3o$88bo$88bo42b3o11b3o$88bo42bobo11bobo$29b3o100bo13bo$30bo57bo42bo
bo11bobo$88bo$30bo46bo10bo10bo39bo$29b3o44b3o19b3o$30bo46bo21bo39bo$
30bo45bobo19bobo11bo13bo11b3o$28bo3bo43bobo19bobo10b3o11b3o$76b3o19b3o
9b2ob2o9b2ob2o$28bo3bo43bobo9bo9bobo11bo13bo$71bo11bo9bo11bo$30bo45b3o
9bo9b3o11bo13bo$77bo7b2o3b2o7bo11bobo11bobo$77bo8bobobo8bo12bo13bo$86b
o3bo21bo13bo$88bo21bo3bo9bo3bo$109bo2bo2bo7bo2bo2bo9bo$109bo2bo2bo7bo
2bo2bo$109b2obob2o7b2obob2o9bo$138b3o$111b3o11b3o3$119bo2$119bo$110bo
7b3o$109bobo16bo$109bobo15b3o$109bobo16bo10bo$109b3o15bobo$127bobo9bo$
110bo16b3o8b3o$109b3o15bobo$134bo$108bo3bo14b3o$107b7o6b2o6bo$105bo4bo
4bo6bo5bo$104b2o2bo3bo2b2o$105bo3bobo3bo2b3o$106b3o3b3o$107bo5bo12b2o$
126b3o$126b2o4$148bo$146b4o$148bo4$131bo$131b2obo$78bo52bo$77b3o$77b3o
2$77b3o8bo22bo$77bobo5b2o3b2o19b2obo$78bo7bobobo20bo$77bobo6bo3bo$88bo
2$91bo$91b2obo$91bo22$70bo3bo$69bobobobo21bo$70bo3bo20bo3bo$77bo17bobo
bo$76bobo15b2o3b2o$77bo19bo$77bo$76bobo$71b2o4bo$70bob2o2b2o$71b2o4bob
o$76bob2o$77bo2$77bo$76bob2o$63bo13bobo38b2o$62bobo11b2o40bo3bo$63bo
52b2ob3obo$115bo2bobobobo$115bo8bo$114bo10bo$114b2o8b2o3$76bo30bo$64bo
8bob2o27bob2o$63bobo10bo30bo15b2o$64bo58b3o$123b2o$74bo3bo$73bobobobo
17bo$74bo3bo16bo3bo$71bo17bo5bobobo$70bobo15bobo3b2o3b2o$71bo17bo7bo$
71bo$70bobo2b3o$71bob2o2bo$71b2obo3bo39b3o$69bobob2o2bo41bo$69b2obo2b
3o$71bo47bo2$71bo$69b2obo$69bobo13bo11bo$71b2o11bobo8bo3bo$85bo9bobobo
$60bo3bo29b2o3b2o$59bobobobo31bo9bo$60bo3bo41bob2o$67bo39bobo$66bobo
16b3o19b2o$67bo20b2o$67bo21bo14b3o3bo$62b2o2bobo16bo3bo14bobo2bobo$61b
o5bo18b3o15b3o3bo$61b2obob2o15b2o$61bo5bobo13b2o22b2o$62b2o2bob2o12bo
24bobo4bo$67bo38bob2o3bobo$107bo6bo$67bo$66bob2o$53bo13bobo$52bobo11b
2o8bobo3bo2b2o$53bo21bob2o2bob2obo9b3o17b2o$76bo5bo14bo18b2o$88bo29b3o
$68bo18b3o7bo15b2o3bobo$67bobo18bobo18b2o3bo$67b2o21b2o17b2o$89b2o29bo
$59b2o27b2o29bobo$54bo4b3o25bo32bo$53bobo3b2o25bo$54bo26bo2b3o30bo$80b
ob2o19b2o11bobo$81bo2bo16bobo13bo$83b2o16b2obo$103bo2$103bo$81b2o3b2o
13b2obo$75bo2bo3bo3bo14bobo3b3o$74bob2ob3obobob2o14b2o2bo2bo$75bo2bobo
bo3bobo14bo3b3o$72bo29bobo$71bobo29bo$72bo30bo$79b3o20bobo$72bo7bo13b
2o7bo$71bobo19b2o11bo3bo$72bo7bo12b2obo8bobobobo$94b3o9bo3bo3$98bo$88b
o8bobo$87bobo8bo$88bo!
How about an infinite xq4_nmkz31 hotel, anyone? Or simplify anywhere of this huge structure first...
(Bonus point: a reaction hidden above may lead to a speed booster/advancer device to accelerate a T-ship.)
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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GUYTU6J
Posts: 1850
Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » April 9th, 2022, 6:27 am

Who was searching asymmetric soups with the Anonymous handle these days?

I am here to announce a good news. The long envisioned blueprint has been completed to give a class of 7-engine forerakes! There is a simple 3c/20 + sideways T-ship collision that emits a suitable forward dot spark via B3i instead of B3a. I have constructed and optimized every periods from 120 to 420:

