Synthesising Oscillators

[mniemiec]

It turns out that it's possible to synthesise it cleanly with just 6 gliders: ...

Nice!

Also, is this useful? Four gliders add stabilizing bookends to a twin bees shuttle: ...

Interesting, although probably not better than the state of the art, as it already takes 4 gliders to make a pair of bookends by themselves. Still, the fact that they are made by hitting the Bs' debris plume is interesting.

[Sokwe]

It turns out that it's possible to synthesise [unix] cleanly with just 6 gliders:

This one has been known for a while.

[gmc_nxtman]

This one has been known for a while.

Oops.. sorry

Anyway, xs19_02egm9a4zc8421 in 10 gliders (possibly reducible), which allows 17.3736 (xs17_2egm9a4zw65) in 16 gliders, and likely other difficult 17-bit still lifes:

Code: Select all

x = 157, y = 32, rule = B3/S23
15bo$16bo$14b3o2$6bo15bobo$7bo15b2o11bo$5b3o15bo11bo$35b3o2$2bobo$3b2o
80bobo$3bo82b2o56bo$86bo58bo$143b3o$52b2o30b2o$52bo6bo24bo6bo31bo31bo$
53bo3b3o25bo3b3o24b2o3b3o24b2o3b3o$19bobo3bo28bobo29bobo27bobobo21bo5b
obobo$19b2o4bobo27b2ob2o22b2o3b2ob2o27b2ob2o16bobo8b2ob2o$20bo4b2o30bo
2bo17bo2b2o6bo2bo28bo2bo16b2o10bo2bo$57bobo19bo3bo5bobo29bobo20b2o7bob
o$21b2o35bo18b3o10bo31bo22b2o7bo$20b2o122bo$22bo2$24bo$23b2o$23bobo2$
3o$2bo$bo!

[mniemiec]

Anyway, xs19_02egm9a4zc8421 in 10 gliders (possibly reducible), which allows 17.3736 (xs17_2egm9a4zw65) in 16 gliders, and likely other difficult 17-bit still lifes: ...

The flip-and-shorten snake converer can shorten by an arbitrarily large number, by moving the two lower gliders SW n spaces and back n steps. This saves 3 gliders:

Code: Select all

x = 35, y = 13, rule = B3/S23
7bobo$8boo$8bo$$6boo$6bo6bo19bo$7bo3b3o17b3o$8bobo16boobo$9booboo13bob
ooboo$5boo4bobbo16bobbo$o4bobo3bobo17bobo$boobbo6bo19bo$oo!

[BobShemyakin]

Anyway, xs19_02egm9a4zc8421 in 10 gliders (possibly reducible), which allows 17.3736 (xs17_2egm9a4zw65) in 16 gliders, and likely other difficult 17-bit still lifes: ...

The flip-and-shorten snake converer can shorten by an arbitrarily large number, by moving the two lower gliders SW n spaces and back n steps. This saves 3 gliders:

Code: Select all

x = 35, y = 13, rule = B3/S23
7bobo$8boo$8bo$$6boo$6bo6bo19bo$7bo3b3o17b3o$8bobo16boobo$9booboo13bob
ooboo$5boo4bobbo16bobbo$o4bobo3bobo17bobo$boobbo6bo19bo$oo!

17.3736 in 11G:

Code: Select all

x = 23, y = 95, rule = B3/S23
5bo$5bobo$5b2o5$obo2bo$b2o2bobo$bo3b2o10bo$16bobo2b2o$15bo2bo3bo$16b2o
b3o$19bo$16b3o$16bo3$b2o$2o$2bo25$6bo$5bobob2o$4bo2bobo$5b2o2bo$7b2o$
7bo$5bobo5bobo3bobo$bo3b2o6b2o4b2o$b2o11bo5bo$obo7b2o$9b2o4b2o$4b2o5bo
2b2o$3bobo10bo$5bo$9b2o$8b2o$10bo26$6bo$5bobob2o$4bo2bobo$5b2o2bo$7b2o
$7bo$8bo$7b2o!

Bob Shemyakin

[Extrementhusiast]

Are there any converters that will convert the above Elkies' P5 variant into either of these?

Unfortunately, Extrementhusiast's snake-to-eater converter doesn't work as shown, as the hook gets in the way. He had previously posted an 82-glider synthesis of the version with the pre-block on 2015-08-02, although if it can be converted from a snake or carrier, this new synthesis would reduce that.

Fortunately, I just found a much better snake-to-eater converter that allows for just that:

Code: Select all

x = 57, y = 20, rule = B3/S23
3bo26bo18bo$2bo2b3o21bo2b3o13bo2b3o$4bo26bo18bo$5bobo2bo21bobo2bo13bob
o2bo$4b2ob4o3bo16b2ob4o12b2ob4o$3bo2bo6bo16bo2bo15bo2bo$3b2o2b2o4b3o
14b2o2b2o13b2o2b2o$8bo26bo2bo15bo$7bo27bobobo14bobo$7b2o24bobobobo15b
2o$29b2o2b2o3bo$30b2o8b2o$4b2o10b3o10bo10bobo$3b2o11bo23bo$2o3bo11bo
14b3o$b2o31bo$o32bo$6bo$5b2o$5bobo!

[gmc_nxtman]

Component extracted from a recent (natural) oscillator synthesis:

Code: Select all

x = 19, y = 22, rule = B3/S23
16bo$16bobo$16b2o2$4bo$2b3o$bo3b2o$o2bo2bo$b5o2$3b3o$2bo2bo$2bobo$3bo$
14bo$13b2o$3b2o8bobo$2bobo$4bo$6b3o$6bo$7bo!

Of course, this isn't an improvement for this particular stator variant, but it might be helpful for other stillater-based oscillators. (Also, this particular stator variant is smaller than the one in LifeWiki by two cells with equal bounding box)

[Bullet51]

From wwei23's 1x256 soup:

Code: Select all

x = 39, y = 41, rule = B3/S23
35bo$o32b2o$b2o31b2o$2o2$24bo$25b2o$24b2o$32b2o$31bo2bo$31bo2bo$32b2o
5$23bo10b2o$22bobo8bob3o$22b2o9bo4bo$34b4o2$34b4o$22b2o9bo4bo$22bobo8b
ob3o$23bo10b2o5$32b2o$31bo2bo$31bo2bo$32b2o$24b2o$25b2o$24bo2$2o$b2o
31b2o$o32b2o$35bo!

Wwei23's soup search would discover a P5 sooner or later.

[gmc_nxtman]

The topic of updating the H-to-H collection came up recently, and I'd like to make obsolete the "-" feature that implies non-glider-constructibility on certain conduits. The following still-lifes make 6 conduits non-trivial:

Code: Select all

Nope.

I've got 2 plans for the still-life in the Fx158 conduit:

Code: Select all

x = 306, y = 57, rule = B3/S23
74bo$72bobo$73b2o$78bo$76b2o$77b2o222b2o$o300b2o$b2o144bo57bo$2o145bob
o55bobo29bo26b3o34b4o$78bo27bo31bo8b2o21bo31bo2b2o27bobobo24bo3bo30bob
o4bo$40b2o30b2o4bobo23b3o6bo22b3o6bo22b3o29b3o29b3ob2o29bo28b3ob2o2b2o
$b3o4b2o29bo2bo28bo2bo3b2o2b2o19bo9bo21bo9bo21bo31bo31bo34bo28bo$3bo3b
obo2b3o21bo2b3o26bo2b3o8bobo15bo2b4o6bo18bo2b4o6bo18bo2b4o25bo2b4o25bo
2b4ob2o27bo26bo2b4ob2o$2bo6bo2bo23b3o29b3o11bo17b3o3bo25b3o3bo25b3o3bo
25b3o3bo2b2o21b3o3bob2o54b3o3bob2o$13bo25bo31bo31bo31bo31bo31bo5bobo
23bo33bo29bo$4bo33b2o30b2o30b2o30b2o30b2o30b2o5bo24b2o62b2o$4b2o$3bobo
71b2o124b2o$76b2o124bobo$6b3o69bo125bo$6bo66b2o$7bo64bobo$74bo15$173b
2o62b2o30b2o30b2o$173b2o62b2o22bobo5b2o30b2o$261b2o$173b4o23b3o34b4o
21bo6b4o28b4o$170bobo4bo21bo3bo30bobo4bo24bobo4bo24bobo4bo$136bobobo
27b3ob2o2b2o25bo28b3ob2o2b2o22b3ob2o2b2o22b3ob2o2b2o$167bo34bo28bo18b
2o11bo31bo$168b3ob2o27bo29b4ob2o11bobo11b4ob2o22bo2b4ob2o$170bob2o55b
2o3bob2o13bo9b2o3bob2o22b3o3bob2o$201bo26bo2bo28bo2bo31bo$229b2o30b2o
31b2o5$260bo$259b2o$255bo3bobo$256b2o$255b2o!

