Small Spaceship Syntheses

[mniemiec]

Better partial syntheses for B29 with trailing glider #2, distilled from existing stdin partials on Catagolue. All that's missing is a way to inject a sideways pi from below. The NW glider can just as easily come from the SW. The parallel SE glider might be problematic to insert; if so, use alternate glider from NE that leaves a junk block that another NE glider can clean up.

Code: Select all

x = 73, y = 31, rule = B3/S23
70bobo$70boo$65bobo3bo$65boo$14boo38boo10bo$14bobo37bobo$7boo5bo32boo
5bo$7bobo3boobbo29bobo3boobbo$7bo11bo27bo11bo$10bo3boo3b3o28bo3boo3b3o
$10boo4boo4bo27boo4boo4bo$16b7o33b7o$17b4o36b4o$$25boo$25bobo$bobo21bo
15bobo$bboo38boo$bbo10boo27bo10boo$13bo39bo$13bo39bo$14bo39bo7$oo38boo
$boo38boo$o39bo!

[Goldtiger997]

Better partial syntheses for B29 with trailing glider #2, distilled from existing stdin partials on Catagolue. All that's missing is a way to inject a sideways pi from below.

I found a suitable pi inserter:

Code: Select all

x = 86, y = 84, rule = B3/S23
o$b2o$2o3bo$6b2o$5b2o12$83bo$81b2o$82b2o5$12bo$13b2o$12b2o28bo$42bobo
3bo$42b2o3bo$7bo7bo31b3o$8b2o6bo$7b2o5b3o5$53bobo$53b2o$54bo$59bobo$
59b2o$60bo3$32b2o$22b2o7bobo$22bobo6b2o$24bo$24b2o5b2o$26bo3bobo$24b3o
3bo$23bo5b2o$22bobo$21bo2bo$21bobo$22bo5$6b2o$7b2o39bo$6bo40b2o$47bobo
2$23b3o$15b2o8bo43b3o$14bobo7bo30b2o12bo$16bo38bobo12bo$6b3o46bo$8bo3b
o27b2o$7bo4b2o26bobo$11bobo26bo$61b3o$61bo$62bo7$84bo$83b2o$83bobo!

Here's a final step for B29 with trailing glider #3, also inspired by a stdin soup:

Code: Select all

x = 76, y = 86, rule = B3/S23
70bo$69bo$59bo9b3o$59bobo$53bo5b2o$53bobo$15bo37b2o$16bo$14b3o$61bo$
60bo$60b3o$30bobo$31b2o$31bo4$12bo$10bobo46bobo$11b2o46b2o6bo$60bo4b2o
$66b2o5$7bo6bo18b2o$8bo6b2o15bo2bo$6b3o5b2o16bo2bo30bo$33b2o31bobo$40b
2o24b2o$39bobo$38bobo$38bo$36bobo$36b2o3$33bo$33bobo$32bobo$34bo$37b2o
$37bo$35bobo4bo$35b2o4bobo$40bo2bo$40bobo$34b2o5bo$34bo3b3o$32bobo3bo$
32b2o5b2o$40bo$32b2o6bobo$31bobo7b2o$31b2o3$11b3o$13bo$12bo11$3o$2bo$b
o2$73b2o$73bobo$58b2o5b2o6bo$57b2o6bobo$6b2o51bo5bo$7b2o3bo$6bo5b2o$
11bobo46b2o$60bobo$60bo!

I'm sure there's something much simpler that also works.

[mniemiec]

Better partial syntheses for B29 with trailing glider #2, distilled from existing stdin partials on Catagolue. All that's missing is a way to inject a sideways pi from below.

I found a suitable pi inserter: ...

Very nice! I hadn't thought about inserting the pi while the B29 was being constructed. (I even tried that predecessor, but the glider passed through the incoming B29). Now the only one missing is the #1 (plus the two 7-bit ones; the stdin inserters for the second one looks like an absolutely horrible Rube-Golderbeg mechanism).