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 1108, y = 59, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
942b3o15b3o49b3o15b3o49b3o15b3o$1012bobo15bobo50bo17bo$941bo3bo13bo3bo
49bo17bo$942b3o15b3o50bo17bo51bo17bo$1013bo17bo50b3o15b3o$1011bo3bo13b
o3bo49bo17bo$943bo17bo50bobo15bobo50bo17bo$732b3o15b3o49b3o15b3o49b3o
15b3o49bobo15bobo118bo3bo13bo3bo$731bo3bo13bo3bo49bo17bo50bobo15bobo
48b2ob2o13b2ob2o48bobo15bobo$663bo17bo49bo3bo13bo3bo49bo17bo119b5o13b
5o47b5o13b5o47bo3bo13bo3bo$661bo3bo13bo3bo49bo17bo50b3o15b3o49bobo15bo
bo49bobo15bobo49b3o15b3o$871b2ob2o13b2ob2o45b2obobob2o9b2obobob2o47bo
17bo51bo17bo$663bo17bo51bo17bo49bobobo13bobobo47b2ob2o13b2ob2o44b2obo
3bob2o7b2obo3bob2o$75bo13bo56bo13bo125b3o11b3o123bo13bo55bo13bo55b3o
11b3o78bo3bo13bo3bo48bobo15bobo48bobobo13bobobo48b3o15b3o46b2o5b2o9b2o
5b2o$73bo3bo9bo3bo53bobo11bobo55b3o11b3o123b3o11b3o51bobo11bobo53bobo
11bobo10b3o15b3o49b3o15b3o49bobo15bobo24b3o11b3o9bo17bo51bo17bo118b2ob
ob2o11b2obob2o$145bobo11bobo54bo3bo9bo3bo50bo3bo9bo3bo52bo3bo9bo3bo50b
obo11bobo11bo17bo23bobo11bobo10bobo15bobo22bo3bo9bo3bo9bo17bo26b3o11b
3o8bo17bo24bo3bo9bo3bo7bobo15bobo25b3o11b3o7b3o15b3o49b3o15b3o$2b3o11b
3o56bo13bo55bobo11bobo54bo3bo9bo3bo51b3o11b3o53bo3bo9bo3bo50bobo11bobo
10bobo15bobo22bobo11bobo10bobo15bobo23b3o11b3o55bobo11bobo6bo3bo13bo3b
o22bo3bo9bo3bo7bobo15bobo25bobo11bobo8bo17bo51bo17bo104bo13bo55bo13bo$
3bo13bo55bo3bo9bo3bo53b3o11b3o56bo13bo125bo13bo52b3o11b3o10bobo15bobo
22b3o11b3o80b3o15b3o25bobo11bobo8bo17bo26bo13bo7bobobobo11bobobobo23bo
bo11bobo55b3o11b3o128bobo11bobo53bobo11bobo$74bobo11bobo361bobo15bobo
49bobo15bobo49b3o15b3o50bo17bo47b2o2bo2b2o9b2o2bo2b2o95bo13bo129bobo
11bobo53bobo11bobo$3bo13bo57bo13bo56bo13bo57bo13bo54bo13bo56bo13bo53bo
13bo11b3o15b3o23bo13bo11bobo15bobo24bo13bo10bobo15bobo25bobo11bobo3bo
4bo4bo7bo4bo4bo21bo13bo7b2o3b2o11b2o3b2o23bobo11bobo56bo13bo56b3o11b3o
56bobo11bobo53bobo11bobo$2b3o11b3o54bo3bo9bo3bo53b3o11b3o55bobo11bobo
52bobo11bobo54bobo11bobo51b3o11b3o53b3o11b3o11bo17bo24bobo11bobo9b3o
15b3o25bobo11bobo6bo3bo13bo3bo23bobo11bobo7b5o13b5o24bobo11bobo55b3o
11b3o56bo13bo57b3o11b3o53b3o11b3o$3bo13bo57bo13bo128bo13bo9b3o15b3o22b
2ob2o9b2ob2o8b3o15b3o25bo13bo9b3o15b3o50bo17bo93b2ob2o9b2ob2o9bo17bo
27bo13bo2bobo9bobo3bobo9bobo19bo13bo10bo17bo27bo13bo$3bo13bo57bo13bo
54bo3bo9bo3bo54bobo11bobo51b5o9b5o8bobo15bobo24bobo11bobo9bo17bo22bo3b
o9bo3bo9b3o15b3o21bo3bo9bo3bo9b3o15b3o22b5o9b5o78b3o15b3o24bobo11bobo
9bo17bo97bobobo9bobobo55bo13bo58bo13bo55bo13bo$bo3bo9bo3bo50bo4bo4bo3b
o4bo4bo48b7o7b7o53bobo11bobo7bo3bo13bo3bo22bobo11bobo10bo17bo25bobo11b
obo49b7o7b7o49b7o7b7o7b5o13b5o22bobo11bobo55b3o11b3o52bobo11bobo54b3o
11b3o54bobobo9bobobo54b3o11b3o56b3o11b3o53b3o11b3o$73bo3bo4bo4bo3bo49b
o4bo4bo3bo4bo4bo49bobobobo7bobobobo6b3o15b3o20b2obobob2o5b2obobob2o7bo
17bo23bobobobo7bobobobo7bo17bo19bo4bo4bo3bo4bo4bo5bo3bo13bo3bo17bo4bo
4bo3bo4bo4bo4b2obob2o11b2obob2o18b2obobob2o5b2obobob2o51b5o9b5o49bobob
obo7bobobobo51b5o9b5o55bo13bo57bo13bo$bo3bo3b3o3bo3bo48bobo9bobobo9bob
o43b2o2bo3bo2b2ob2o2bo3bo2b2o47b2o2bo2b2o5b2o2bo2b2o45b2obo3bob2o3b2ob
o3bob2o6bo17bo22b2o2bo2b2o5b2o2bo2b2o5b3o15b3o17b2o2bo3bo2b2ob2o2bo3bo
2b2o3b7o11b7o15b2o2bo3bo2b2ob2o2bo3bo2b2o4bobobo13bobobo18b2obo3bob2o
3b2obo3bob2o49b2obob2o7b2obob2o3bo5bo11bo5bo19b2o2bo2b2o5b2o2bo2b2o49b
2obob2o7b2obob2o53b3o11b3o56bo13bo56bo3bo9bo3bo51bo3bo9bo3bo$9b3o62b3o
5bo5b3o50bo3bobo3bo3bo3bobo3bo49b2o3b2o7b2o3b2o47b2o5b2o5b2o5b2o5bo3bo
13bo3bo21b2o3b2o7b2o3b2o7bo17bo19bo3bobo3bo3bo3bobo3bo2bo4bo4bo7bo4bo
4bo14bo3bobo3bo3bo3bobo3bo6b3o15b3o20b2o5b2o5b2o5b2o51bobobo9bobobo49b
2o3b2o7b2o3b2o51bobobo9bobobo55bo13bo55bo3bo9bo3bo53b7o7b7o49b7o7b7o$
3bo6bo6bo124b3o3b3o5b3o3b3o51b5o9b5o8bo17bo22b2obob2o7b2obob2o7bobo15b
obo23b5o9b5o8bo17bo20b3o3b3o5b3o3b3o2b2o2bo3bo2b2o5b2o2bo3bo2b2o14b3o
3b3o5b3o3b3o8bo17bo22b2obob2o7b2obob2o53b3o11b3o51b5o9b5o53b3o11b3o
196bo4bo4bo3bo4bo4bo45bo4bo4bo3bo4bo4bo$32b3o15b3o49b3o15b3o20bo5bo7bo
5bo8b3o15b3o25bo13bo9bobo15bobo95bo13bo8bo3bo13bo3bo19bo5bo7bo5bo4bo3b
obo3bo7bo3bobo3bo16bo5bo7bo5bo125bo13bo54bo13bo56bo13bo127bo3bo3b3o3bo
3bo50b2o2bo3bo2b2ob2o2bo3bo2b2o43b2o2bo3bo2b2ob2o2bo3bo2b2o$31bo3bo13b
o3bo18bo5bo7bo5bo10bo17bo50bobo15bobo25bo13bo8b2ob2o13b2ob2o48bobo15bo
bo25bo13bo76b3o3b3o9b3o3b3o232bo13bo206b3o59bo3bobo3bo3bo3bobo3bo45bo
3bobo3bo3bo3bobo3bo$18b3o10bo3bo13bo3bo49bo17bo119b5o13b5o47b5o13b5o
47bo3bo13bo3bo46bo5bo11bo5bo382b3o63bo6bo6bo54b3o3b3o5b3o3b3o47b3o3b3o
5b3o3b3o$18bobo12bo17bo50b3o15b3o49bobo15bobo49bobo15bobo49b3o15b3o
322bo139bo61b3o6b3o124bo5bo7bo5bo49bo5bo7bo5bo$18bobo69b3o78b2ob2o13b
2ob2o45b2obobob2o9b2obobob2o47bo17bo51bo17bo243b3o5bo3bo127b3o5bo3bo
60bo$33bo17bo39bo9bobobo13bobobo37b3o7b2ob2o13b2ob2o30b3o11b2obo3bob2o
7b2obo3bob2o97b3o74b3o67b3o123bo7b3o66b3o60bo7b3o77bo3bo68b3o$bo16bobo
11bobo15bobo38bo9bobobo13bobobo38bo9b3o15b3o23bo7b3o12b2o5b2o9b2o5b2o
27b3o6b3o51bo7b3o75bo69bo60b3o6b3o52bo8bo8bo50bo7b3o60bo8bo8bo70b3o69b
obo$3o15bobo12bo17bo38b3o10bo17bo30b3o60bobo7bo7b3o4b2obob2o11b2obob2o
28b3o7bo51bobo7bo7b3o56b3o67b3o68b3o7bo52b3o14bo3bo47bobo7bo7b3o50b3o
14bo3bo51bo88bobo$bo17bo12bobo15bobo20bo7b3o18b3o15b3o29b3o6b3o8b3o15b
3o21b5o14bobo58bo59b5o14bobo56b3o6b3o58b3o6b3o60bo62bo16bobo47b5o14bob
o51bo16bobo51b3o160b3o67b3o$bo30bobo15bobo19b3o6b3o5bobobo9bo17bo22bo
8bo7b3o9bo17bo22b2ob2o84bo50b2ob2o65bo8bo7b3o50bo8bo7b3o69bo52b3o16bo
48b2ob2o67b3o16bo51b2ob2o15bo53bo16bobo71bo69bo$3o6b3o6b3o9bobobobo11b
obobobo17b3o7bo6bobobo49b3o15bobo51b3o15bobo49bo16b3o50b3o15bobo47b3o
15bobo49b3o15bobo51bo16b3o52bo15bo3bo47b3o15bobo51bo15bo3bo51bo16bobo
51b3o15bobo61b3o67b3o$3o6b3o5b5o7b2o2bo2b2o9b2o2bo2b2o35bo51b3o15b3o
52bo15b2ob2o47b3o16bo52bo15b2ob2o46b3o15b3o49b3o15b3o50b3o16bo71bo50bo
15b2ob2o68bo69b2ob2o51bo17bo62b3o6b3o58b3o6b3o$obo7bo5b2obob2o7b2o3b2o
11b2o3b2o17b3o15b3o69bo52b3o14b2ob2o48bo17bo51b3o14b2ob2o65bo69bo52bo
17bo53bo17bo49b3o14b2ob2o50bo17bo53bo15b5o51bo72bo8bo7b3o50bo8bo7b3o$b
o15bobobo9b5o13b5o18bobo16bo50b5o68b3o15b3o48bobo14bo3bo49b3o15b3o46b
5o65b5o67bobo14bo3bo49b2ob2o10bo4bo4bo44b3o15b3o49b2ob2o10bo4bo4bo47bo
bo15bobo51b3o6b3o6b3o52b3o15bobo49b3o15bobo$3o15b3o12bo17bo21bo70bo70b
3o66bobo68b3o66bo69bo69bobo86bo3bo47b3o85bo3bo51bo13b2obobob2o48b3o6b
3o5b5o51b3o15b3o49b3o15b3o$obo16bo13bo17bo20bobo138b2obob2o13b3o48b3o
14bo3bo47b2obob2o13b3o188b3o14bo3bo64bo9bobo40b2obob2o13b3o64bo9bobo
46bo7b3o2b2obo3bob2o47bobo7bo5b2obob2o69bo69bo$3o139b5o66b2obob2o7bo6b
o49bobo66b2obob2o7bo6bo47b5o65b5o67bobo67b3ob3o6b2o5b3o46b2obob2o7bo6b
o49b3ob3o6b2o5b3o50bo3bo5b3o3b2o5b2o49bo15bobobo50b5o65b5o$143b3o64b3o
b5ob3o56bo11bo11bo46b3ob5ob3o60b3o67b3o63bo11bo11bo48b3ob3ob3o2b2ob2o
50b3ob5ob3o59b3ob3ob3o2b2ob2o56bo2bo2bo5bo5b2obob2o49b3o15b3o53bo69bo$
14bo69bo58b3o8bo55b3o3bo3b3o2bo58b3o7bo55b3o3bo3b3o2bo57b3o8bo58b3o8bo
59b3o7bo57bo2bo3bo2bo2b3o52b3o3bo3b3o2bo56bo2bo3bo2bo2b3o58bo2bo2bo67b
obo16bo$11bob2o66bob2o58b3o5bob2o55b2o3bobo3b2o2bo59bo7b2o55b2o3bobo3b
2o2bo57b3o5bob2o58b3o5bob2o60bo7b2o57bo3bobo3bo3bo5bo5bo41b2o3bobo3b2o
2bo56bo3bobo3bo3bo5bo5bo47b2obob2o67b3o69b5o65b5o$14bo36bo32bo36bo32bo
36bo20b3o3b3o4bo35bo23bo8bo36bo20b3o3b3o4bo35bo32bo36bo32bo36bo23bo8bo
36bo21b3o3b3o39bo20b3o3b3o4bo35bo21b3o3b3o39bo69bo69bo31b3o35bo31b3o
35bo$24bo25b3o41bo25b3o41bo25b3o19b3o3b3o13bo25b3o41bo25b3o19b3o3b3o
13bo25b3o41bo25b3o41bo25b3o41bo25b3o41bo25b3o19b3o3b3o13bo25b3o41bo25b
3o25b3o13bo25b3o41bo25b3o30b3o8bo25b3o30b3o8bo25b3o$21bob2o26bo39bob2o
26bo39bob2o26bo39bob2o26bo39bob2o26bo39bob2o26bo39bob2o26bo39bob2o26bo
39bob2o26bo39bob2o26bo39bob2o26bo39bob2o26bo39bob2o26bo39bob2o26bo31b
3o5bob2o26bo31b3o5bob2o26bo$24bo17bo7bobo41bo17bo7bobo41bo17bo7bobo41b
o17bo7bobo41bo17bo7bobo41bo17bo7bobo41bo17bo7bobo41bo17bo7bobo41bo17bo
7bobo41bo17bo7bobo41bo17bo7bobo41bo17bo7bobo41bo17bo7bobo41bo17bo7bobo
41bo17bo7bobo41bo17bo7bobo$34bo7bo7bobo51bo7bo7bobo51bo7bo7bobo51bo7bo
7bobo51bo7bo7bobo51bo7bo7bobo51bo7bo7bobo51bo7bo7bobo51bo7bo7bobo51bo
7bo7bobo51bo7bo7bobo51bo7bo7bobo51bo7bo7bobo51bo7bo7bobo51bo7bo7bobo
51bo7bo7bobo$31bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o
48bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o
48bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o48bob2o7bo7b3o
48bob2o7bo7b3o48bob2o7bo7b3o$34bo8bo6bobo51bo8bo6bobo51bo8bo6bobo51bo
8bo6bobo51bo8bo6bobo51bo8bo6bobo51bo8bo6bobo51bo8bo6bobo51bo8bo6bobo
51bo8bo6bobo51bo8bo6bobo51bo8bo6bobo51bo8bo6bobo51bo8bo6bobo51bo8bo6bo
bo51bo8bo6bobo$45bo11bo57bo11bo57bo11bo57bo11bo57bo11bo57bo11bo57bo11b
o57bo11bo57bo11bo57bo11bo57bo11bo57bo11bo57bo11bo57bo11bo57bo11bo57bo
11bo$41bo3bo4b3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b
3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o
58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o58bo3bo4b3o$51bo69bo69bo69bo69bo69bo
69bo69bo69bo69bo69bo69bo69bo69bo69bo69bo$43bo7bo61bo7bo61bo7bo61bo7bo
61bo7bo61bo7bo61bo7bo61bo7bo61bo7bo61bo7bo61bo7bo61bo7bo61bo7bo61bo7bo
61bo7bo61bo7bo!
As usual the design is adjustable: from p400 on, advancing the T-to-T+blinker pair by 14 ticks with respect to the 5-engine dot sparker increases the period by 20.