The second still-life seems like it should be trivial somehow, but I can't come up with a good way.

[mniemiec]

I've got 2 plans for the still-life in the Fx158 conduit: ...

50 gliders:

Code: Select all

x = 177, y = 81, rule = B3/S23
50bo$48bobo$49boo$54bo77bo$52boo76bobo$53boo76boo$o97bo$boo95bobo32bo$
oo96boo33bobo$54bo15bo19bo19bo19bobboo15boboo$28boo18boo4bobo11b3o6bo
10b3o6bo10b3o17b3o17b3oboo$b3o4boo17bobbo16bobbo3boobboo7bo9bo9bo9bo9b
o19bo19bo$3bo3bobobb3o9bobb3o14bobb3o8bobo3bobb4o6bo6bobb4o6bo6bobb4o
13bobb4o13bobb4oboo$bbo6bobbo11b3o17b3o11bo5b3o3bo13b3o3bo13b3o3bo13b
3o3bobboo9b3o3boboo$13bo13bo19bo19bo19bo19bo19bo5bobo11bo$4bo21boo18b
oo18boo18boo18boo18boo5bo12boo$4boo$3bobo47boo76boo$52boo76bobo$6b3o
45bo77bo$6bo42boo$7bo40bobo$50bo4$148bo$149bo$147b3o3bo$143bo7boo$144b
oo6boo$99bobo41boo$100boobbo$54bo45bo3bobo$55bo9bo38boo$53b3o9bobo107b
oo$65boo85bo22boo$58bo25boo18boo19bo19bo5bo$18bo39bobobbo21bo19bo17b3o
17b3o5b3o19b4o$10boboo4bobo9boboo16boboo4boobboo16bobo17bobo17bobo17bo
bo27bobo3bo$8b3oboo4boo8b3oboo14b3oboo8bobo13b3oboo14b3oboo14b3oboo14b
3oboo24b3oboo$7bo19bo19bo29bo19bo19bo19bo16bobo10bo$4bobb4oboo4bo5bobb
4oboo3boo5bobb4oboo3boo15bobb4oboo10bobb4oboo10bobb4oboo10bobb4oboo10b
oo8bobb4oboo$4b3o3boboo3boo5b3o3boboobbobbo4b3o3boboobbobbo14b3o3boboo
10b3o3boboo10b3o3boboo10b3o3boboo11bo8b3o3boboo$7bo9bobo7bo8bobbo7bo8b
obbo17bo19bo19bo19bo29bo$6boo18boo9boo7boo9boo17boo18boo18boo18boo28b
oo$152b3o$152bo$57bo95bo$56boo$56bobo5$70bo$16bo53bobo$14bobo53boo$15b
oo39bo55bobo$57bo55boo13bo$17bo37b3o14bo40bo12boo$11boboboo54bo55boo$
12boobboo27bobbo22b3o$12bo36bo$35bo9bo3bo15bo8boo$15boo17bobo9b4o14bob
o7bobo16boo18boo38boo$15boo18boo28boo7bo18boo18boo38boo$$13b4o16b4o26b
4o26b4o16b4o36b4o$10bobo3bo13bobo3bo23bobo3bo23bobo3bo13bobo3bo7bo25bo
bo4bo$8b3oboo14b3oboo24b3oboo24b3oboo14b3oboo9bo24b3oboobboo$7bo19bo
29bo29bo19bo15b3o21bo$4bobb4oboo10bobb4oboo20bobb4oboo20bobb4oboo10bo
bb4oboo6boo22bobb4oboo$4b3o3boboo10b3o3boboo20b3o3boboo20b3o3boboo10b
3o3boboo5boo10bo12b3o3boboo$7bo19bo29bo29bo19bo13bo8boo15bo$6boo18boo
28boo28boo18boo22bobo13boo3$125boo$125bobo$125bo!

EDIT: #4 from 50 gliders 2 different ways:

Code: Select all

x = 175, y = 113, rule = B3/S23
108bo$98bo7boo$99boo6boo$98boo$103bo$104boo$103boo$65bo$66boo59boo18b
oo18boo$65boo30bobo25bobbo16bobbo16bobbo$70bo27boo25b3o17b3o17b3o$68b
oo3b3o22bo$69boobbo14boboo16boboo13booboboo13booboboo13booboboo$74bo
13boobo16boobo12boboboobo12boboboobo12boboboobo$72bo52bo19bo18boo$72b
oo$71bobo27boo35boo$100bobo36boobbo$102bo4bo30bo3boo$105bobo34bobo$
106boo$115boo$108b3o3boo$110bo5bo$109bo$143bo$144boo$143boo$$148bo$
137bo8boo$135bobo9boo$136boo14bo$106bo34bo9bo$107bo34bo8b3o$105b3o32b
3o$56bo52bo44boo$55bo6bo45bo45bobo$46bo8b3o3bo46b3o17boo18boo4bo12boo$
44bobo14b3o64boo18boo15bobbo$37bobo5boo118b3o$38boo$38bo6bo29booboboo
23booboboo13booboboo13booboboo13booboboo$45boo27boboboobo22boboboobo
12boboboobo12boboboobo12boboboobo$44bobo27boo28boo18boo18boo18boo4$58b
3o$58bo$59bo8$102bo$100boo$97bo3boo$95bobo7bo$96boo7bobo$105boo$$140bo
bo$140boo$141bo$57boo18boo28boo18boo8boo8boo18boo$55bobbo16bobbo26bobb
o15boobbo7b4o4boobbo15boobbo$55b3o17b3o27b3o17b3o8booboo4b3o15bob3o$
91bo31bo14boo3bo19bo$55booboboo11b4oboboo10bo10b4oboboo10bob3oboboo10b
ob3oboboo12b3oboboo$46bo7boboboobo11bobboboobo8b3obboo6bobboboobo10bo
3boboobo10bo3boboobo14boboobo$44bobo7boo20bo17bobo9bo14boo3bo14boo3bo
19bo$45boo28boo19bo8boo18boo18boo18boo$87boo$47b3o38boo$49bo37bo$48bo
8boo$57bobo44b3o$57bo34b3o9bo$44bo8b3o38bo10bo$44boo9bo37bo$6boo35bobo
8bo$5b3o$5b3o$3boboobo$bobobb3o$bboo3bo$19b6o35bo$16bobbo5bo34bobo86bo
$4bobo7boo3bo40boobboo81bobo$5boo4bo3boo3bo4bo37boo42bo7bo32boo$5bo4bo
bo9boo41bo15bo19bo4bo6boo16bo19bo$oo8boo28bo19bo19bobo17bobo3b3o5boo
14bobo17bobo19bo$boo36bobo17bobo17bobo17bobo27bobobo15bobobo15bobobo$o
38boo18boo18boo18boo28boobbo15boobbo15boobbo$7boo28boo18boo18boo18boo
7b3o18boo4boo12boo4boo12boo4boo$4boobbo25boobbo15boobbo15boobbo15boobb
o7bo17boobbo15boobbo15boobbo$3bob3o25bob3o15bob3o15bob3o15bob3o9bo15bo
b3o15bob3o15bob3o$3bo29bo19bo19bo19bo29bo19bo19bo$4b3oboboo22b3oboboo
12b3oboboo12b3oboboo12b3oboboo22b3oboboo12b3oboboo12b3oboboo$6boboobo
24boboobo14boboobo14boboobo14boboobo4boo18boboobo14boboobo14boboobo$6b
o29bo19bo19bo19bo9bobo17bo19bo19bo$5boo28boo18boo18boo18boo9bo18boo18b
oo18boo$$105bo$105boo$104bobo$109bo$108boo$108bobo!