Here's a final step for B29 with trailing glider #3, also inspired by a stdin soup: ... I'm sure there's something much simpler that also works.

A #3 side-injector was already known. The one on the left with the rear cleanup glider coming from the same direction was already known (I think I may have gotten it from the Wiki or something) (EDIT: It's from catagolue). On Jan. 4 I found a way to use a clean-up glider from the other side (right image), which is usually easier for synthesis purposes, and does the clean up faster.

Code: Select all

x = 80, y = 33, rule = B3/S23
30bo39bo$29boo38boo$23bo5bobo31bo5bobo$22boo38boo$22bobo3boobobo28bobo
3boobobo$26bo7boo30bo7boo$19bo5bo4bo5boo21bo5bo4bo5boo$20boo3bobbobb6o
23boo3bobbobb6o$19boo38boo3$21bo39bo$22boo38boo$15boo4boobb3o27boo4boo
bb3o$16boo9bo28boo9bo$15bo10bo28bo10bo4$17bo39bo$17boo38boo$16bobo37bo
bo9$3o75boo$bbo74boo$bo77bo!

[Mr. T]

Is there a synthesis for this c2 p8 beehive-puffer. My tries of searching were fruitless.

Code: Select all

x = 23, y = 19, rule = B3/S23
12b3o5b3o$12bo2bo3bo2bo$2b3o11bo5bo$bo2bo4b5ob2obo3bo$4bo4bo3bob2o5bo$
o3bo2bo3b3o5bobo$o3bob5o4b2o$4bobo4bo$bo2bobob2obo$8b2o3$8b2o$7bo2bo$
8b2o2$8b2o$7bo2bo$8b2o!

[AlbertArmStain]

On a scale of one to ten, how close am I?

Code: Select all

x = 44, y = 28, rule = B3/S23
9bo$6b4o$6b2o29bo$4bo30b5o$4b4o26bo5bo$3bo9bo19bob2o2bo$2b3o2bo4b2o19b
o2bo2b4o$3b3o5b2obo19b2o6bo$4bo6bobo22b5o$5b3obobobo22bo3b2o$5bo2b2o27b
2o3bo$6b2o3bo19b2o5b4o$7b4o20bo2bobo$32b3ob4o$5b4o26bo4bob2o$4b2o3bo24b
o2b2obob2o$3bo2b2o26b3obobo$3b3obobo22b2o6bo$2bo6bo21bo2bo5b2o$b3o5b2o
20bobo2b2o$3o2bo4b3o19bo4bo$bo10bo20b4o$2b4o25bobo$2bo28b2o2b2o$4b2o30b
o$4b4o27bo$7bo28b3o$38bo!

This feels doable

Code: Select all

x = 21, y = 20, rule = B3/S23
2b2o$b4o$2ob2o$b2o5bo2bo$7bo3bo8bo$6b2o2b4ob3o$7bo7b3o$20bo2$2b7o7b2o
2bo$2bo6bo4bo5bo$2bo10bo6bo$3bo5bo3bo6bo$7bo5b5o$3bo2bo$2bo$2bo3bo7b3o
$2b4o7b5o$12b2ob3o$13b2o!

[googleplex]

Is there any way to convert the one on the left to the one on the right?

Code: Select all

x = 62, y = 35, rule = B3/S23
5$20bobo28bobo$20b2o29b2o$21bo30bo4$18bobo28bobo$18b2o29b2o$19bo30bo2$
4b3o4bo11bo11b3o4bo11bo$3bo2bo3b3o9b3o9bo2bo3b3o9b3o$6bo3bob2o2bobo2b
2obo12bo3bob2o2bobo2b2obo$2bo3bo4b3o2b2o3b3o9bo3bo4b3o2b2o3b3o$6bo4b2o
4bo3b3o13bo4b2o4bo3b3o$3bobo15b3o10bobo5bo9b3o$22b2o29b2o3$28bo$7bo16b
obo2bo8bo$6b3o19bo8b3o$5b2obo27b2obo$5b3o28b3o$5b3o28b3o$6b2o29b2o!