For lower periods, the longest-lasting head-on 2T annihilation solves p40 and p80:

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 190, y = 49, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
69bo13bo85bo13bo$68bobo11bobo83bobo11bobo$68bobo11bobo83bobo11bobo$68b
obo11bobo83bobo11bobo$68b3o11b3o83b3o11b3o$6bo13bo$5b3o11b3o47bo13bo
85bo13bo$6bo13bo47b3o11b3o83b3o11b3o$6bo13bo88bo13bo$5b3o11b3o45bo3bo
9bo3bo22b3o11b3o42bo3bo9bo3bo$5b3o11b3o44b7o7b7o21b3o11b3o41b7o7b7o$5b
obo11bobo42bo4bo4bo3bo4bo4bo75bo4bo4bo3bo4bo4bo$6bo13bo42b2o2bo3bo2b2o
b2o2bo3bo2b2o17b5o9b5o37b2o2bo3bo2b2ob2o2bo3bo2b2o$5b3o11b3o42bo3bobo
3bo3bo3bobo3bo20bo13bo40bo3bobo3bo3bo3bobo3bo$5bobo11bobo43b3o3b3o5b3o
3b3o77b3o3b3o5b3o3b3o$5b3o11b3o44bo5bo7bo5bo20b5o4bo4b5o40bo5bo7bo5bo$
108b3o11b3o$108b3o5bo5b3o$13bo94b3o4b3o4b3o$22bo112b3o15b3o$13bo8bo13b
o17bo11b3o67bo17bo11b3o$12b3o6b3o11bobo15bobo11bo99bo$22bo12bobo15bobo
19b3o47bo9b3o15b3o19b3o$21b3o11bobo15bobo10b3o6b3o46b3o8b3o15b3o10b3o
6b3o$3b3o16bo12b3o15b3o10b3o7bo8bo38bobo8bobo15bobo10b3o7bo8bo$2bo3bo
59bobo15b3o38bo9b3o15b3o10bobo15b3o$2bo3bo15bo13bo17bo11b3o15b3o37b3o
9bo17bo11b3o15b3o$4bo15b2ob2o10b3o15b3o11bo38b3o15bobo40bo$83b5o19bo8b
o8bo57b5o$4bo29bo3bo13bo3bo28bo21bo77bo$3bobo13b3ob3o7b7o11b7o48b3o7bo
$4bo8bo3b3ob3ob3o3bo4bo4bo7bo4bo4bo23b5o27b3o5b5o55b5o$3bobo11bo2bo3bo
2bo2b2o2bo3bo2b2o5b2o2bo3bo2b2o23b3o18bobobo13bo3bo56b3o$3bobo7bo3bo3b
obo3bo3bo3bobo3bo7bo3bobo3bo15bo8b3o18bobobo13bobobo47bo8b3o$bobobobo
4b3o3b3o3b3o5b3o3b3o9b3o3b3o16b2obo5b3o20bo16b3o48b2obo5b3o$2o2bo2b2o
24bo5bo5bo5bo5bo17bo30b3o36bo29bo$b2o3b2o37bo19bo41bo37bo19bo$2b5o38bo
19b2obo76bo19b2obo$4bo13b2o24bo20bo52b2o24bo20bo$4bo13b3o34bo62b3o34bo
$18b2o35b2obo59b2o35b2obo$28b2o16bo8bo72b2o16bo8bo$28b3o9bo87b3o9bo$
28b2o13bo84b2o13bo$36b3o3b3o91b3o3b3o$36b3o97b3o$40b3o97b3o$42bo99bo$
41b2o98b2o!
The missing forerake periods are 20 (not possible with this idea), 60 and 100 now. Provided existence of an appropriate sparker, the T-ship insertion shown in the p28 pseudo-p14 gun is viable.

Note that this is not directly for an extensible memory loop as only one T-ship blinker can live inside.

A bonus 8-engine p120 siderake:

Code: Select all

#C [[ TRACK 0 -3/20 ]]
x = 62, y = 48, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
4bo13bo21bo13bo$3b3o11b3o18bo3bo9bo3bo$3b3o11b3o$40bo13bo$3b3o11b3o18b
o3bo9bo3bo$3bobo11bobo19bobo11bobo$4bo13bo21bo13bo$3bobo11bobo18bo3bo
9bo3bo$40bo13bo$11bo28bo13bo$35bo4bo4bo3bo4bo4bo$11bo26bo3bo4bo4bo3bo$
10b3o20bobo9bobobo9bobo$39b3o5bo5b3o$20bo$19b3o$18b2ob2o14bo5bo7bo5bo$
20bo2$b3o16bo16b3o$bobo15bobo16bo$2bo17bo17bo$2bo8bo8bo16b3o$2bo15bo3b
o23b3o7bo$o3bo6bo5bo2bo2bo12bobobo5b3o6b3o$bobo6b3o4bo2bo2bo12bobobo6b
o7b3o$17b2obob2o14bo$bobo33b3o15b3o$5o14b3o16bo16bobo$b3o52bo$2bo52bob
o$14b2o$14b3o$14b2o29bo$24b2o19b2obo$24b3o18bo$24b2o9bo$35b2obo$35bo7$
5bo$5b2obo$5bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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GUYTU6J
Posts: 1850
Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » April 16th, 2022, 12:07 am

I have just updated the LifeWiki page. Two of the new oscillators, p18 and p140 respectively, are based on early disturbed flintstone-y barge:

Code: Select all

x = 46, y = 26, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
3b2o29bo$3bo3bo25bobo$2bob3obo17b2o4bobo$3bobobo18bo6bo$25bobo$26bo11b
o2bo$10bo15bo10bob2ob2o$9bobo13bobo10bo2bobo$2b3o5bo15bo$bobo$obo18bo
20bo$bo18bobo18b3o$21bobo16b2obo$22bo18b2obo$43bobo$44bo2$39bo$22bobo
2bo10bobo$22b2ob2obo10bo$24bo2bo11bo$38bobo$32bo6bo$31bobo4b2o$30bobo$
31bo!
Well, when testing catalysts these broken and not fixable things are rather common :(

Code: Select all

#C Would-be p36, p48, p57 and p64 oscs
x = 95, y = 23, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
6b2o16b2o18b2o28bo2bo$6bo3bo13bo3bo15bo3bo23b2ob2obo$5bob3obo11bob3obo
13bob3obo22bobo2bo$6bobobo13bobobo15bo3bo$46bo$16bo18bo19bo36bo$15bobo
16bobo17bobo15b3o16bobo$4b3o9bo5b3o8bobo6b3o8bobo16bobo17bo$4bobo15bob
o9bo7bobo9bo4bo11bob2o16b2o$3bob2o14bob2o16bob2o13bobo9bobo19bobo$2bob
o15bobo17bobo13b2obo11bo19bob2o$3bo17bo19bo13b3o34bo$55b3o$28bobobo$
27bob3obo$bobobobobo18bo3bo$ob3ob3obo20b2o16bo$bo3bo3bo38b3o$b2o5b2o
34bo2bobo$43bob3o$44bo2b2obo$49b2o$50bo!
Two other similar starting points that I have not experimented with:

Code: Select all

x = 7, y = 32, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
4b2o$bo3bo$ob3obo$bobobo5$4b3o$3bobo$2bobo$3bo9$4b2o$bo3bo$ob3obo$bobo
bo5$2b3o$bobo$obo$bo!
Obviously, the plan is to arrange one or more copies of these, plus stable catalysts or periodic sparkers, until the barge is re-ignited.
---
Speaking of plans, I reviewed earlier posts of this thread and there was a crude one back in early 2020, the ancient era when little was understood about signal circuitry. Skip this part of analysis if impatient.
GUYTU6J wrote:
February 28th, 2020, 9:40 am
To-do list and my comments:
0. apgsearch the rule extensively
1. develop syntheses with c/2 T's for everything (I hope its low period isn't a severe drawback, but this leads to a small number of 2T collisions and therefore syntheses [need at] least 3T)
2. search for elementary spaceships, especially diagonal ones (unfortunately orthogonal searches with ntzfind doesn't work for me)
3. develop technologies based on p28/p44/p240 and possibly p30 (being a potential advantage, the first three gives off similar sparks; and don't forget the large collection of guns in catagolue)
4. develop technologies based on c/2 and 3c/20 spaceships, and corderships
5. attract other's attention to the rule (very hard as there're too many interesting OCAs)
Point 0 and 5 are undoubtedly constantly applicable. Pretty much the same for point 2 (should I share ikpx2 search backup files?).
In my opinion point 1 can be expanded to
Develop T-ship synthesis for everything, standard or slow-salvo ones, starting with exhaustively enumerating collisions between 3T, 4T, T+cloverleaf or other common objects, and building respective databases.
Even in plain Life, projects like 3G enumeration and octohash have meet numerous issues and limitations regarding at least search space and duplicate/missing results. Considering that the cloverleaf has a period of 240, and that p28 and p44 oscillators are also common, and that all of these are sparky enough to induce tons of uninteresting results, equivalent projects here will be faced with bigger challenge. Definitely need some help from experienced enthusiasts here.
Point 4 for 3c/20o and 14c/92d is in a slightly better situation, but the art of engineered spaceships is certainly not mature.
Finally, I have been omitting point 3 more or less in practice, because more efforts are made in stable technologies and that has turned out to be very fruitful. Compact and fast periodic devices like in Life's p30 and p46 realm can still be favorable sometimes, though, so don't give it up!
Another item to be added to the list is the search for low-period sparkers, especially p7 domino, p10 domino and p11 dot ones as they will allow for more oscillators to be built.

In summary: REQUEST FOR COOPERATION!

EDIT: the p48 is fixed with either of two p4 sparkers. The form that will be included in the oscillator collection will use the left one (which was also used in a p92 gun) for a slightly smaller population.

Code: Select all

x = 27, y = 17, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo$2o2bo5bobo$o2bob2o4bobo$2b2o8bo$4bo7bo5b2o$5b3o3bobo5bo$ob2o3bo5b
o4bobo$2obo15bo2$7bo12bo2bo$6bobo10bob2obo$7bo5bo10bo$7b2o4bo6b2o2b2o$
14bo6b2o3bo$13bobo3bobo3b2o$14bobo2b2o$15bo!
EDIT2 next day: it just occured to me that there are a large family of least-common-multiple oscillators, each consisting of two pairs of B3i dot sparkers hassling two blinkers. The first two available periods are 12 and 14:

Code: Select all

x = 69, y = 29, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
14bo36bo3bo$13b3o34bobobobo$51bo3bo$48bo9bo$11bobobobo29bobo7bobo$11bo
bobobo30bo4bo4bo$52b3o$53bo10bo$13b3o47bobo$14bo29bo19bo$43bobo21bo$
44bo16bo4bobo$22b6o13bo20bo4bo$19bob2o4b2obo9bobo4bo10bobo2bo$3b6o3b3o
b3o3b6o13bo4bo4b3ob3o4bo4bo$ob2o4b2obo33bo2bobo10bo4bobo$3b6o32bo4bo
20bo$40bobo4bo16bo$41bo21bobo$16bo27bo19bo$15b3o25bobo$44bo10bo$54b3o$
13bobobobo30bo4bo4bo$13bobobobo29bobo7bobo$50bo9bo$53bo3bo$15b3o34bobo
bobo$16bo36bo3bo!
I need some time to tabulate these... Before that, here is an excessively sparky p160 gun:

Code: Select all

x = 44, y = 23, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
7bo$6bobo$7bo2$15b2o$16bo$15bobo$16bobo$7b2o8bo$6bo$bo4bo$obo3b2o$bo$b
2o$14bo$12b3o26b3o2$11bo16bo$9b3o$8bo19bo$8b2o5bo11b3o$14bobo$15bo!
Partial p6

Code: Select all

x = 6, y = 12, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
b2ob2o$bo3bo$2b3o$2bo2$bo$2o$o2bo2$2bo$bobo$2b2o!
EDIT on April 20:
Partial p20?

Code: Select all

x = 11, y = 12, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
6bo$5bobo$6bo2$9b2o$5b3ob2o$bo3bobob2o$obo2bobo$bo4bo$6bo$5bobo$6bo!
Almost p19 gun:

Code: Select all

x = 17, y = 19, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
7b2o$8bo$7bo$bo5b2o$obo6bo$bo$14bo$2b3o5bo2bobo$2bo6b2o3bo$2b2o6bo2b2o
$4bo9bobo$13bob2o$8bo5bo$6b2obo$6bobo2$b3o$b3o$2bo!
#C [[ PASTET 17 PASTEMODE 6 PASTE o! 12 8 ]]
#C [[ PASTET 18 PASTEMODE 6 PASTE o! 12 8 ]]
#C [[ LOOP 19 GPS 10 THEME Mono Y -2 ]]
But look, the mechanism do work if it is elongated! And there is also a new period quadrupler (4× pulse divider) for the known B-heptomino signal — a class of guns and B factories with period of the form (43+24n)×4^m are thus constructed.