EDIT 2: #2 (20.6975) from 40, based on 17.1256 (17#197)

Code: Select all

x = 176, y = 92, rule = B3/S23
obo93bo$boo5bo88bo$bo7boo46bobo4bo30b3o$8boo48boo4bobo$58bo5boo12boo
18boo36boo$78boo18boo35bobo3bobo$21bo38bo76bo3boo$20bo40boo79bo$20b3o
37boo102bo$84boo18boo18boo18boo17bobo$22bo23boboo6bo9boboo14boboboo14b
oboboo14boboboo14boboboo14boboboo$21boo23boobo7boo7boobo16boobo16boobo
16boobo16boobo16boobo$21bobo32boo27bo19bo19bo11boo6bo19bo$46b3o17b3o
17b3o17b3o17b3o9boobbo3b3o17b3o$13bo31bobbo9bo6bobbo19bo19bo19bo8bo3b
oo5bo19bo$13boo30bobo10boo5bobo73bobo$12bobo31bo10bobo6bo3$61boo$60bob
o$62bo8$90bo$91boo$90boo$94bobo30boo$94boo24bo6b3o3bo$95bo25boo3boboo
3bobo$120boo4b3o4boo$127bo$110b3o17b3o41boo$14bo9bo19bo18boo18boo18boo
18boo49boo$13bobo7bobo17bobo16bobbo16bobbo16bobbo16bobbo27bo$14boboboo
4boboboo8bobo3boboboo12boboboboo12boboboboo12boboboboo12boboboboo22bob
oboboo$16boobo6boobo9boo5boobo13booboobo13booboobo13booboobo13booboobo
23booboobo$15bo9bo13bo5bo19bo19bo19bo19bo29bo$10b3o3b3o6boboo16boboo
16boboo16boboo16boboo16boboo26boboo$12bo5bo7bobo8boo7bobo17bobo17bobo
17bobo17bobo27bobo$11bo26boo$13bo3boo18bo$12boo3bobo$12bobobbo6$38bo$
37bo$37b3o$34boo$34boo$13bo29bo$12boboboboo22boboboboo$13booboobo23boo
boobo$15bo29bo$15boboo26boboo$16bobo27bobo6$95bobo$91bo3boo$92boobbo$
55bo35boo39bobo$56bo3bo18boo18boo31boo$54b3oboo18bobbo16bobbo3b3o16bob
o6bo$22bo36boo17bobbo16bobbo3bo19boo3bo$20bobo3bo52boo18boo5bo18bobboo
$21boobbo103boo$13bo11b3o5bo19bo19bo19bo19bo4boo13bo4boo18boo$12bobobo
boo12bobobobooboo9bobobobooboo9bobobobooboo9bobobobooboo9bobobobbo12bo
bobobbo14bobobbo$13booboobo3boo8booboobobobo9booboobobobo9booboobobobo
9booboobobobo9boob3o14boob3o13b3ob3o$15bo7bobo9bo6bo12bo6bo12bo6bo12bo
6bo12bo19bo15bo3bo$15boboo4bo11boboo16boboo16boboo16boboo16boboo16bob
oo12boobboboo$16bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo$105b3o
21boo$105bo24boo$106bo22bo$$133b3o$133bo$134bo!

EDIT 3: I am not going to attempt the other 3, lest my brain melt.

[gmc_nxtman]

50 gliders...

Nice! Here's a corollary-snipe down to 44:

Code: Select all

x = 283, y = 54, rule = B3/S23
276bo$74bo196bo3bo$72bobo197b2ob3o$73b2o196b2o$78bo$76b2o200b2o$77b2o
198b2o$o145bo132bo$b2o143bobo56bo$2o144b2o57bobo29bo31bo$78bo27bo31bo
31bo31bo2b2o27bobobo27bobobo$40b2o30b2o4bobo23b3o6bo22b3o6bo22b3o29b3o
29b3ob2o26b3ob2o$b3o4b2o29bo2bo28bo2bo3b2o2b2o19bo9bo21bo9bo21bo31bo
31bo31bo$3bo3bobo2b3o21bo2b3o26bo2b3o8bobo15bo2b4o6bo18bo2b4o6bo18bo2b
4o25bo2b4o25bo2b4ob2o22bo2b4ob2o$2bo6bo2bo23b3o29b3o11bo17b3o3bo25b3o
3bo25b3o3bo25b3o3bo2b2o21b3o3bob2o22b3o3bob2o7b2o$13bo25bo31bo31bo31bo
31bo31bo5bobo23bo31bo12b2o$4bo33b2o30b2o30b2o30b2o30b2o30b2o5bo24b2o
30b2o14bo$4b2o275b2o$3bobo71b2o124b2o67b2o6b2o$76b2o124bobo66bobo8bo$
6b3o69bo125bo68bo$6bo66b2o$7bo64bobo$74bo5$178bo$50bo61bo65bobo$51bo
58bobo65b2o$49b3o3bo55b2o51bo71bobo$45bo7b2o110bo71b2o13bo$46b2o6b2o
57bo49b3o14bo56bo12b2o$45b2o60bobob2o66bo71b2o$108b2o2b2o39bo2bo22b3o$
108bo48bo$143bo9bo3bo15bo8b2o$79b2o30b2o29bobo9b4o14bobo7bobo20b2o30b
2o30b2o$54bo24b2o30b2o30b2o28b2o7bo22b2o30b2o30b2o$15bo31bo5bo$13b3o
29b3o5b3o21b4o28b4o28b4o26b4o30b4o28b4o28b4o$10bobo29bobo29bobo3bo25bo
bo3bo25bobo3bo23bobo3bo27bobo3bo25bobo3bo7bo17bobo4bo$8b3ob2o26b3ob2o
26b3ob2o26b3ob2o26b3ob2o24b3ob2o28b3ob2o26b3ob2o9bo16b3ob2o2b2o$7bo31b
o16bobo12bo31bo31bo29bo33bo31bo15b3o13bo$4bo2b4ob2o22bo2b4ob2o10b2o10b
o2b4ob2o22bo2b4ob2o22bo2b4ob2o20bo2b4ob2o24bo2b4ob2o22bo2b4ob2o6b2o14b
o2b4ob2o$4b3o3bob2o22b3o3bob2o11bo10b3o3bob2o22b3o3bob2o22b3o3bob2o20b
3o3bob2o24b3o3bob2o22b3o3bob2o5b2o10bo4b3o3bob2o$7bo31bo31bo31bo31bo
29bo33bo31bo13bo8b2o7bo$6b2o30b2o30b2o30b2o30b2o28b2o32b2o30b2o22bobo
5b2o$54b3o$54bo$55bo193b2o$249bobo$249bo!

EDIT: This still life (in F150) looks like it should be trivial but I don't have a "proof of constructibility" yet:

Code: Select all

x = 8, y = 11, rule = B3/S23
2o$obo$2bo$b2ob2o$4bo$4bo$3b2ob2o$5bobo$5bo$3bobo$3b2o!

EDIT2: Got it in 28 gliders:

Code: Select all

x = 506, y = 29, rule = B3/S23
396bo$394bobo$395b2o$86bo58bo194bo25bo31bo$85bo60bo193bobo22bobo29bobo
$85b3o56b3o186bobo4b2o23bobo29bobo$116b3o29b3o130bo52b2o30bo31bo$84bo
195bo31bo21bo4bo4bo$85bo180bo13b3o28bobo26b2obobo$6bo70bobo3b3o5bobo
173bo3bo30b2o7bobo20b2o3b2o2bobo$6bobo69b2o11b2o172b3ob2o12b3o15bo2bo
7bo20bo2bo7bo25b2o30b2o30b2o30b2o30b2o$6b2o70bo13bo177b2o11bo17bo2bo
28bo2bo33bobo29bobo29bobo29bobo29bobo$284bo17b2o30b2o10b3o23bo31bo31bo
25bo5bo31bo$37bo36b3o8bo8b3o18b2ob2o27b2ob2o27b2ob2o27b2ob2o27b2ob2o
27b2ob2o27b2ob2o27b2ob2o2bo24b2ob2o27b2ob2o27b2ob2o23bo3b2ob2o27b2ob2o
$5b3o28bobo37bo7bobo7bo21bobo29bobo29bobo29bobo29bobo29bobo29bobo29bob
o4bo24bobo29bobo29bobo22b3o4bobo31bo$5bo7bo22bobo36bo8bobo8bo20bobo29b
obo29bobo29bobo29bobo29bobo29bobo29bobo29bobo29bobo29bobo29bobo31bo$6b
o6bobo21b2ob2o43b2ob2o27b2ob2o27b2ob2o27b2ob2o27b2ob2o27b2ob2o27b2ob2o
27b2ob2o27b2ob2o27b2ob2o27b2ob2o27b2ob2o22b2o3b2ob2o27b2ob2o$13b2o24bo
bo45bobo29bobo29bobo29bobo29bobo29bobo29bobo29bobo29bobo29bobo29bobo
29bobo21bobo5bobo29bobo$10b2o27bo47bo31bo31bo31bo31bo31bo31bo31bo31bo
31bo31bo31bo25bo5bo31bo$9b2o27b2o46b2o30b2o30b2o30b2o30b2o29bobo29bobo
29bobo29bobo29bobo29bobo29bobo29bobo29bobo$5b2o4bo198bo9bo24b2o30b2o
30b2o30b2o30b2o30b2o30b2o30b2o30b2o$bo3bobo203b2o5b2o$b2o2bo204b2o7b2o
$obo$218bo$217b2o$209b3o5bobo$209bo$210bo!