Code: Select all

x = 191, y = 80, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
25b2obo6bo53b2obo4bo7bo57b2obo4bo5bo7bo$24bo2b2o5bobo51bo2b2o3bobo5bob
o55bo2b2o3bobo3bobo5bobo$19bo5b2o8bo47bo5b2o6bo7bo51bo5b2o6bo5bo7bo$
18bobo61bobo71bobo$19bo63bo73bo$38bo69bo79bo$34bo2bobo64bo2bobo74bo2bo
bo$31bob2o3bo62bob2o3bo72bob2o3bo$34bo2b2o65bo2b2o75bo2b2o$38bobo67bob
o77bobo$37bob2o66bob2o76bob2o$26bo5bo5bo51bo5bo5bo5bo55bo5bo5bo5bo5bo$
24b2obo2b2obo54b2obo2b2obo2b2obo58b2obo2b2obo2b2obo2b2obo$24bobo3bobo
55bobo3bobo3bobo59bobo3bobo3bobo3bobo4$19bo63bo73bo$18bobo61bobo71bobo
$19bo63bo73bo11$20bo4b2obo6bo48bo4b2obo4bo7bo52bo4b2obo4bo5bo7bo$19bob
2obo2b2o5bobo46bob2obo2b2o3bobo5bobo50bob2obo2b2o3bobo3bobo5bobo$13bo
6bobo2b2o8bo41bo6bobo2b2o6bo7bo45bo6bobo2b2o6bo5bo7bo$12bobo61bobo71bo
bo$13bo63bo73bo$38bo69bo79bo$34bo2bobo64bo2bobo74bo2bobo$31bob2o3bo62b
ob2o3bo72bob2o3bo$34bo2b2o65bo2b2o75bo2b2o$38bobo67bobo77bobo$37bob2o
66bob2o76bob2o$20bo5bo5bo5bo45bo5bo5bo5bo5bo49bo5bo5bo5bo5bo5bo$18b2ob
o2b2obo2b2obo48b2obo2b2obo2b2obo2b2obo52b2obo2b2obo2b2obo2b2obo2b2obo$
18bobo3bobo3bobo49bobo3bobo3bobo3bobo53bobo3bobo3bobo3bobo3bobo4$13bo
63bo73bo$12bobo61bobo71bobo$13bo63bo73bo11$8bo6bo4bo4b2obo6bo36bo6bo4b
o4b2obo4bo7bo40bo6bo4bo4b2obo4bo5bo7bo$7bob2o3bobo2bob2obo2b2o5bobo34b
ob2o3bobo2bob2obo2b2o3bobo5bobo38bob2o3bobo2bob2obo2b2o3bobo3bobo5bobo
$bo6bobo4bo4bobo2b2o8bo29bo6bobo4bo4bobo2b2o6bo7bo33bo6bobo4bo4bobo2b
2o6bo5bo7bo$obo61bobo71bobo$bo63bo73bo$38bo69bo79bo$34bo2bobo64bo2bobo
74bo2bobo$31bob2o3bo62bob2o3bo72bob2o3bo$34bo2b2o65bo2b2o75bo2b2o$38bo
bo67bobo77bobo$37bob2o66bob2o76bob2o$8bo5bo5bo5bo5bo5bo33bo5bo5bo5bo5b
o5bo5bo37bo5bo5bo5bo5bo5bo5bo5bo$6b2obo2b2obo2b2obo2b2obo2b2obo36b2obo
2b2obo2b2obo2b2obo2b2obo2b2obo40b2obo2b2obo2b2obo2b2obo2b2obo2b2obo2b
2obo$6bobo3bobo3bobo3bobo3bobo37bobo3bobo3bobo3bobo3bobo3bobo41bobo3bo
bo3bobo3bobo3bobo3bobo3bobo4$bo63bo73bo$obo61bobo71bobo$bo63bo73bo!
It is worth noting that originally the backfire section cannot be followed by normal transport section, which is why I need to adjust and subsequently come across the quadrupler. This inconvenience has just been removed as I am writing:

Code: Select all

x = 35, y = 21, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
15b2o$9bo5bo3b2obo6bo$8bobo3bob3o2b2o5bobo$bo7bo5bobob2o8bo$obo$bo$15b
o16bo$14b2o5b2o8bobo$13b2o6b3o8bo$14b2o5b2o8b2o$32bobo$31bob2o$8bo5bo
5bo5bo5bo$6b2obo2b2obo2b2obo2b2obo$6bobo3bobo3bobo3bobo4$bo$obo$bo!
Other T-to-B converters with similar linear geometry adapt well, changing base to p50 and p115 as shown below. Coincidentally, 43+24*3=115.

Code: Select all

x = 37, y = 50, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
23b2obo4bo$22bo2b2o3bobo$17bo5b2o6bo$16bobo$17bo16bo$33bobo$28b2o4bo$
27bobo3b2o$28b2o4bobo$33bob2o$34bo$24bo$22b2obo4bo$22bobo4bobo$30bo3$
17bo$16bobo$17bo11$7b2o14bob2o$8bo10bo3b2obo$7bo10bobo$bo5b2o10bo$obo
32bo$bo32bobo$35bo$30b2ob3o$30bo2bo2bo$30b2o3b2o3$8bo11bo$6b2obo9bobo$
6bobo11bo6bo$26bob2o$27bobo$bo$obo$bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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GUYTU6J
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » April 24th, 2022, 9:34 am

GUYTU6J wrote:
April 16th, 2022, 12:07 am
Two other similar starting points that I have not experimented with:

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x = 7, y = 32, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
4b2o$bo3bo$ob3obo$bobobo5$4b3o$3bobo$2bobo$3bo9$4b2o$bo3bo$ob3obo$bobo
bo5$2b3o$bobo$obo$bo!
The first flintstone-y barge has the right clearance to be ignited by cloverleaf as in the p344 oscillator. Among new discoveries is the following p1044 gun that is a bit too high in period.

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x = 68, y = 68, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
10bo13bo$9bobo11bobo$10bo7bo5bo$10b2o5bobo$8bobo4b2obo$8b2obo3bobo$10b
o4b3o2$62b2o$62bo3bo$61bob3obo$62bobobo5$63bo$62bobo$63bobo$64bo4$66bo
$65bobo$66bo17$bo$obo$bo4$3bo$2bobo$3bobo$4bo5$bobobo$ob3obo$bo3bo$4b
2o2$57bo$50bo5bob2o$49bobo5bobo$48bobo5b2o$43bo5bo7bo$42bobo11bobo$43b
o13bo!
FYI the LifeWiki article has just been updated, and now the collection located in RLE:Glimmeringgardenoscillators contains 720 oscillators. This page (EDIT: corrected spelling) is under construction as well, and the p40 dot sparker to be used is this one:

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x = 26, y = 23, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
7bo$6bobo$7bo2$15b2o$11bo4bo$11b2o2bobo$12b2o2bobo$11b2o4bo2$bo$obo$bo
$b2o15b2o$18b2o2bo$23bobo2$11bo11bo$9b3o$8bo$8b2o6bo$15bobo$16bo!
Last edited by GUYTU6J on April 26th, 2022, 11:57 pm, edited 1 time in total.
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

hotdogPi
Posts: 937
Joined: August 12th, 2020, 8:22 pm

Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by hotdogPi » April 24th, 2022, 10:00 am

Have you tried my search program yet? It should work fine, since the two common things that would cause it to fail (S0 or S1e present or common natural c/4 spaceships larger than 3×3) do not exist in this rule.
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉟,㊱,㊳S,㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,70,72,74S,75,76S,80,84,90,96,100,102S,108,110,114G,116,117G,120,126G,128S,138,147,154,156,196S,217,486,576

S: SKOP
G: gun

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GUYTU6J
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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » April 24th, 2022, 10:43 am

hotdogPi wrote:
April 24th, 2022, 10:00 am
Have you tried my search program yet? It should work fine, since the two common things that would cause it to fail (S0 or S1e present or common natural c/4 spaceships larger than 3×3) do not exist in this rule.
Honestly, no. Most of the oscillators were found by manually placing stable catalysts one by one against a selected active region, replacing broken ones if any, and figuring out how to complete a cycle. Simple still lives like tub, fishhook and xs12_2523ad2 are already versatile enough for most purposes as I understand them, and the ocassional appearances of sparkers (e.g. p12 #11, p76 #5, p92 #6, p128 #3 in the current collection) simply indicate that I have not been able to get any stable catalyst to work.

There is definitely some search space out here not yet reached with multiple active regions in some symmetry, though. No shortage of potential starting points:

Code: Select all

x = 305, y = 6, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
bo20bo19bo18b3o$3o18b3o17b3o17bobo19bo17b3o17bo21bo17bo19bo21bo17b3o
17b3o17bo2bo15bobo17bo3bo$2bo17b2obo16b2o18bob2o17bo18bo2bo16b3o37b3o
17b3o19b3o16bo2bo15b2obo16bob3o15b3o17b5o$21bo19bo18b2o18b3o17bo3bo15b
ob2o16b2obo16b3o19bo19bob2o14bo3bo16bo19bo2bo15bobo17bo3bo$104bo18bo
16bobo18bo20bo18bo2bo16bob2o$104bo18bo16b3o40bo16bo!

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x = 25, y = 7, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
7bo13bo$6bobo11bobo$3bo3bo13bobo$ob2o2b2o14b3o$3bo3bobo$6bob2o$7bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

User avatar
GUYTU6J
Posts: 1850
Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
Contact:

Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » May 1st, 2022, 12:12 pm

I kept thinking about the caber tosser problem with c/2 and 3c/20 spaceships. After reading a bit about Life's sawtooth patterns using tractor beams, I did some math and rendered the idea in LaTeX

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\documentclass{ctexart}
\begin{document}
\section{Caber-tosser calculations}
Let $d_0$ be the initial distance between a stationary base and a receding spaceship with speed $v_r$. A faster spaceship with speed $v_a$ starts from the base and approaches the slower receding one, then sends a signal (either a spaceship or an object pulled by periodic tractor beam) with speed $v_b$ back to the base. When the signal returns to the base, the distance between receding spaceship and the base becomes $d_1$. We have:
\[d_{1a}=v_rt_{1a}=v_r\frac{d_0}{v_a-v_r}=\frac{v_r}{v_a-v_r}d_0\]
\[d_{1b}=v_rt_{1b}=v_r\frac{d_0+d_{1a}}{v_b}=\frac{v_r}{v_b}(d_0+v_r\frac{d_0}{v_a-v_r})=\frac{v_r}{v_b}\frac{v_a}{v_a-v_r}d_0\]
\[d_1=d_0+d_{1a}+d_{1b}=(1+\frac{v_r}{v_a-v_r}+\frac{v_r}{v_b}\frac{v_a}{v_a-v_r})d_0=\frac{v_a(v_b+v_r)}{v_b(v_a-v_r)}d_0\]
\[t_1=t_{1a}+t_{1b}=\frac{d_{1a}}{v_r}+\frac{d_{1b}}{v_r}=\frac{1}{v_a-v_r}d_0+\frac{1}{v_b}\frac{v_a}{v_a-v_r}d_0=\frac{v_a+v_b}{v_b(v_a-v_r)}d_0\]
In subsequent $n$-th trip, apparently $d_{n+1}=\frac{v_a(v_b+v_r)}{v_b(v_a-v_r)}d_n$ and $t_{n+1}=\frac{v_a+v_b}{v_b(v_a-v_r)}d_n$ holds for all $n$$>$1. So
\[d_n=[\frac{v_a(v_b+v_r)}{v_b(v_a-v_r)}]^nd_0\]
\[T_n=\sum_{i=1}^n{t_i}=\frac{v_a+v_b}{v_b(v_a-v_r)}\sum_{i=0}^{n-1}{d_i}=\frac{d_0(v_a+v_b)}{v_b(v_a-v_r)}\frac{1-[\frac{v_a(v_b+v_r)}{v_b(v_a-v_r)}]^n}{1-[\frac{v_a(v_b+v_r)}{v_b(v_a-v_r)}]}=([\frac{v_a(v_b+v_r)}{v_b(v_a-v_r)}]^n-1)\frac{d_0}{v_r}\]
Let $k=\frac{v_a(v_b+v_r)}{v_b(v_a-v_r)}$, then it simplifies to
\[d_n=k^nd_0\]
\[T_n=(k^n-1)\frac{d_0}{v_r}\]
In the world of cellular automata the time is discrete, so for convenience the expansion factor $k$ should be an integer. Given $v_a$ and $v_r$, we can choose $k$ and calculate
\[v_b=\frac{v_rv_a}{(k-1)v_a-kv_r}\]
then adjust the period of tractor beam to match $v_b$.
\end{document}
In case no LaTex-rendering program is available, here is a screenshot:
caber_tosser_calculations.png
caber_tosser_calculations.png (72.85 KiB) Viewed 595 times
Well, this could apply to any cellular automata with the appropriate technologies. Here in Glimmering Garden, plugging in v_a=0.5 and v_r=0.15 gives candidates v_b=3/(14k+8) for k≥2. On the other hand, this blinker-pulling mechanism from last year may operate at a speed of 4/(p-8) where p is the base gun period. The first integer pair solution for 3/(14k+8)=4/(p-8) is k=4 and p=56, meaning that with a p56 blinker-puller a sawtooth with expansion factor 4 can be constructed. ...And p56 is where Julia does its job perfectly!
The result is a compact sawtooth as shown below. Minimum population of 241 cells is reached at generations 280*(4^n-1)/3.