EDIT3: Great work Extrementhusiast... three more ingenious syntheses. And they're all in their standard stator variants, too - very nice!

[Extrementhusiast]

And here are the other three catalysts:

Code: Select all

x = 652, y = 241, rule = B3/S23
363bo$364b2o$232bo130b2o$230b2o$231b2o2$385bo$385bobo$210bo174b2o$208b
obo$209b2o2$461bo$459bobo$460b2o$380bo$260bo120bo$215bo44bobo116b3o$
214bo45b2o121bobo20bo$214b3o166b2o22bo$210bobo155bo15bo20b3o$211b2o31b
o44bo37bo41b2o30bo$211bo33b2o10bo30bo37bo41b2o29bobo6bobo57bo5bo$244b
2o9b2o31b3o35b3o35bo35b2o6b2o59b2obobo$256b2o28bo37bo40b2o42bo58b2o3b
2o25bo$284bobo35bobo39b2o99b2o31bobo$285b2o36b2o79b2o58bobo32b2o$320bo
83bo25bo6b2o27bo10b2o$223bo33b2o31b2o4b2o20bobo15b2o50b2o15bo4b2o19b2o
4bo4b2o28bo4bo4b2o17b2o2b2o17bo3b2o$223bobo32bo30bo2bo4bo21b2o11bo4bo
46bo4bo16bo4bo18b2o6bo4bo27bobo4bo4bo12b2o2bobo3bo12b2o2bobo3bo$223b2o
32bo32b3o3bo33b3o3bo45b3o3bo16b2o3bo26b2o3bo29b2o3b2o3bo13bo3b2o3bo13b
o3b2o3bo$144b2o3bo18bo16bo25bo44bo38bo33bo5bo45bo5bo16bo4bo26bo4bo34bo
4bo15b3o4bo15b3o4bo$141bo2bobo2bobo7bo6b3o14b3o23b3o42b3obo33b4obo30bo
bob4obo44bob4obo14bob4obo24bob4obo28b2o2bob4obo15bob4obo15bob4obo$139b
obo2bo4b2o9bo4bo3b2o11bo3b2o20bo3b2o39bo3bobo32bo3bobo29bobobo3bobo31b
3o8b2obo3bobo12b2obo3bobo18b3o3b2o3bobo27b2o3b2o3bobo15b2o3bobo15b2o3b
obo$140b2o16b3o4b2o2bobo9bobo2bobo18bobo2bobo37bobobo2bo35bo2bo30bo5bo
2bo33bo14bo2bo18bo2bo20bo7bo2bo36bo2bo19bo2bo19bo2bo$170bo11bo4bo20bo
4bo39bo3b2o37b2o38b2o33bo16b2o20b2o20bo9b2o38b2o21b2o21b2o$285bo114bob
o31b3o26b2o6bo$142b2o18bo122b2o74b2o38b2o31bo29b2o4b2o$141bobo18b2o53b
2o27b2o36bobo75b2o5b2o30bo33bo27bo6bobo$143bo17bobo26b3o24b2o28b2o112b
o6bobo32b2o$192bo53bo3b2o118bo32bobo$164b3o24bo50b2o5b2o69b2o81bo$164b
o28b2o23b2o23b2o6bo67bobo$165bo27bobo22b2o22bo78bo$193bo13b3o$209bo$
208bo51$508bo$509bo$418bo88b3o$419bo$417b3o2$441bo$439b2o$328bo111b2o
69bobo5bo64bobo$327bo183b2o5bo66b2o$327b3o182bo5b3o4bo5bo53bo36bobo$9b
o500bo13bo6bobo89b2o$10bo309bo163bo26bo12b3o4b2o20bo69bo$8b3o310bo14bo
148bo23b3o5bo36b2o73bo$271bo47b3o5bo7bo130bo16b3o29bobo35b2o3bo68b2o$
271bobo52bo8b3o47bobo24bobo46bo3bo21b2o27b2o32b2o7b2o34bo4bo23bo3b2o$
47bobo221b2o53b3o56b2o25b2o48b2ob3o18bo2bo33b2o24bobo6b2o33bobo4bobo
22b2o$48b2o52bo30bo143bo108bo26bo47b2o23bo2bo21b3o8bobo26bo42b2o4b2o
22b2o$11bo16bo19bo12bobo36bobo5bo24bobo84bobo20bo26bo4b2o210b2o24bo8b
2o65bobo$2bo6b2o15b2o17bo15b2o38b2o5bobo19bo2b2o61bo23b2o20bobo24bobo
4b2o179b2o24b2o27bo5b2o70b2o4bo$obo4bo2b2o15b2o14bobo16bo45b2o21bo63bo
25bo20b2o25b2o59bo51bobo72b2o24b2o33b2o34b3o33bo5b3o44b2ob2o$b2o2bobo
36b2o83b3o31bo19b2o10b3o17b2o21b2o25b2o25bo36bobo15bo10bo16bo6b2o50bo
27bo25bo34bo32bo4bo3bo33bo3bo17b2o3bo15bobobobo$6b2o67bo8b2o27b2o18bo
3b2o18b2o2b2o19bobo14b3o12bobo2b2o16bobo2b2o20bobo2b2o20bobo32bo2bobo
14bobob2o6bobo13bobob2o3bo27b3o2b2o15bobobo2bo16b2o2bobobo2bo14b2o2bob
obo2bo23b2o2bobobo2bo25bo4bobobobo2bo28bobobobo2bo11b3obobobo2bo9b3o3b
obo2bo$53b2o18bobo8bobo15bo10bobo16bobo2bobo14bo2bobo2b2o15bo2bo8b2o6b
o11bo2bo4b2o13bo2bo4b2o5bo11bo2bo4bobo16bo2bo2bo24bo5bobob2o15bobob2o
6b2o14bobob2o33bob2o16bobob4o14bo2bo2bobob4o12bo2bo2bobob4o21bo2bo2bob
ob4o29bo2bobob4o23bo3bo2bobob4o10bo4bobob4o8bo4bobob4o$53bobo18b2o4bob
obobo16b2o3b2obobobo17bobobobo13bobobobo18bobob2o7bobo6bo9bobob2o5b2o
10bobob2o5b2ob2o11bobob2o4bo16bobob2obo18b3obobo6b2o16b2ob2o6b2o15b2ob
2o5b2o28bo4bo13b2ob2o19b2o2b2ob2o17b2o2b2ob2o26b2o2b2ob2o35b2ob2o29bo
3b2ob2o15b2ob2ob2o13b2ob2ob2o$51b2o2bo23bob2o2bo16b2o4bob2o2bo19b2o2bo
15b2o2bo4bo15b2o2bo7bo19b2o2bo5b2o11b2o2bo5b2o2b2o11b2o2bo22b2o2bob2o
19bo2b2o8b3o14bo3b3o3bobo15bo3b3o2b2o48bo3b3o21bo3b3o19bo3b3o17b2o9bo
3b3o33bo3b3o24b3o4bo3b3o16bo3b3o14bo3b3o$51bo3b2o22bo3b2o14b2o11b2o22b
2o18b2o4b2o17b2o30b2o21b2o25b2o25b2o22bo11b2o2bo14bob2o2bo3bo17bob2o2b
o52bob2o2bo21bob2o2bo19bob2o2bo16bobo9bob2o2bo33bob2o2bo31bob2o2bo16bo
b2o2bo14bob2o2bo$52b3o25b3o4bo10bobo7bob2o22b2o18b2o6bobo14b2o30b2o21b
2o8bo16b2o8b2o15b2o35bobo18bobo25bobo6bo49bobo25bobo23bobo21bo10bobo
37bobo35bobo20bobo18bobo$54bo27bo3bo13bo7b2obo21bobo17bobo22bobo29bobo
20bobo8b2o14bobo7b2o15bobo36bo20bo34b2o50bo27bo25bo34bo39bo27b2o$75b3o
8b3o43bobo19bo24bo31bo22bo8bobo15bo5b2o3bo15bo5b2o14b2o70bobo7bo197bob
o$75bo57bo134b2o25b2o14b2o32b2ob2o41b2o199bo$23b3o50bo5b2o45b3o135bo
26bo15bo33bobobobo40bobo$23bo48bo8b2o4b3o18b2o21bo165b3o46bobo$24bo47b
2o9bo3bo13b2o5bobo19bo2b2o162bo$20b2o32b2o15bobo14bo11bobo5bo24bobo
156b2o4bo$20bobo22b2o6b2o47bo30bo157bobo$20bo25b2o7bo237bo$8bo36bo3b3o
$8b2o39bo387b2o$7bobo40bo386bobo$437bo64$471bo$439bo32b2o$224bobo212bo
bo29b2o$187bo36b2o213b2o$188bo3bo32bo104bo142bo72bo$186b3o4bo136bobo
104bo34bo74bo$191b3o136b2o28bobo75b2o2bo29b3o70b3o$256bo103b2o75b2o2bo
58bo$187bo67bo105bo79b3o35bo18bobo47bo$188bo8bo21bobo33b3o208bobo8b2o
20b2o46bo$186b3o8bobo19b2o104bo113bo27b2o9b2o67b3o$197b2o21bo32bo72bo
36bo29bobo41bobo4bo22bo28bo4bo18bo$161bo27bo61bobo70b3o35bo30b2o38b2o
3b2o4bobo50bob2o17bobo21bo$94bobo30bo32bo27bo63b2ob3o104b3o29bo39b2o8b
2o49b3o2b2o17b2o22b2o$95b2o26bo2bo33b3o5bo19b3o25bo38bo66b2o29b2o78bo
108b2o$95bo28bob3o37b2o46b3o39bo27b2o35bobo7b2o19bobo10b2o13b2o13b2o
16b2o4bobo16b2o4bo58b2o16b2o2b2o27bo3b2o17bo3b2o$122b3o38bo3b2o23b2o
19bo34bo35bo13b2o2b3o18bo7bo2bo17bo4bo7bobo12bo2bo11bobo15bo2bo2b2o17b
o2bobobo18b2o2b2o28b2o4bo15bobo3bo26bobo3bo16bobo3bo$92b3o67b2o28bo20b
2o33b3o34b3o11b2obo29b3o18b5o7bo15b3o11bo18b3o3bo18b3ob2o19b2o2b2o4b3o
21b2o3bo16b2o3bo27b2o3bo17b2o3bo$94bo10bo21b2o33bobo16b2o11bo20bo6bo
28bo36bo9bo4bo170bo27bo21bo15bobo14bo22bo$93bo10bo21bo2bo27b2o23b2o6b
5o16b5o5b2o23b6o31b6o41b5o18b5o23b5o7bo20b5obo18b5obo18b5obo4bo22b5obo
15b5obo14b2o10b5obo12b2o2b5obo$96bo7b3o18bo2bo25bo2bo23bo5bo2bo17bo2bo
9bobo19bo2bo33bo2bo43bo2bo4bo14bo2bo4bo19bo2bo4bo5b2o17bo2bo4b2o15bo2b
o4b2o15bo2bo4b2o24bo2bo4b2o12bo2bo4b2o14bo8bo2bo4b2o12bo3bo4b2o$96b2o
27b3o6bo19b3o2bo27b3o2bo15b3o2bo29b3o2b2o30b3o2b2o40b3o2b2obo14b3o2b2o
bo19b3o2b2obo5bobo16b3o2b2o18b3o2b2o18b3o2b2o27b3o2b2o15b3o2b2o26b3o2b
2o16b3o2b2o$95bobo30b3o3bobo20b3o30b3o18b3o32b2obo33b2obo43b3obo18b3ob
o23b3obo28b3ob3o18b3ob3o18b3ob3o27b3ob3o15b3ob3o26b3ob3o16b3ob3o$127bo
3bo2b2o20bo32bo20bo34bo2bo33bo2bo4b3o36bo22bo27bo32bo6bo17bo6bo17bo6bo
26bo6bo14bo6bo25bo6bo15bo6bo$127b2ob2o24b2o31b2o19b2o33b2o26bo8b2o8bo
36b2o21b2o26b2o31b2o23b2o23b2o32b2o20b2o31b2o21b2o$137b2o132bobo17bo
10bo$136b2o134b2o19b3o5b2o$138bo78b3o73bo7bobo81b3o$217bo76bo92bo$108b
3o99b2o6bo167bo5b3o147b2o$108bo100bobo62b3o115bo150b2o$109bo101bo4b2o
58bo20b2o94bo148bo$217b2o56bo15bo5bobo84b2o$98b3o115bo73b2o5bo85bobo$
100bo189bobo92bo$99bo204bo$303b2o$278b2o23bobo$279b2o$278bo!

[dvgrn]

And here are the other three catalysts...

Aha, just barely in time for the news to make it into the Golly 3.0 pattern collection. Nice work!

-- I'm not exactly sure what the discussion of these syntheses is doing here, though. I guess y'all are allowed to synthesize p1 oscillators on this thread if you want to...

[Goldtiger997]

Reduced some small oscillators:

11->10, 12->10, and 12->10:

Code: Select all

x = 118, y = 39, rule = B3/S23
35bo39bo39bo$35bobo37bobo37bobo$35b2o38b2o38b2o6$2bo39bo39bo$3bo39bo
39bo$b3o37b3o37b3o2$17bo39bo39bo$18bo39bo39bo$16b3o37b3o37b3o$2bobo37b
obo37bobo$3b2o38b2o38b2o$3bo12b2o25bo12b2o25bo12b2o$17b2o38b2o38b2o$
16bo39bo39bo4$26bo39bo39bo$b3o21b2o14b3o21b2o14b3o21b2o$3bo21bobo15bo
21bobo15bo21bobo$2bo39bo39bo4$3o23b2o12b3o23b2o12b3o$2bo23bobo13bo9bo
12b2o15bo$bo9b3o12bo14bo10b2o13bo13bo19b2o$13bo37bobo46b2o$12bo89bo2$
86b3o$88bo$87bo!

14->12:

Code: Select all

x = 83, y = 70, rule = B3/S23
5bobo$6b2o$6bo6$63bobo$63b2o$4bo59bo$5bo$3b3o3$2bo$obo$b2o20$43bo$43bo
bo$43b2o2$31bo12bo$32bo10b2o$30b3o10bobo8bo$54bobo$27b3o24b2o21b2o$29b
o20b2o25bo$28bo21bobo25bobobo$50bo31bo$78bo3bo$78bo$78bobobo$81b2o10$
29b2o$28bobo$30bo3$67b2o$67bobo$67bo!

Found a cheaper carrier-to-bipole converter, which gives cheaper syntheses of some oscillators:

Code: Select all

x = 27, y = 9, rule = B3/S23
12b2o$2bo8bo2bo6b2o$obo8bobo7bo$b2o9bo10bo$22b2o$3b3o18b2o$5bo18bo$4bo
21bo$25b2o!

I will post an updated collection of small oscillator syntheses soon.

Is this 8G?

Here you go, along with an inducting boat instead of a beacon for the same cost, or a beehive for one more glider:

Code: Select all

x = 137, y = 40, rule = B3/S23
4bo47bo47bo$5b2o46b2o46b2o$4b2o46b2o46b2o4$19bo47bo47bo$19bo4bo42bo4bo
42bo4bo$19bo4bobo40bo4bobo40bo4bobo$24b2o46b2o46b2o9$2o46b2o46b2o$b2o
10bo35b2o10bo35b2o10bo$o10bobo2bo31bo10bobo2bo31bo10bobo2bo$12b2o2bobo
41b2o2bobo41b2o2bobo$16b2o46b2o46b2o12$127b3o$76b3o48bo$76bo51bo$29b2o
46bo57bo$29bobo102b2o$29bo104bobo!

.

Reduced to 7 gliders:

Code: Select all

x = 16, y = 32, rule = B3/S23
10bo$3bo5bo$bobo5b3o$2b2o5$2o5bo$b2o2bobo$o5b2o3$10bo$10bobo$10b2o2$9b
o$8b2o$8bobo10$14b2o$13b2o$15bo!