Code: Select all

x = 54, y = 69, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
29bo13bo$28b3o11b3o$28bobo11bobo$29bo13bo$28b3o11b3o$28bobo11bobo$29bo
13bo3$27b5o9b5o$27bo3bo9bo3bo$27bobobo9bobobo$28b3o11b3o3$36bo2$36bo$
35b3o3$27b3o$28bo18b3o$48bo$28bo$27b3o18bo$16b3o9bo18b3o$17bo10bo19bo$
26bo3bo17bo$17bo28bo3bo$16b3o7bo3bo$17bo28bo3bo$17bo10bo$15bo3bo28bo2$
15bo3bo$48b2o$17bo26b2o6b2o$44b3ob2ob3o$44b2o6b2o$48b2o2$29bo$28bobo
13bo$13b3o13bo$14bo18b3o8bo$34bo6b2ob2o$14bo25b2obo$34bo6bo2$45bo4bo$
19b2o24bo3bobo$18bobo18b2o4bo4bo$18b2o18bobo$38b2o2$4b3o$4bo2bo16b3o$
4b3o2bo2b3o9bo2bo$6bo2bo2b3o9b3o2bo2b3o$bo4b3o4bo12bo2bo2b3o$obo18bo4b
3o4bo$bo9bobobo4bobo$11bobobo5bo9bobobo$31bobobo$13bo$12b3o18bo$12b3o
17b3o$32b3o!
Adding a period-140 T-ship gun to the side yields a caber tosser trivially. With the same expansion factor as the last c/4o-based caber tosser, this one is definitely much simpler!

Code: Select all

x = 94, y = 69, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
38bo13bo$37b3o11b3o$37bobo11bobo$38bo13bo$37b3o11b3o$37bobo11bobo$38bo
13bo3$36b5o9b5o$36bo3bo9bo3bo$36bobobo9bobobo$37b3o11b3o3$45bo2$45bo$
44b3o3$36b3o$37bo18b3o$57bo21bo$37bo40bob2o$36b3o18bo21bobo$25b3o9bo
18b3o20b2o$26bo10bo19bo$35bo3bo17bo30b2o$2bo23bo28bo3bo11b2o$3o22b3o7b
o3bo30b3o12bo2b2o2bo$b2o23bo28bo3bo11b2o11b2o6b2o$26bo10bo47bo2b2o2bo$
24bo3bo28bo$64b2o5b2o15b2o$24bo3bo35bo7bo11bo$57b2o7b5o13b2o$26bo26b2o
6b2o2bob3obo11bob2o$53b3ob2ob3o2b2o3b2o10bo2bo$53b2o6b2o4b3o2bo9b3o$
57b2o7bo3b2o11bo$66b2o$38bo48bo$37bobo13bo26bo2bo2bobo$22b3o13bo48bo$
23bo18b3o8bo$43bo6b2ob2o$23bo25b2obo$43bo6bo2$54bo4bo$28b2o24bo3bobo$
27bobo18b2o4bo4bo$27b2o18bobo$47b2o2$13b3o$13bo2bo16b3o$13b3o2bo2b3o9b
o2bo$15bo2bo2b3o9b3o2bo2b3o$10bo4b3o4bo12bo2bo2b3o$9bobo18bo4b3o4bo$
10bo9bobobo4bobo$20bobobo5bo9bobobo$40bobobo$22bo$21b3o18bo$21b3o17b3o
$41b3o!
The hardest part is the 3c/20o flotilla. The following 2-engine T-to-blinker converter could have worked if it survives from the impact of T-ships on the other lane.

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x = 28, y = 22, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
20bo$18bo3bo$6bo$5bobo12bo$5bobo10bo3bo$5bobo11bobo$5b3o12bo$18bo3bo$
6bo13bo$5b3o12bo$15bo4bo4bo$4bo3bo9bo3bo$3b7o3bobo9bobo$bo4bo4bo7b3o$
2o2bo3bo2b2o$bo3bobo3bo$2b3o3b3o6bo5bo$3bo5bo$11b3o$12bo2$12bo!
While looking for a replacement, I came across several reactions. Nothing satisfying, unfortunately.

Code: Select all

x = 330, y = 47, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
2b3o13b3o$2bobo13bobo$2bobo13bobo2$2bobo13bobo$2bobo13bobo$3bo15bo2$2b
3o13b3o$b5o11b5o$2obob2o9b2obob2o109bo11bo$bobobo11bobobo109b3o9b3o$2b
3o13b3o111bo11bo$3bo15bo57bo53bobo9bobo$63bo11bo3bo51bobo9bobo$62bobo
66b3o9b3o$62bobo12bo53bobo9bobo$62bobo10bo3bo46bo23bo29bo15bo$62b3o11b
obo52b3o9b3o33b3o13b3o$77bo54bo11bo34b3o13b3o$63bo11bo3bo52bo11bo160bo
17bo$62b3o12bo101b3o13b3o46b3o13b3o41b3o15b3o$77bo101bobo13bobo46bobo
13bobo42bo17bo$61bo3bo6bo4bo4bo97bo15bo48bo15bo42bobo15bobo$10b3o47b7o
8bo3bo99bobo13bobo47bo15bo42bobo15bobo$11bo46bo4bo4bobobo9bobo160bo15b
o42b3o15b3o$57b2o2bo3bo2b2o6b3o164bo3bo11bo3bo40bobo15bobo$58bo3bobo3b
o175bobo13bobo36bo11bo5bo11bo$59b3o3b3o236b3o15b3o$60bo5bo7bo5bo56b3o
104bobo13bobo42bo17bo$68b3o67bo104b5o11b5o41bo17bo$69bo174b3o13b3o$
245bo15bo$69bo5$187b3o$188bo5$252b3o$253bo59b3o$314bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

User avatar
GUYTU6J
Posts: 1850
Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
Contact:

Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » May 19th, 2022, 9:20 am

It looks like there is still someone out here interested in this rule — there are a few more downloads for the topmost pattern file.
GUYTU6J wrote:
August 10th, 2021, 1:27 pm
As for periodic technology, I just realized there is a general scheme for creating T-ship guns and reflectors using high-period dot sparkers. Two examples at p25 and p30 is demonstrated below...

Code: Select all

x = 95, y = 40, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
78bo2$78bo$77b3o5$3b3o$3b3o$4bo78bo$82bobo$83bo2$15b2o61bo$14bobo60b3o
$14b2obo58bobobo$16bo2b3o53b2o3b2o$21bo54b5o$9bo7bo2b2o56bo$8bobo6bobo
58bo$9bo7b3o2$24bo51bo3bo$23bobo50b5o$24bo3$10bo17bo36bo23bo$9bobo15bo
bo34bo25bo$3b3o4bo17bo4b3o$3bo2bo25bo2bo$2bo33bo24bo5bo2bo6bo6bo2bo5bo
$2bo5bo21bo5bo23b3o4b4o5b3o5b4o4b3o$2bo6bo8b3o8bo6bo24bo5bo2bo13bo2bo
5bo$3bo5bo8b3o8bo5bo$2bobo3b2o9bo9b2o3bobo$2obob3o23b3obob2o25bo25bo$o
bo33bobo26bo23bo$b2o33b2o!
The p25 and p30 guns above have been obsoleted by results from gencols search described here.
p25

Code: Select all

x = 153, y = 28, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
b2o28b2o25b2o21b2o48b2o$obo27bobo25bobo19bobo26b2o19bobo$2obo26b2obo
20bo2bob2o19b2obo25bobo18b2obo$2bo2b3o24bo2b3o15b2o3bo23bo2b3o16b2o2bo
b2o20bo2b3o$7bo29bo14b2o33bo15bobo3bo27bo$3bo2b2o25bo2b2o15b2o28bo2b2o
15bobo27bo2b2o$3bobo27bobo19bob2o24bobo17b3o27bobo$3b3o27b3o19b3o25b3o
20b4o23b3o$56bo49bo2bo$10bo29bo9bo39bo15b3o31bo$9bobo27bobo7bobo37bobo
9bo37bobo$10bo29bo9bo39bo9bobo37bo$101bo2$150b2o$148bobobo$20b2o121b3o
b3ob2o$20bobo119b2o3bo2bo$19bob2o118b2o7b2o$15b3o2bo121b2o5b2o$15bo$
15b2o2bo130bo$17bobo130bo$17b3o122bo4bob2o$141bobo3b3o$12bo129bo5bo$
11bobo$12bo!
p30 (and simplification)

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x = 64, y = 44, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
12b3o4bo2bo29b3o4bo2bo$12bobo3b6o28bobo3b6o$12b3o4bo2bo29b3o4bo2bo3$7b
3o39bo$b2o4bobo38b3o$2o9bo29b3o4b4o$3o3b4obo31bo4bo2bo$2o9bo28bob2o4b
2ob3o$b2o4bobo33bo4bo2bo$7b3o31b3o4b4o$48b3o$49bo12$5bo$6bo3$o2bo5bo$
4o4b3o$o2bo5bo4bo$13bob2o$14bobo$6bo8bo$5b3o$14bo2bo$13b4obo$14bo2bo2$
15bo$14bobo$13bob2o$14bo!
p48 (and simplification)

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x = 57, y = 50, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
10bo2bo4bo2bo$9bob2obo2bob2obo$10bo2bo4bo2bo2$35bo2bo4bo2bo$bo32bob2ob
o2bob2obo$obo7bo2bo21bo2bo4bo2bo$bo7b6o$10bo2bo$55bo$43bo2bo7bobo$43b
4o8bo$10bo2bo4bo2bo21bo2bo$9bob2obo2bob2obo$10bo2bo4bo2bo2$35bo2bo4bo
2bo$35b3obo2bob2obo$38bo4bo2bo$37b2o8$29bo$28b3o3$26bobobobo$26bobobob
o2$35bo2bo4bo2bo$28b3o3bob2obo2bob2obo$29bo5bo2bo4bo2bo2$25bo28bo$24bo
bo26bobo$24bobo16bo2bo7bo$25bo17b4o$30b3o10bo2bo$30b3o$31bo2$35bo2bo4b
o2bo$35b3obo2bob2obo$38bo4bo2bo$37b2o!
That post was concerned about p54, for which there are lots of outputs (only part of which shown below) in other geometries...