[mniemiec]

-- I'm not exactly sure what the discussion of these syntheses is doing here, though. I guess y'all are allowed to synthesize p1 oscillators on this thread if you want to...

These are a few missing components for gluing together Herschel conduits. Since those conduits form oscillators, syntheses of these components are necessary steps in synthesizing those oscillators - which makes them totally on-topic for this thread.

EDIT:

Reduced some small oscillators: ...

These should also indirectly reduce several larger variants.

14->12: ...

12->11:

Code: Select all

x = 160, y = 61, rule = B3/S23
96bo$94boo$95boo7$60bo$59bo$59b3o$$57bo$58bo$56b3o81bo$140bobo$140boo$
117boo18boo$117boo18boo$61bo4bo$62boobo$61boobb3o$112boob3o14boob3o14b
oob3o$112bo19bo19bo$113bo3bo15bo3bo15bo3bo$$113b3obobo13b3obobo13b3obo
bo$118boo18boo18boo$$122boo18boo$121bobo17bobo$20boo38boo55bo4bo14bo4b
o$19bobbo36bobbo53bobo17bobo$20boo38boo54bobbo16bobbo$obo37b3o74boo18b
oo$boo39bo$bo24bo14bo24bo59bo19bo$25bobo37bobo57bobo17bobo$bb3o20bobo
37bobo57bobo17bobo$4bo21bo39bo59bo19bo$3bo$143b3o$145bo$144bo14$103boo
$102boo$104bo!

Found a cheaper carrier-to-bipole converter, which gives cheaper syntheses of some oscillators: ...

This will definitely reduce many larger variants!

[gmc_nxtman]

Should give 17.3796 (xs17_08ehik8z2552) in ten gliders:

Code: Select all

x = 21, y = 19, rule = B3/S23
8b3o2$6bo5bo$6bo5bo$6bo5bo2$obo5b3o$b2o9b3o4bo$bo9bo3bo2bo$11bo4bob3o$
11bo4bo$12bo3bo$3bo9b3o$3b2o12b2o$2bobo12bobo$17bo$9b3o$11bo$10bo!

[BlinkerSpawn]

Should give 17.3796 (xs17_08ehik8z2552) in ten gliders:

Code: Select all

x = 21, y = 19, rule = B3/S23
8b3o2$6bo5bo$6bo5bo$6bo5bo2$obo5b3o$b2o9b3o4bo$bo9bo3bo2bo$11bo4bob3o$
11bo4bo$12bo3bo$3bo9b3o$3b2o12b2o$2bobo12bobo$17bo$9b3o$11bo$10bo!

It's a tight fit, but it works:

Code: Select all

x = 33, y = 30, rule = B3/S23
8bo$9b2o$8b2o$18bo$18bobo$obo15b2o$b2o28bo$bo28bo$12bobo15b3o$13b2o$
13bo7$18b2o$18bobo$18bo2$16b2o$15bobo$3bo13bo$3b2o24b2o$2bobo24bobo$
29bo$9b3o$11bo$10bo!

[Goldtiger997]

I found a 6 glider ship to tripole component:

Code: Select all

x = 40, y = 16, rule = B3/S23
obo$b2o$bo$13bo$14b2o10bo3bo$13b2o9bobob2o$19b3o3b2o2b2o$19bo13b2o$20b
o12bobo$34b2o$36b2o$36bo2bo$38b2o$30bo$29b2o$29bobo!

This improves some oscillators, but one it does not improve is tripole tie ship. Luckily, I found an alternate way of reducing it to 9 gliders (shown with a variant that creates an elevener instead):

Code: Select all

x = 73, y = 24, rule = B3/S23
30bobo37bobo$30b2o12bo25b2o$22bobo6bo13bo16bobo6bo$23b2o18b3o17b2o$17b
o5bo33bo5bo$15bobo37bobo$16b2o38b2o$13b2o10bo3b2o22b2o10bo3b2o$12bobo
10b2ob2o22bobo10b2ob2o$14bo9bobo3bo23bo9bobo3bo9$26b2o38b2o$25b2o38b2o
$21b2o4bo39bo$b2o17b2o$obo19bo$2bo!

[Goldtiger997]

Okay, here is the updated small oscillators syntheses collection:

oscill3-15.zip

Contains the cheapest syntheses for all oscillators up to 15 bits.

(22.35 KiB) Downloaded 228 times

Are there any improvements to syntheses that I've missed?
Also, I've been wondering if there is an alternate format I could put the syntheses in, that would enable them to be combined with chris_c's display_synth script more easily.
Lastly, am I correct that there are only 2 unsolved 16-bit oscillators?:

Code: Select all

x = 23, y = 6, rule = B3/S23
2o13b2o4b2o$obo2b3o7bobo4bo$19bobo$o2b2obo8bo2bo$bo5bo8bo3b3o$bo4b2o8b
o!

Edit 6/10/2017: added the blocker synthesis that I missed (thanks gmc_nxtman), and added several more recent oscillator syntheses.

[gmc_nxtman]

There's a 5G blocker synthesis straight from the LifeWiki:

Code: Select all

#N blocker_synth
#O Boris Shemyakin
#C Glider synthesis of blocker
#C http://conwaylife.com/wiki/blocker
x = 64, y = 21, rule = B3/S23
16bobo22bo$16b2o24bo$17bo22b3o$28b2o14b2o$27bo2bo12bo2bo$28b2o14b2o4$
10bobo10bobo13bobo13bobo$11b2o13bo15bo15bo$11bo10bo4bo2b2o6bo4bo2b2o6b
o4bo2b2o$7b3o12b2obo2bob2o6b2obo2bob2o6b2obo2bob2o$9bo16b2o14b2o14b2o$
8bo4$2o$b2o$o!

[hkoenig]

Also, I've been wondering if there is an alternate format I could put the syntheses in, that would enable them to be combined with chris_c's display_synth script more easily.


Object constructions are not arbitrary bit patterns, but consist of other objects (mostly Gliders) interacting to form new objects. So instead of recording bit patterns, record the objects.

Not familiar with “display_synth”, and a quick search didn’t turn it up anywhere. But years ago, when I was working on cataloging constructions, I came to the conclusion that it was better to work at the object level. I came up with a way to specify constructions with that in mind--

A simple Honeyfarm construction from an intermediate Block--

Code: Select all

{
	6.4 [4,-6] L
	6.4 [-1,-1]
	6.4 [8,-1]
	6.4 [4,3] L
} X
{
	4.1 [1,-1] X
	{
		5P4H1V1.1 [3,3] NW
		5P4H1V1.1 [-1,0] NE P2
	}
	5P4H1V1.1 [5,-1] SW P1 -8
}

Every object takes one line. All objects start out in a standard or canonical form. The object specifier (I use my own , but could easily use something like the w-code) is followed by the offset needed in square brackets. After that are the transformations (phasing, direction or symmetry information) needed to properly locate and describe the object (L = Rotate Left, H = Flip Horizontal Axis, etc.). For periodic objects, Pn says how may gens to advance the object. Objects can be grouped with { }, which also can be followed by transformations that apply to the group as a whole. Objects marked with ‘X’ are ignored, but as in this case, can be used to display where the resulting objects will appear.

For constructions with multiple steps, the objects and groups can also be marked with the number of generations to advance or delay in placing the group. In this case, the third Glider is backed up by 8 generations to allow the first collision to stabilize. (Since we know the period and direction of moving objects, this is trivial.)

Of course, you’d have to come up with some tools to create and display constructions in this format. At a minimum, you’d need to be able to convert to/from RLE. (Which is about as far as I’ve gotten with it.)

I’ve also worked, off-and-on, on a SQLite database, which incorporates this along with the RLE and other information like source and result objects

[dvgrn]

Also, I've been wondering if there is an alternate format I could put the syntheses in, that would enable them to be combined with chris_c's display_synth script more easily.
...
Not familiar with “display_synth”, and a quick search didn’t turn it up anywhere...

The display_synth script is an effort by chris_c in the past year to catalogue syntheses systematically. It's available on GitHub, and it already supports some oscillator syntheses -- here's the URL to look up a blinker, for example.

This ZIP archive has all the recipes that are checked in on GitHub (as of right now) (I think)... which makes an apgcode lookup work for all still lifes up to 16 bits. (The link showing a blinker synthesis only works up to 12-bit still lifes.)

Until just now I didn't even dare look at the format of the min_paths.txt file, which stores the incremental recipes. Looks like the following are all of the period-2 oscillators currently covered -- but that includes various cheap constellations, such as xp2_xccy3252zgw8kicz3. Ordinarily these wouldn't be assigned an apgcode, they'd be separated into their component parts first -- but here they're used in multi-stage constructions of other objects.

Code: Select all

0;xp2_032hv04a6ze;0;13,-42,28,-91,34,-124;5,5;19,24,22,11;-12,-82,-6,-77,3,-58;8,7,0,1,1,0
0;xp2_032hv04acze;1;14,-47,27,-82,33,-87;4,8;20,27,23,14;-15,-129,-9,-96,2,-63;8,8,0,1,1,0
0;xp2_033ze;1;;0,8;6,7;7,-37;1,1,0,1,1,0
0;xp2_033zs;1;;-14,65;10,8;-19,-94;3,22,1,0,0,-1
0;xp2_0696z7;0;;-3,19;9,8;-1,-32;3,2,1,0,0,1
0;xp2_0696zsy166;1;20,-39;1,6;20,27;-1,-81;19,7,0,-1,1,0
0;xp2_07z4aic;1;;-3,21;9,7;-7,-45;-2,10,0,1,-1,0
0;xp2_07z7;1;;1,5;7,7;3,-20;0,1,0,1,1,0
0;xp2_07zs;1;;-5,29;10,5;0,-42;5,4,1,0,0,1
0;xp2_0c48chbgzy1121z66zyhggg07;1;;-16,139,-8,85,-5,110,0,7,2,71;47,89;-14,-170,-10,-176;34,42,0,-1,-1,0
0;xp2_0c4o7hzggg11074;0;15,-53,22,-60,31,-100,42,-110;8,7,8,38;27,22,35,37;-8,-111,-3,-91;14,16,0,1,-1,0
0;xp2_0dbgyc7z2ldxsy2cicz011;0;;-10,47,-10,160,13,97,14,6;74,122,80,154;10,-173;33,47,0,1,-1,0
0;xp2_0s01110sy733zg8g222z0p4jzw11;0;20,-70;4,7,14,21;39,26;0,-85,4,-293,11,-97;7,-6,0,1,1,0
0;xp2_1110ok8;0;;0,8;8,11;-9,-52;2,8,0,1,-1,0
0;xp2_1110oo;0;;1,5;16,36;-5,-48;7,17,1,0,0,-1
0;xp2_1110s;0;;-1,14;13,5;9,-27;14,4,-1,0,0,-1
0;xp2_1118kic;0;;0,8;6,8;-2,-25;8,7,-1,0,0,1
0;xp2_111y0s;0;;0,7;7,12;-3,-29;1,1,0,1,1,0
0;xp2_111y1ey98kk8;0;28,-105;3,8;33,23,50,92;-15,-180;14,10,0,1,1,0
0;xp2_1784ozx34a4zzy67;1;;-5,29,-4,49,5,8;17,27,23,20,24,46,31,49;0,-82;19,22,0,-1,-1,0
0;xp2_253y2s;0;;-6,31;17,6;-4,-54,5,-44;4,12,1,0,0,-1
0;xp2_2552ze;1;;-5,28;12,5;0,-41;8,10,-1,0,0,-1
0;xp2_2552zy6e;0;;;2,5,17,29;-10,-41,-8,-59;5,13,0,-1,-1,0
0;xp2_2596zy1ggg070gggzy5e;0;;-3,21,1,43;15,5;-2,-91;17,20,0,-1,-1,0
0;xp2_2a54;0;7,-20;5,6;15,8;3,-22;6,2,0,1,1,0
0;xp2_318c;0;;0,8;6,8;1,-21;8,3,-1,0,0,1
0;xp2_33ws;0;;-1,13;10,6;5,-26;8,3,-1,0,0,1
0;xp2_33y97;0;;0,7;17,40;-5,-52;10,13,0,-1,-1,0
0;xp2_33yfs;1;23,-85;3,7;42,72;-14,-154;13,10,0,1,1,0
0;xp2_33ze;0;;1,5;10,22;-12,-68;4,6,1,0,0,1
0;xp2_33zy0888y1sx33;1;;-13,62,11,8;26,44,32,21,40,28;-5,-109;8,22,1,0,0,-1
0;xp2_33zy5e;1;;-2,16;6,7;-3,-33;5,-2,0,-1,1,0
0;xp2_33zyb7;0;;;4,16,8,7;-3,-29;13,5,-1,0,0,1
0;xp2_66x7e;1;;-21,91;16,8;-23,-107;7,25,0,-1,1,0
0;xp2_696o8gy8ezw32023;1;;-20,112,-1,38,0,64,1,6;38,40,46,43,54,102;-13,-173,2,-125;19,26,0,1,1,0
0;xp2_699m88gzx121ze;0;8,-19,12,-41;5,6;13,5;4,-33;12,9,-1,0,0,-1
0;xp2_7;0;;0,7;;-4,-31;7,3,1,0,0,1
0;xp2_7e;0;;-3,21;11,8;0,-34;1,8,0,1,1,0
0;xp2_7xs;1;;;2,9,10,5;-1,-21;1,4,0,-1,1,0
0;xp2_7zw6952;1;;;1,5;0,-17;-3,7,0,1,-1,0
0;xp2_7zx33;1;;;2,7,11,32;-4,-45;-3,12,0,1,-1,0
0;xp2_7zy733;1;;;2,7;-7,-37,6,-20;-4,4,1,0,0,-1
0;xp2_7zzzyhezyd1110s0111;1;;0,7;96,220;-16,-232;34,32,0,1,1,0
0;xp2_8o0u93z01221zy6e;0;24,-86;-7,53,2,27,7,6;23,8;-15,-179,0,-66;-2,21,1,0,0,-1
0;xp2_exgbhc84czx1221;0;15,-39,22,-45,30,-58;1,6,9,26;30,20;14,-56;10,5,0,1,1,0
0;xp2_g88mp2sgz11zy5e;0;16,-56,41,-98,50,-169;1,16;20,6,34,40;5,-103;22,15,0,-1,-1,0
0;xp2_ggg070gggzy0ezx8kk8w33;1;;-11,57,-3,22;9,6,20,45;-5,-69;1,4,1,0,0,1
0;xp2_gw7z3;0;;;2,8,11,8;-3,-20;1,0,1,0,0,1
0;xp2_og8lb8ozx32ggg070gggzy5e;1;26,-94,36,-114;-12,81;29,8;-8,-177,-6,-147,3,-130;16,20,-1,0,0,1
0;xp2_ow7z1;0;;;4,8;-5,-21,-4,-49;5,5,0,-1,1,0
0;xp2_s01110sx4aa4zw222;0;13,-45;3,6;22,33;-7,-71;5,2,0,1,1,0
0;xp2_s01110szw222;0;;0,7;;-5,-36;1,1,1,0,0,1
0;xp2_s01110szw222y2cc;0;;-4,25;13,8;8,-38;13,-1,0,-1,1,0
0;xp2_s01110szw222zzyacc;0;;0,10;6,6;-16,-93;3,-13,-1,0,0,1
0;xp2_w7zccx356zy066y0111;1;;-5,29;7,6;0,-41;4,-2,-1,0,0,1
0;xp2_wog4cj96ze;0;19,-49,20,-70,33,-93;1,7,3,37;29,27,30,10;-5,-106;11,11,1,0,0,-1
0;xp2_x2596zkq2koz12452xo4ozy51ggg;0;19,-66,37,-86;7,18;23,7,40,7;15,-70,18,-30;11,6,0,1,1,0
0;xp2_x62sgc453z7;0;;;6,25,14,8;-5,-37,-1,-43;-2,6,1,0,0,1
0;xp2_xccy3252zgw8kicz3;1;;;2,8;-3,-20;10,7,0,-1,-1,0
0;xp2_xggy02552w66xooz6ao74z032zy56996wgzyb3;0;14,-46,33,-122;5,5;26,9,27,33;-9,-110,-4,-127;-9,18,1,0,0,-1
0;xp2_y2696zyc8kcz66yje;1;15,-53,33,-87;-2,41,3,7,17,18;41,9;13,-67,23,-61;9,18,1,0,0,-1
0;xp2_y3352y469d2sgzwgggy8ey01023zey1ezw111;1;25,-71,30,-90;-4,58,0,8,10,33;26,21,38,16;-8,-157;20,6,0,-1,1,0

It's not exactly a human-friendly format, but it's definitely compact, and it works at the object level. Looks like there are lists of pairs of (lane, timing) values, for each of the four input directions in NE, SE, SW, NW order, if I'm reading it all right ...? And the final ";x,y,0,1,1,0" specifies an orientation, in the same affine-transformation format that's used by various Golly scripting commands.