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x = 252, y = 29, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
b2o38b2o26b2o45b2o38b2o30bo19bo28bo$bo3b2o34bo3b2o18b2o3bo41b2o3bo34b
2o3bo29bob2o15b2obo25b2obo$ob3obo33bob3obo18bob3obo40bob3obo33bob3obo
23b2o4bobo15bobo4b2o20bobo4b2o$bobobo14b2o19bobobo20bobobo42bo3bo35bob
obo23b2obo2b2o19b2o2bob2o21b2o2bob2o$20bo3b2o41b3o105b2o4b2ob2o2bo19bo
2b2ob2o4b2o15bo2b2ob2o4b2o$4bo14bob3obo18bo22bobo21b2o21bobo14b2o22b2o
18bobo4b3o2bobo17bobo2b3o4bobo14bobo2b3o4bobo$3b3o14bobobo18b3o22bobo
20bo3b2o14bo3bobo13bo3b2o13b6obo18bo6bo4b2o17b2o4bo6bo15b2o4bo6bo$2bo
2b2o35bo2b2o16b3o4bo19bob3obo13b3obo2bo12bob3obo13bobo3b2o18b2o41b2o
27b2o$2b4o36b4o17bo2bobob2o19bobobo14bo2b3o2bo12bobobo14bo3bobobo15bob
o43bobo26bobo$3b2o38b2o19b3ob3o40b5o2bo32bo6bo15b2obo41bob2o25bob2o$
32bo2bo33bo24bo17bo2b3o16bo16b2o2b3o18bo24b2o17bo28bo$24b4o65b3o37b3o
20bo44bo3b2o$24bo2bo64bo2b2o35bo2b2o34b2o27bob3obo24b2o$5bobobo14b3o
18bobobo12bobobo25b4o13bobobo18b4o13bobobo17bo3b2o24bobobo25bo3b2o$4bo
b3obo33bob3obo10bob3obo25b2o13bob3obo18b2o13bob3obo15bob3obo53bob3obo$
4b2o3bo34b2o3bo12bo3b2o41bo3b2o34bo3b2o16bobobo28bo26bobobo$8b2o14bobo
bo19b2o12b2o45b2o38b2o52b3o$23bob3obo144bo27bo2b2o27bo$23b2o3bo66bobob
o35bobobo33b3o26b4o27b3o$27b2o65bob3obo33bob3obo31bo2b2o26b2o27bo2b2o$
94b2o3bo34b2o3bo32b4o56b4o$98b2o38b2o33b2o58b2o2$205bobobo$204bob3obo$
175bobobo24b2o3bo25bobobo$174bob3obo27b2o24bob3obo$174b2o3bo54b2o3bo$
178b2o58b2o!
...but a p6 sparker just suffices.

Code: Select all

x = 24, y = 26, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
16bo$15bobo$15b2o$17b3o$16bobobo$13b2obo3bob2o$13bob2o3b2obo$18bo$17b
3o$6b2o10bo$6bo3b2o$5bob3obo$6bo3bo7bo$bo5bo$obo5bobo$bo6bo2bo$7bo2b3o
$6b3o2bo5$10bobobo$9bob3obo$9b2o3bo$13b2o!
Unfortunately, the p17 results are negative.

Code: Select all

x = 58, y = 29, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo29bo$10bobo27bobo$o7bo2bo18bo7bo2bo$5o3b3o19b5o3b3o$9bo29bo$bobo
27bobo4$9bobo27bobo$3bo29bo$2b3o3b5o19b3o3b5o$bo2bo7bo18bo2bo7bo$obo
27bobo$bo29bo2$8bo9b2o36bo$7bobo7b2o30b2o4bobo$8bob2o6b2o26bo2bo4bobo$
9bobo5b3o25b3ob3o3bo$9b3o32bo2bob2ob2o$44bobo2b2o2bo$47bobobobo$47bo2b
2o2bobo$17b3o27b2ob2obo2bo$9b3o5bobo25bo3b3ob3o$9b2o6b2obo23bobo4bo2bo
$10b2o7bobo21bobo4b2o$9b2o9bo23bo!
That basically rules out the possibility of one of my wishes.
GUYTU6J wrote:
June 8th, 2021, 9:14 am
I think finding a true period-11 T-ship gun using copies of said p11 is possible.
In summary, using gencols to combine two sparky oscillators to construct guns is a worthwhile skill for OCA explorers to get familiar with, if scarce time does not permit indefinitely many manual copy-and-paste tests like Abhpzta usually does. Oh and don't bother applying gencols to a common oscillator — something else called apgsearch will do it for you.
EDIT: no, a p12 sparker cannot support a p23 partial *facepalm

Code: Select all

x = 17, y = 28, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
6b2o2$8bo$7b3o$3bo2bobobo2bo$3bobob3obobo$2ob2o2bobo2b2ob2o$o7bo7bo$2b
o4b3o4bo$bobo4bo4bobo$2bo11bo$7b3o2$5b2obob2o$5b7o$5b2obob2o4$9b3o4$5b
2obob2o$5b7o$5b2obob2o2$7b3o!
#C [[ STOP 23 ]]
If only there is a p24 blinker factory...!

Code: Select all

x = 21, y = 15, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
4bo$3b3o$3b3o4$5bo11bo$3o2b2obo8b2obo$5bo11bo4$3b3o$3b3o$4bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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Period1GliderGun
Posts: 135
Joined: March 9th, 2022, 1:50 am
Location: I am everywhere and nowhere.

Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by Period1GliderGun » May 19th, 2022, 6:12 pm

p34 gun, based on the first p17 partial by GUYTU6J and a p34 century sparker:

Code: Select all

x = 37, y = 33, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
14bo9bo$13bobo7bobobo$3b2o6b2obo9bob3o5b3o$3bo3bo2b2obo11bo2b2o6bo$3b
4o4b3o10b2o2bo3bo3bo$12bo12b3o4bo2bo$26bo2$32bo$6bo16bo2bo4b3o$5b3o4b
4o6bo3bo3bo2b2o$5bob2o2bo3bo6bo6b2o2bo$4bob2o6b2o6b3o5b3obo$3bobo25bo
bobo$4bo29bo4$2bo$bobo$2bob3o5b2o$3bo2bo6b2o$3bo2bo3b4o$3b3o5b2o4$2b2o
5b3o$b4o3bo2bo$2o6bo2bo$b2o5b3obo$11bobo$12bo!
It's OK to abbreviate my username to "P1GG," but never, never, call me "pig."

Code: Select all

x = 36, y = 9, rule = B3/S23
23bobo$21bo3bo$13bo7bo$12b4o4bo4bo8b2o$11b2obobo4bo12b2o$2o8b3obo2bo3b
o3bo$2o9b2obobo6bobo$12b4o$13bo!
[[ STEP 30 ]]

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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » May 19th, 2022, 9:28 pm

Period1GliderGun wrote:
May 19th, 2022, 6:12 pm
p34 gun, based on the first p17 partial by GUYTU6J and a p34 century sparker:

Code: Select all

x = 37, y = 33, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
14bo9bo$13bobo7bobobo$3b2o6b2obo9bob3o5b3o$3bo3bo2b2obo11bo2b2o6bo$3b
4o4b3o10b2o2bo3bo3bo$12bo12b3o4bo2bo$26bo2$32bo$6bo16bo2bo4b3o$5b3o4b
4o6bo3bo3bo2b2o$5bob2o2bo3bo6bo6b2o2bo$4bob2o6b2o6b3o5b3obo$3bobo25bo
bobo$4bo29bo4$2bo$bobo$2bob3o5b2o$3bo2bo6b2o$3bo2bo3b4o$3b3o5b2o4$2b2o
5b3o$b4o3bo2bo$2o6bo2bo$b2o5b3obo$11bobo$12bo!
There is already a smaller p34 gun using a different engine. But wait, the gun-building idea may fill some gaps at odd multiples of 17, like 51, 85, 119, ... That is what's worth pursuing.

It seems hard to find a right way to perturb the spark, though. One of the attempts made a p32 (17+15) oscillator by chance:

Code: Select all

x = 35, y = 13, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo17b2o$10bobo$11bob2o11bo2b2o2bo$12bob2o9b2o6b2o$12b3o11bo2b2o2bo$
13bo$4b2o23b2o$21bo$bo2b2o2bo11b3o$2o6b2o9b2obo$bo2b2o2bo11b2obo$22bob
o$4b2o17bo!
Failed p49:

Code: Select all

x = 35, y = 21, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
21bo$21bo8bo$21b2o6bobo$22b2o6bo$11bo10b2o9bo$10bobo2bo11bo4bobo$11bob
6o9bo4bo$4bo7bob2o2bo7bo2bo$3bobo6b2obo2bob3o5bo4bo$4bo6b4o2bobo2bo4bo
4bobo$bo10bo9bo10bo$obo4bo4bo2bobo2b4o6bo$bo4bo5b3obo2bob2o6bobo$5bo2b
o7bo2b2obo7bo$bo4bo9b6obo$obo4bo11bo2bobo$bo9b2o10bo$4bo6b2o$3bobo6b2o
$4bo8bo$13bo!
#C [[ STOP 49 ]]
EDIT: It took gencols about 9 minutes each to test the C4_1-symmetric p57 for both chirality combination. A gem:

Code: Select all

x = 66, y = 32, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
3bo$2bobo$3bo21bo$24bobo$25bo$42bo$12b3o26bobo$12bobo27bo21bo$13b2o48b
obo$64bo2$45b2obobo8bo$6b3o10b2o26b5o7bo$6bobo9bobo27bobo7bo$6b2o10b3o
36b3o$58bo$57b3o$58bo$12b2o$12bobo31bo$12b3o30b3o$46bo$bo43b3o$obo43bo
7bobo$bo21bo21bo7b5o$22bobo20bo8bobob2o$23bo$40bo$39bobo$40bo21bo$61bo
bo$62bo!
I haven't tried stable circuitry to see if a smaller p57 gun exists.

EDIT2 next morning: Got it! p51 T-ship gun and B-heptomino factories:

Code: Select all

x = 133, y = 31, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
21bo59bo39bo$20bobo57bobo37bobo$11bo9bo2bo7bo38bo9bo2bo7bo18bo9bo2bo7b
o$10bobo9b3o3b5o37bobo9b3o3b5o17bobo9b3o3b5o$o7bo2bo11bo36bo7bo2bo11bo
16bo7bo2bo11bo$5o3b3o18bobo28b5o3b3o18bobo8b5o3b3o18bobo$9bo59bo39bo$b
obo57bobo37bobo2$21bobo57bobo37bobo$29bo59bo39bo$9bobo8b5o3b3o38bobo8b
5o3b3o18bobo8b5o3b3o$3bo16bo7bo2bo31bo16bo7bo2bo11bo16bo7bo2bo$2b3o3b
5o17bobo29b3o3b5o17bobo9b3o3b5o17bobo$bo2bo7bo18bo29bo2bo7bo18bo9bo2bo
7bo18bo$obo57bobo37bobo$bo59bo39bo$20bo59bo39bo$19bobo46bo10bobo37bobo
$20bo46bobo10bo39bo$20bo47bo11b2o26bo11b2o$21bo85bobo11bo$19b2o87bo11b
obo$18bobo100bo$19bo$72bo$71bobo$72bo$106bo$105bobo$106bo!
(gencols? What gencols? I am making these by hand today!)
An entertaining coincidence lies in the appearance of a p1224 oscillator (=17×72), which is the second one known and is shown below to the right of the last one:

Code: Select all

x = 113, y = 67, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
6bo94bo$5bobo7b2o32bo50bobo$6bo8bo3bo2bo10bo14bobo40bo9bo2bo7bo$14bob
3ob2obo8b3o14bo40bobo9b3o3b5o$3bo11bobobo2bo8b2ob2o44bo7bo2bo11bo$2bob
o26bo2b2o44b5o3b3o18bobo$3bo19bo5b2o4b2o52bo$bo20b3o5b3obobo44bobo$obo
5b3o11bob2o5bo2b3o$bo5bo2bo13bo76bobo$109bo$9bo13bo65bobo8b5o3b3o$4bo
2bo7bo6bo3bo2bo53bo16bo7bo2bo$4b2o8bob2o3bob3ob2ob2o50b3o3b5o17bobo$
15bobo4bo3bo2bo2bo48bo2bo7bo18bo$22b2o7bobo46bobo$12bo19bo48bo$11bobo$
12bo87bo$99bobo$25b2o36bo36bo$26bo35bobo$25bobo35bo21bo$26bo57bobo$85b
o$39b3o3$38b3o$39bo2$39bo33$68bo$67bobo$68bo!
Also a p51 oscillator:

Code: Select all

x = 32, y = 18, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
20bo$19bobo$20bo2bo7bo$12bo8b3o3b5o$11bobo8bo$b2o5b3obo15bobo$2o6bo2bo
$b4o3bo2bo$2b2o5b3o$20bobo$28bo$19b5o3b3o$3b3o4bo8bo7bo2bo$3bo2bo3bo
18bobo$3bo2bo4bo18bo$2bob3o$bobo$2bo!
In the afternoon: aha, now this two-engine p34 edge-shooter does break the record! (38×19 vs 31×20)

Code: Select all

x = 38, y = 50, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo19bo$10bobo17bobo$11bo19bo2$14bo2bo18bo$13bob2obo16bobo$14bo2bo18b
o2$22b3o$21bo3bo$2o5bob2o14bo$o6b3o14b2o$2bo5bo$bobo$2bo11bobobo2bo2bo
7bo$13bob3ob2ob2obo5bobo$5bo8bo3bo2bo2b2o6b2o$4bobo7b2o$5bo12$15b2o$2b
o14bo$bobo10bo2bo$2bob3o6b2ob2o$3bo2bo7bo$3bo2bo6b2o$3b3o23bo$20bo7bob
o$20b2o5bobo$21bo4b2o$9b3o15b2o$bo6bo2bo$obo5bo2bo$bo6b3obo$2o9bobo4b
2o$12bo6b2o7bo$17bobo3bo4bo$16bobo8bo$17bo8bob2o$23bo3bobo!
I have made hour-worth efforts to find the right catalysis for a p85 T-ship gun, which ended up at 33×36:

Code: Select all

x = 32, y = 31, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
12bo$2o9bobo7b2o$bo7b2obo5bo3bo$obo5b2obo5bob3obo$bo7b3o6bobobo5bo$10b
o16bobo$28bo3$4bo$3b3o4b4o$3bob2o2bo3bo$2bob2o6b2o$bobo$2bo$11b3o$11bo
2bo$2bo10b2o$bob4o11bo$2bobo2bo9bobo$2b2o3b2o9bobo$2bo3b2o11bo$2bo2bo
6bo$3b3o5b3o$4bo6bo2bo$9b2o3bo15bo$8b2o3b2o5bo8bobo$9bo2bobo4bobo8bo$
4bo5b4obo4bo9b2o$2b2obo8bo$2bobo!
EDIT on 23rd: just two days later, the traditional p34 engine wins back the title of driving the smallest p34 T-ship gun by appending the better-clearance edge-shooting mechanism hiding in plain sight. 30×19 is marginally smaller than 31×20, surely:

Code: Select all

x = 26, y = 19, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo$10bobo$11bo2$14bo2bo2b2o$13bob2ob2obo$14bo2bo2$22b3o$21bo3bo$2o5b
ob2o14bo$o6b3o14b2o$2bo5bo$bobo18b2o$2bo11bobobo2bo$13bob3ob3o$5bo8bo
3bo$4bobo10bobo$5bo12bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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Posts: 135
Joined: March 9th, 2022, 1:50 am
Location: I am everywhere and nowhere.

Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by Period1GliderGun » May 23rd, 2022, 6:10 pm

GUYTU6J wrote:
May 19th, 2022, 9:28 pm
In the afternoon: aha, now this two-engine p34 edge-shooter does break the record! (38×19 vs 31×20)

Code: Select all

x = 38, y = 50, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo19bo$10bobo17bobo$11bo19bo2$14bo2bo18bo$13bob2obo16bobo$14bo2bo18b
o2$22b3o$21bo3bo$2o5bob2o14bo$o6b3o14b2o$2bo5bo$bobo$2bo11bobobo2bo2bo
7bo$13bob3ob2ob2obo5bobo$5bo8bo3bo2bo2b2o6b2o$4bobo7b2o$5bo12$15b2o$2b
o14bo$bobo10bo2bo$2bob3o6b2ob2o$3bo2bo7bo$3bo2bo6b2o$3b3o23bo$20bo7bob
o$20b2o5bobo$21bo4b2o$9b3o15b2o$bo6bo2bo$obo5bo2bo$bo6b3obo$2o9bobo4b
2o$12bo6b2o7bo$17bobo3bo4bo$16bobo8bo$17bo8bob2o$23bo3bobo!
Broken again, with a 28x20 (EDIT: actually 28x19, thanks to GUYTU6J for catching that) p34 gun based on the original mechanism:

Code: Select all

x = 28, y = 19, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo$10bobo$11bo2$14bo2bo$13bob2obo$14bo2bo4$2o5bob2o$o6b3o$2bo5bo$bo
bo20bob2o$2bo11bobobo2bo2b2obo$13bob3ob3o$5bo8bo3bo$4bobo7b2o2b2o$5bo
!
It is based on this reaction, which turns an R into a T by way of a dot spark or basically anything with a protruding cell (snake in this case):

Code: Select all

x = 28, y = 7, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
b2o9b2o8b2o$2bo10bo9bo$3o8b3o7b3o2$3bo10bo9bob2o$13bobo8b2obo$14bo!
Perhaps, since the unstabilized p34 creates an R, it is possible to make an even smaller gun. However, I had trouble fitting the appropriate still life in.

Also, is there a collection of known guns somewhere?
Last edited by Period1GliderGun on May 24th, 2022, 10:29 pm, edited 1 time in total.
It's OK to abbreviate my username to "P1GG," but never, never, call me "pig."

Code: Select all

x = 36, y = 9, rule = B3/S23
23bobo$21bo3bo$13bo7bo$12b4o4bo4bo8b2o$11b2obobo4bo12b2o$2o8b3obo2bo3b
o3bo$2o9b2obobo6bobo$12b4o$13bo!
[[ STEP 30 ]]

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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » May 24th, 2022, 6:23 am

Period1GliderGun wrote:
May 23rd, 2022, 6:10 pm
Broken again, with a [28×19] p34 gun based on the original mechanism:

Code: Select all

x = 28, y = 19, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo$10bobo$11bo2$14bo2bo$13bob2obo$14bo2bo4$2o5bob2o$o6b3o$2bo5bo$bo
bo20bob2o$2bo11bobobo2bo2b2obo$13bob3ob3o$5bo8bo3bo$4bobo7b2o2b2o$5bo
!
Another two columns off by sacrificing edge-shooting capability... Nice catch, anyway.
It is based on this reaction, which turns an R into a T by way of a dot spark or basically anything with a protruding cell (snake in this case):

Code: Select all

x = 28, y = 7, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
b2o9b2o8b2o$2bo10bo9bo$3o8b3o7b3o2$3bo10bo9bob2o$13bobo8b2obo$14bo!
Perhaps, since the unstabilized p34 creates an R, it is possible to make an even smaller gun. However, I had trouble fitting the appropriate still life in.
The reaction has been used everywhere for a long time. The tricky part is accommodating a nearby tub catalyst, which sometimes cannot be replaced with a fishhook tail due to B5j. In these cases, I have to let the B-heptomino travel farther before converting it to a T-ship.

Code: Select all

x = 29, y = 28, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
3bo19bo$2bob2o16bobo$3bo2b2obo13bob2obo$6bob2o15bob2o2$3b2o17b2o$4b2o
17b2o$4bo18bo12$2o18b2o$o19bo$b3o17b3o$3bo2b2obo13bob2obo$6bob2o15bob
2o2$3b2o17b2o$4b2o17b2o$4bo18bo!
Also, is there a collection of known guns somewhere?
A number of guns are listed in the oscillator stamp collection on my LifeWiki article. If you want a better organization, we would need to convince Catagolue programmers to adapt the CGoL gun system to INT rules with non-glider spaceships.

---
I prefer not to post bare-handed, so here is a p68 T-ship shuttle:

Code: Select all

x = 43, y = 24, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo$10bobo$o7bo2bo$5o3b3o$9bo$bobo4$9bobo29bo$3bo36bobo$2b3o3b5o11bo
5bo7bo2bo$bo2bo7bo11b2obo2b5o3b3o$obo21bo14bo$bo29bobo4$39bobo$33bo$
32b3o3b5o$31bo2bo7bo$30bobo$31bo!
Here are two new B-heptomino/cloverleaf hasslers, a p642 and a p1044 (another existing high period after the p1224 coincidence :roll: ):

Code: Select all

x = 117, y = 67, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
7bo62bo$6bobo60bobo$7bo62bo3$2b2o61b2o$2bo62bo$bob2o59bob2o$2bobo60bob
o6$6bo62bo39bo$5b3o60b3o37bob2o$5bob2o59bob2o37bobo$4bo62bo40b2o$2b2o
61b2o$b3o60b3o48bo$2bobo60bobo46bobo$3b2o61b2o47bo24$51bo$50bobo$51bo
2$57b2o$55bobo$55b2obo$23bobo31bo$23b2obo$25bo$24b2o3$20bo78bobo$19bob
o77b2obo$20bo80bo$100b2o3$96bo$95bobo$96bo!
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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silversmith
Posts: 203
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Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by silversmith » June 10th, 2022, 10:57 pm

Naszvadi wrote:
March 2nd, 2020, 3:21 am
Random manual search yields a p44 gun - probably known - as it was mentioned before, extracting T ships is easy:

Code: Select all

snip
Apparently a catalyst works for this purpose as well, making a one engine gun.

Code: Select all

x = 29, y = 23, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
14bo$14b2o$15bo2$16b2o9bo$16bobo7bobo$17b2o8bo$20b2o4b2o$21b2o6$2o$b2o
$4b2o$4bobo$5b2o2$7bo$7b2o$8bo!
Edit: known
A simulator with the tools I couldn’t find elsewhere: https://www.silversimulations.com/arise/

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Re: 熠熠种花 - Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c)

Post by GUYTU6J » June 10th, 2022, 11:32 pm

Before making this post, a message appended to last post wrote:Last bumped by GUYTU6J on 2022年6月11日,Saturday,10时57分07秒.
Whoops, I clicked on this button accidentally when trying to save a view of this thread for archival purpose:
It seems to only appear in the threads created yourself, so bumping someone else's thread is not doable.
It seems to only appear in the threads created yourself, so bumping someone else's thread is not doable.
bump.png (34.65 KiB) Viewed 155 times
Curiosly it also changed the post time, which was originally May 24 or so. Sorry, silversmith.
Rambling aside, there is a fresh update to my LifeWiki article last night. The most important advancement is:
GUYTU6J wrote:
July 2nd, 2021, 8:23 am
...
Anyway, the B-heptomino track without emission can be constructed at p28 or above, taking out 29, 31, 33, 35 from the list of unknown periods...

Code: Select all

x = 115, y = 109, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
11bo$10bobo21b2o61b2o$11bo4b2o2b2o5bo6bo3bo59bo5bo$16bo3bo4b2obo4bob3o
bo6bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob2o4b2obo$15bob3ob3obobo
6bobobo6bob2o2bob2o2bob2o2bob2o2bob2o2bob2o2bob2o2bob2o2bob2ob3obobo$
16bo3bo2bo3b2o17bo5bo5bo5bo5bo5bo5bo5bo5bo5bo$17bo28bo41bo$16b2o2b2o
23bobo14bo12b3o9bobo14bo$9bo7bo4bo11b3o11b3o5bo6b2o9bo3bo11b3o5bo6b2o$
3bo4b3o11bo11bobo9bo3bo4b3o6bo13bo9bo3bo4b3o6bo$2bobo2bo2bo8bob2o11bob
o7b2o4bo3bo7b3o12b2o7b2o4bo3bo7b3o6bo$3bo3bo26b2o7b2o4bo5bo12bo5b3o8b
2o4bo5bo14bobo$3b2o39b3o8b2o10bo18b3o8b2o14bo$6bo20bobobo8bo4bo10b2o
29bo10b2o$4b2o2bo6bo10bob3obo5b3obo2bo5bo5bo5bo5bo5bo5bo5bo5bo5bo$4bo
4bobob2obo10bo3bo5bo3bob3obo2bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3b
obo9bo$b2obo4bo2b2obo11b2o8b2o3bo2bob3obo5bo5bo5bo5bo5bo5bo5bo5bo6b2ob
ob2o$bobo5bo37bo2bo55b3obobo$3b2o5b2o95bo2bo$4bo105bo$3bobo9bo93bob2o$
4bo9bobo87bo2bo2bobo$9bo5bo88b3o3bo$8b3o94bo3b2o$3b2o3bob2o$4bo2bo2b2o
98b2o$3bob2o4b2o2bo84bo10bo$4bo2b2obobobobo81b2obo7b2obo$10b3o2bo82bob
o8bobo$100b2o$3b2o95bo$4bo94bobo$3bobo9bo84bo$4bo9bobo87b2o5bo$15bo87b
4o3bob2o$103bo2b2o3bobo$3b2o4bo94b3o3b2o$4bo3b3o87b2o5bo5bo$3bobob2o2b
o3bo82bobo9bobo$4bo3b4o2bobo83bo10bo$9b2o4bo84b2o$99bo$3b2o93bobo$4bo
94bo2b3o$3bobo6b2obo83bo4bo$4bo7b3obo81b4o2bo5bo$11bo3bo86bo3b4obo$12b
o84b3o7bo2bo$3b2o7bo85bo7bo3b2o$4bo93bo7b2o$3bobo3bo5bo81bobo4b3o$4bo
3b3o3bobo81bobo4bo4bo$7bo2bo4bo83bo9bobo$7bo102bo$3b2o99bo5b2o$4bobo
94b3ob2o$3bobo2bo6bo83bo3bob2o$4bo4bobob2obo81bob3o2b2o3bo$9bo2b2obobo
81bo9bobo$9bo6bo93bo$3b2o5b2o4bo93b2o$4bo10b3o$3bobo93bo$4bo9b3o81bobo
2b2obo3bo$9bo5bo83bo4b3o2bobo$8b3o4bo89bo4bo$8bob2o2bobo93b2o$7bob2o4b
o$7bo3bob2o84bo$3bo3bo3bo2bo83bobo9bo$2bobo5bo3bobo82bo9bobo$3bo11b2o
93bo$3b2o105b2o$bobo$b2obo94bo$3bo94bobob3o2bo2bo$14bo84bo3bo2b4obo$
13bobo88bo2bo2bo$9bo4bo89b3o3b2o$8b3o2b2o90bo$3bobo2bob2o2bobo82bo$2bo
b2o7bob2o81bobo9bo$3bo10bo84bo9bobo$3b2o105bo$110b2o$4b2o96b3o$4bo94bo
4bo$2bobo93bob2o2bo5bo$2b2obo93bo2bo3b4obo$4bo102bo2bo$4b2o100bo3b2o$
2bobo59bo2bo38b2o3bobo$2b2obo3bo5bo5bo5bo5bo5bo5bo5bo5bo5bob3obo2bo3b
2o8b2o11bo4b3o3bob2o$4bo3b3o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3b
obo2bob3obo3bo5bo3bo10bobo4bo4bo$7bo2bo4bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
2bob3o5bob3obo10bo9b2o$6b2o13b2o27b2o11b2o9bo8bobobo$bo5b2o13bo9b2o17b
ob2o9bo45b2o$obo18bob2o8b2o9b2o6b2o9bob2o7b2o35bo$bo4bo8b2o5b2o5b3obo
9bobo8bo2b2o5b2o5b3o2bo8b3o11b2o9bobo$5b2o8bo5b2o6bob2o10bobo11bo5b2o
6bo2b2obo7bo13bo6bo4bo$15bo2bobo8b2ob2o9b3o11bo2bobo8b2ob2o9b2o12bo2bo
5bo$4b2o10b2o2b2o11bo18bo5b2o2b2o9b2o25b3o2bo$6bo13b2o10bo29b2o24bo16b
o2bo$14bo5bo5bo5bo5bo5bo5bo5bo5bo5bo17b2o3bo2bobobo6b3obo$10bobob3ob2o
bo2b2obo2b2obo2b2obo2b2obo2b2obo2b2obo2b2obo2b2obo6bobobo6bobob3ob3obo
7bo$9bob2o4b2obo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo6bob3obo4bob2o
4bo3bo$10bo5bo59bo3bo6bo5b2o2b2o4bo$16b2o61b2o21bobo$103bo!
Compressed to p27 on June 2:

Code: Select all

x = 111, y = 111, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
59bo21bo$45bo12bobo19bobo$44bobo12bo9bo11bo$12b2o27bo3bo3b2o3bo13bobo
6bo$12bo2bo9bo2b2o5bo4bob3ob3obo2bobo3b3o7bo6bobo23bo$14bobo7bob2obo4b
obo4bobobobobo4bo4bo2b2obo11bo23bobo$15bo9bo9bo30bo10bo24bo$5bo35bo22b
obo8bo2bo13bo$4bobo8b3o22b3o10b3o19bo15b3o$5bo9bo2bo11b2o5bob2o2bo12b
2o7bo2b2o5b3o4bo8bo2bo$14b3obo12b2o4bobobob2o12bo3b2obobo2bo12b2o6b3ob
2o$18bo11b2o6bobob2o9bo3bo8bo2bo8bob3o5bo4b2o$17bo12bo6b4o13b3o9b3o9b
2obo6b2o16b2o$78bo28bo$38b3o8bo5bo9bo12bo9bo11bo4bo$10bo5bobobobobo14b
o8bob2o2bob2obo4bobo10bob2obo4bobo4bo5b3obobo$9b3o3bob3ob3obo23bobo3bo
2b2o5bo12bo2b2o5bo4bobo4bobo2bo$8bo2bo4bo3bo3bo69bo3bo3bo$7b2obo8bobo
6bo65b2o3b3o$8b3o9bo6bobo62bobo$10bo17bo62bobobo$12bo2bo76bobo$11b2obo
bo77b2o$15bo78bo$93bobo9bo$94bo9bobo$105bo$10bo80bo13bo$bo7b3o3b2o73bo
bo13bo$obo8b2o3bo74bo13b2o$bo9bo3bo82b2obo$12bo2bo83b3o$4bo2bo3b4obo
83bo$3bob2o2bo5bo$4bo4bo95bo$7b3o94bobo$105bo$98bob2o$96bob2o$95b2obob
2o$3bo92bob2ob2o3bo$2bobo4b3o88bob2obobo$3bo5bo2bo86bo2bo3bo$12bo86b3o
3b2o$6b2o2b3o2bo84bo5bobo$5bo3bo4bobo88bobobo$7bo2bo4bo90bobo$5bo99b2o
$5bo4bo84bo10bo$4bo5bo83bobo8bobo$bo2bo90bo10b2o$obob2o9b2o77b2o$bo14b
o$9b3o3bo83bo2bo3bo$9bo2bo2bo79bo2bo3bo2bobo$4bo3bo3bobobo77bobobo3bo
3bo$3bobo2bo3bo2bo79bo2bo2bo$4bo3bo2bo83bo3b3o$94bo14bo$15b2o77b2o9b2o
bobo$3b2o10bo90bo2bo$3bobo8bobo83bo5bo$4bo10bo84bo4bo$4b2o99bo$2bobo
90bo4bo2bo$bobobo88bobo4bo3bo$2bobo5bo84bo2b3o2b2o$4b2o3b3o86bo$4bo3bo
2bo86bo2bo5bo$3bobob2obo88b3o4bobo$4bo3b2ob2obo92bo$9b2obob2o$11b2obo$
9b2obo$5bo$4bobo94b3o$5bo95bo4bo$95bo5bo2b2obo$10bo83bob4o3bo2bo$9b3o
83bo2bo$9bob2o82bo3bo9bo$4b2o13bo74bo3b2o8bobo$4bo13bobo73b2o3b3o7bo$
5bo13bo80bo$5bo$4bobo9bo$5bo9bobo$16bo78bo$15b2o77bobob2o$16bobo76bo2b
o$15bobobo62bo17bo$16bobo62bobo6bo9b3o$9b3o3b2o65bo6bobo8bob2o$8bo3bo
3bo69bo3bo3bo4bo2bo$5bo2bobo4bobo4bo5b2o2bo12bo5b2o2bo3bobo23bob3ob3ob
o3b3o$4bobob3o5bo4bobo4bob2obo10bobo4bob2obo2b2obo8bo14bobobobobo5bo$
5bo4bo11bo9bo12bo9bo5bo8b3o$3bo28bo$3b2o16b2o6bob2o9b3o9b3o13b4o6bo12b
o$16b2o4bo5b3obo8bo2bo8bo3bo9b2obobo6b2o11bo$15b2ob3o6b2o12bo2bobob2o
3bo12b2obobobo4b2o12bob3o$16bo2bo8bo4b3o5b2o2bo7b2o12bo2b2obo5b2o11bo
2bo9bo$17b3o15bo19b3o10b3o22b3o8bobo$18bo13bo2bo8bobo22bo35bo$8bo24bo
10bo30bo9bo9bo$7bobo23bo11bob2o2bo4bo4bobobobobo4bobo4bob2obo7bobo$8bo
23bobo6bo7b3o3bobo2bob3ob3obo4bo5b2o2bo9bo2bo$33bo6bobo13bo3b2o3bo3bo
27b2o$29bo11bo9bo12bobo$28bobo19bobo12bo$29bo21bo!
This is the second known period-27 oscillator after the T-ship loop, and it has no p3 or p9 rotors.
What happened? Well, one day ago a second forward conduit for B-heptomino transportation that has a repeat time of 27 ticks was found. It moves 17 cells in 37 ticks, both coprime with the old 6-cell 12-tick one:

Code: Select all

x = 37, y = 21, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
25b3o$25bob2o7$33bo$32bobo$33bo$5b3o$5bob2o12bo$20bobo$21bo$2o$bo4bo
19bo$obo2b3o4bo12b3o$bo3bob2o2bobo6bo4bob2o6bo$12bo6bobo12bobo$20bo14b
o!
Following that, a turn was invented and applied to the p27 construction successfully. Sadly, despite its better potential for a low-period signal duplicator, none have been found. A simple split with repeat time 28 exists, but the extra V or W pentomino defies stable catalysis...

Code: Select all

x = 28, y = 27, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
obo9bo$2obo7bobo$2bo9bo7$16b3o$16bobo$3bobobobobo2b3obo$2bob3ob3obobo
2bo$3bo3bo3bo2bo3b5o$6bobo6b3ob4o$7bo8bo2bob2o$17bobo$12bo$11bobo$12bo
2$17bo$16b3o$11bo4bob2o$10bobo13bo$11bo13bobo$26bo!
Last but not least, a p165 partial that is similar to but worse than the p101 one:

Code: Select all

x = 28, y = 16, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
26bo$25bobo$26bo3$6b2o$6bo$7b3o$9bo2$3bo$2bobo$obobo$2o2b2o5bo$10b3o$
10bob2o!
#C [[ STOP 165 ]]
Why do most natural OCA rules tend to get a diminishing span of interest and go into oblivion, like a lost civilization leaving little records for its beauty and power?

I have been focusing on this rule, now in industrial era:

熠熠种花 - Glimmering Garden

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