So this is a very limited special-purpose format -- it wouldn't be so easy to adapt it to allow *WSS inputs, for example. I suppose it might be doable by adding three more (lane, timing) lists, but you wouldn't want to call them "glider_lists"...

Anyway, the display_synth.py script builds a tree structure from these mysterious streams of numbers, and uses that to figure out what incremental recipes need to be displayed -- see edge_from_string(s) for details.

No idea what the most efficient way would be to contribute new objects directly to this database... @chris_c?

[Extrementhusiast]

Lastly, am I correct that there are only 2 unsolved 16-bit oscillators?:

Code: Select all

RLE

Not anymore:

Code: Select all

x = 155, y = 92, rule = B3/S23
obo$b2o$bo12$106bo6bo$106bobo2b2o$106b2o4b2o8$62bobo49bo$63b2o49bobo$
63bo50b2o14$59bobo$60b2o$60bo2$57b3o$59bo$58bo88b2o$61bo13b2o3bo66bobo
2b3o$61b2o12b2o2bobo$60bobo16b2o66bo2b2obo$148bo5bo$148bo4b2o28$99b2o$
99bobo$99bo8$126b2o$126bobo$126bo!

With this potential reduction to two similar symmetric oscillators, you can get up to two free copies of cis boat on trans long bookend with claw!

Code: Select all

x = 41, y = 25, rule = B3/S23
38bobo$38b2o$39bo$35bo$34bo$34b3o6$25bo5bo4bo$24bobo5b2obo$8b3o2b2o5b
2o2b2o5b2o2b3o$10bob2o5bobo$9bo4bo5bo2$5b2o$6b2o$5bo3$3o$2bo$bo!

[Kazyan]

Now that's a deal you can't pass up!

We have a few fresh models on a brand new 21-bit p3 oscillator, to whoever can supply the base still life. Available in snake, trans, and cis (not pictured, but can be achieved with one obvious converter from the trans version that I can't be bothered to look up).

Code: Select all

x = 76, y = 34, rule = B3/S23
61bo$60bo$22bo37b3o$22bobo$14bo7b2o$14bobo$11bo2b2o44bo$12bo46bo$10b3o
46b3o9bo$54bobo12b2o$53bo16b2o$10b2o41bo6b2o$10bobo2b2o36bo2bo3bobo2b
2o$11b2o2bobo35b3o5b2o2bobo$16bo4bo44bo4bo$19b2o48b2o$7b2o11b2o48b2o$
7bo2bobo34b6o4b2obobo$9b3obob2o29bo5bo4bob3obob2o$13bobobo34bo10bobobo
$6bo4b3obobo28bo4bo4bo4b3obobo$5bobo2bo5bo31b2o5bobo2bo5bo$5b2o4bo9b4o
30b2o4bo9b4o$12bo8bo3bo20bo15bo8bo3bo$13bo7bo24b2o15bo7bo$5b2o5b2o8bo
2bo19bobo7b2o5b2o8bo2bo$3obobo43b3obobo$2bo2bo46bo2bo$bo49bo$8b3o47b3o
$8bo49bo$2b3o4bo42b3o4bo$4bo49bo$3bo49bo!

[mniemiec]

Using the carrier-base still-life is cheaper by 9 gliders. If a synthesis for the snake-base still-life is found first, it could be cheaper to convert it into the carrier-base with 6 gliders (2nd row, 1st step) before assembly, although to make the snake-base oscillator, that wouldn't be optimal (6 gliders to turn snake to carrier before, and 4 to change it back later). Other than trivially growing the hook, I have no clue how to make either one. For completness, here are the complete syntheses so far from the base still-lifes:

Code: Select all

x = 292, y = 85, rule = B3/S23
149bo$149bobo$141bo7boo$22bo118bobo115bo$20bobo115bobboo117bo$21boo
116bo108bo9b3o3bo$137b3o46bo62bo4bo7boo$23bo61bo101boo58b3o5boo6boo$
18bo3bo61bo101boo66boo$19boob3o22boo28boo5b3o20boo28boo$18boo27bobo27b
obo27bobobboo23bobobboo$48boo28boo28boobbobo23boobbobo$87bobo23bo29bo
4bo$87boo57boo31bo105boo$14boo28boo28boo12bo15boo28boo11boo15boo4bo9b
oo12boo4bo29bo23boo4bo24bo4bo$14bobbobo24bobbobo24bobbobo24bobbobo24bo
bbobo24bobbobobo7boo5bo7bobbobobo22boobobobo22bobbobobo25bobobo$7bo8b
3oboboo22b3oboboo22b3oboboo5b3o14b3oboboo22b3oboboo22b3obbo12bobo9b3o
bbo22bob3obbo24b3obbo24b3obbo$8bo11bobobo25bobobo25bobobo4bo20bobobo
25bobobo40boo59b3o$6b3o9b3obobo18bo4b3obobo18bo4b3obobo5bo12bo4b3obobo
18bo4b3obobo23b3o27b3o27b3o17bo9b3o27b3o$17bo5bo18bobobbo5bo18bobobbo
5bo18bobobbo5bo18bobobbo5bo23bo19boo8bo29bo19bo9bo29bo$18bo23boo4bo23b
oo4bo23boo4bo23boo4bo9b4o15bobo18boo7bobo27bobo27bobo27bobo$5b3o11bo
29bo29bo29bo29bo8bo3bo34bo$7bo12bo29bo29bo29bo29bo7bo19bobo27bobo27bob
o27bobo27bobo$3o3bo12boo28boo28boo21boo5boo21boo5boo8bobbo16boo28boo
28boo28boo28boo$bbo98bobo23b3obobo$bo100bo26bobbo$128bo$135b3o$62bo72b
o$63bo65b3o4bo$61b3o67bo$65b3o62bo$67bo4b3o$66bo5bo$73bo14$258bo$257bo
$257b3o3$142bo$140bobo114bo$141boo113bo$256b3o9bo$143bo61bo45bobo12boo
$8bo129bo3bo61bo45bo16boo$6bobo5bo124boob3o22boo28boo5b3o20boo21bo6boo
$7boo3boo124boo27bobo27bobo27bobobboo16bobbo3bobobboo$13boo153boo28boo
28boobbobo15b3o5boobbobo$207bobo23bo29bo4bo$207boo57boo$44boo162bo58b
oo21bo$5bobo6boobobo24bobbobo24boobobo24boobobo24boobobo24boobobo24boo
bobo24boobobo14b6o4boobobo24boobobobo$6boo6bob3oboboo22b3oboboo12bo7bo
b3oboboo20bob3oboboo20bob3oboboo20bob3oboboo20bob3oboboo5b3o12bob3obob
oo9bo5bo4bob3oboboo20bob3obbo$6bo13bobobo25bobobo12boo11bobobo25bobobo
25bobobo25bobobo25bobobo4bo20bobobo14bo10bobobo$18b3obobo23b3obobo11b
oo10b3obobo18bo4b3obobo18bo4b3obobo18bo4b3obobo18bo4b3obobo5bo12bo4b3o
bobo8bo4bo4bo4b3obobo23b3o$10bo6bo5bo23bo5bo23bo5bo18bobobbo5bo18bobo
bbo5bo18bobobbo5bo18bobobbo5bo18bobobbo5bo11boo5bobobbo5bo23bo$3bo6boo
6bo29bo22bo6bo24bo4bo24bo4bo23boo4bo23boo4bo23boo4bo23boo4bo9b4o15bobo
$3boo4bobo7bo29bo21boo6bo29bo29bo29bo29bo29bo13bo15bo8bo3bo$bbobo15bo
29bo19bobo7bo29bo15boo12bo29bo29bo29bo12boo15bo7bo19bobo$12b3o4boo28b
oo28boo28boo16boobbo7boo28boo28boo21boo5boo11bobo7boo5boo8bobbo16boo$
12bo60b3o50bo3boo89bobo23b3obobo$13bo59bo56bobo89bo26bobbo$74bo173bo$
255b3o$182bo72bo$183bo65b3o4bo$181b3o67bo$185b3o62bo$187bo4b3o$186bo5b
o$193bo!