EDIT: this spark works, is there any way to get it in there?

Code: Select all

x = 22, y = 22, rule = B3/S23Super
16.A$14.2A$15.2A4$3A4.A6.A4.A$A2.A2.3A3.2A4.3A$A4.2A.A4.2A3.A.2A$A3.4A
11.3A$A5.2A11.3A$.A.A6.C8.3A$8.C.C8.2A4$3.A$2.3A$2.A.2A$3.3A$3.3A$3.2A
!

[dvgrn]

Is there any way to convert the one on the left to the one on the right?

Tangential question -- what else will have to be done to "the one on the right" to make it into a working rake?

[googleplex]

Is there any way to convert the one on the left to the one on the right?

Tangential question -- what else will have to be done to "the one on the right" to make it into a working rake?

It's this P8 dependent glider reflector. I'm gonna try and make a gun which fires these reflectors to continuously reflect gliders. Obviously you could do this at a higher period with something from jslife-moving like this:

Code: Select all

x = 30, y = 51, rule = B3/S23
2$8bo$6bobo$7b2o7$11bo$9bobo$10b2o7$14bo$12bobo$13b2o5$22bo$21b3o$17b
o2b2obo$15bobo2b3o$16b2o3b2o2$11b3o$10bo2bo$13bo$9bo3bo$9bo3bo$13bo$10b
obo2$24b3o$24bo2bo$24bo$24bo3bo$24bo$25bobo!

but the low period of this reaction is enticing.

[May13]

Partial final step of synthesis of the Wasp (8/22 columns solved (+ a bit of frontend)):

Code: Select all

x = 62, y = 24, rule = B3/S23
7bo$bo3bobo$2bo3b2o$3o13bo9bo$13b2obo8bo$6b2o4bo3bo8b3o$7bo4bo2bo$12bo
$5b3o13b2o$6bo14bobo$14bobob2obobo$13bob3obob2o$11b3o36bo3bo$10bo3bob
3o28bobob2ob3o$10bobobobo2bo26bo2bo6b2ob2o$9b2ob2o4b2o21b2o2b2o2bo3bo
2bo2b2o$41b2obob2o2bo2bo4bo2bo$7bo32bo3bo4b2o$8bo31bobobo2bo2b2o$6b3o
11b3o26bo$20bo20b3o$10bo10bo$9b2o$9bobo!
[[ STOP 10 ]]

Is there any way to extend this partial? I am interested in the SE corner.

[Goldtiger997]

Brain in 99 gliders:

Code: Select all

x = 1857, y = 77, rule = B3/S23
1782bo47bo$1783bo45bo$1781b3o45b3o5$1786bo39bo$1787bo37bo$1785b3o37b3o
2$1802bobo$1797bo5b2o$1795bobo5bo$332bo187bo1257bo8bo8b2o27bo8bo$330bo
bo187bobo1256bo8bo35bo8bo$331b2o187b2o1255b3o6b3o35b3o6b3o$1774bo63bo$
1772bobo63bobo$1773b2o63b2o3$1778bo55bo$113bo145bo1519bo53bo$111bobo
145bobo1515b3o53b3o$112b2o145b2o75bo179bo$125bo121bo89b2o175b2o1276bo$
125bobo117bobo88b2o177b2o1275b2o$125b2o119b2o1543bobo$5bo824bo31bo89bo
bo23bobo$3bobo825b2o27b2o91b2o23b2o$4b2o341bo157bo324b2o29b2o90bo25bo$
9bo229b2o101bo5b2o9b2o11b2o118b2o9b2o5bo$7b2o229bo2bo101bo3b2o9bo2bo9b
o2bo116bo2bo9b2o3bo568bo15bo103bo15bo103bo15bo103bo15bo103bo15bo103bo
15bo103bo15bo$8b2o229b2o100b3o15b2o11b2o107b2o9b2o15b3o89b2o7b2o109b2o
7b2o109b2o7b2o98b2o9b2o7b2o9b2o95bo2b2o7b2o2bo103bo2b2o7b2o2bo103bo2b
2o7b2o2bo103bo2b2o7b2o2bo103bo2b2o7b2o2bo103bo2b2o7b2o2bo103bo2b2o7b2o
2bo$482bo119bo7bo111bo7bo111bo7bo100b2o9bo7bo9b2o96bo3bo7bo3bo103bo3bo
7bo3bo103bo3bo7bo3bo103bo3bo7bo3bo103bo3bo7bo3bo103bo3bo7bo3bo103bo3bo
7bo3bo$124b2ob2o115b2ob2o115b2ob2o113bob2ob2o113bob2ob2obo111bob2ob2ob
o92bo18bob2ob2obo18bo80bo11bob2ob2obo11bo99bob2ob2obo111bob2ob2obo111b
ob2ob2obo111bob2ob2obo111bob2ob2obo111bob2ob2obo111bob2ob2obo$123bobob
obo113bobobobo113bobobobo108b2o3bobobobo108b2o3bobobobo3b2o103b2o3bobo
bobo3b2o89b2o12b2o3bobobobo3b2o12b2o94bobobobo113bobobobo113bobobobo
113bobobobo113bobobobo113bobobobo113bobobobo113bobobobo$123bobobobo
113bobobobo113bobobobo108bo2bobobobobo108bo2bobobobobobo2bo103bo2bobob
obobobo2bo88b2o5bo7bo2bobobobobobo2bo7bo5b2o88b2obobobobobobob2o103b2o
bobobobobobob2o103b2obobobobobobob2o103b2obobobobobobob2o103b2obobobob
obobob2o103b2obobobobobobob2o103b2obobobobobobob2o103b2obobobobobobob
2o$124bo3bo115bo3bo115bo3bo111b2ob2o3bo111b2ob2o3b2ob2o107b2obobo2b2ob
2o95bobo9b2obobobobob2o9bobo93bob2obobobobob2obo103bob2obobobobob2obo
103bob2obobobobob2obo103bob2obobobobob2obo103bob2obobobobob2obo103bob
2obobobobob2obo103bob2obobobobob2obo103bob2obobobobob2obo$117bobo133bo
bo94b2o149b2o221b2o103b2o13b2ob2o13b2o100b2ob2o115b2ob2o115b2ob2o115b
2ob2o115b2ob2o115b2ob2o115b2ob2o115b2ob2o$b2o7b2o106b2o119b3o11b2o94bo
bo7b3o9b3o117b3o7bobo1278bo47bo$obo7bobo105bo135bo77b2o17bo149bo17b2o
310b2o27b2o338b2o118b2o9b2o107b2o9b2o107b2o9b2o107b2o9b2o87bobo17b2o9b
2o17bobo$2bo7bo322b2o183b2o312b2o25b2o339bobo117bobo7bobo107bobo3bo3bo
bo107bobo3bo3bobo107bobo3bo3bobo83bo4b2o17bobo3bo3bobo17b2o4bo$332bo
187bo310bo29bo216b2o121bo11b2o106bo9bo109bo3bobo3bo109bo3bobo3bo109bo
3bobo3bo85b2o22bo3bobo3bo22b2o$1077bobo133bobo230bo119bo119bo89b2o28bo
28b2o$118b2o133b2o824bo133bo557b3o65b3o$119b2o131b2o82bo179bo565b2o
125b2o228bo13bo109bo5bo113bo5bo83bo29bo5bo29bo$118bo135bo81b2o177b2o
78bo12b2o113b2o12bo345b2o123b2o230bo11bo109bobo3bobo111bobo3bobo81bo
29bobo3bobo29bo$335bobo177bobo77b2o10b2o115b2o10b2o344bo3b2o117b2o3bo
227b3o11b3o108bobobobo113bobobobo113bobobobo$594bobo12bo113bo12bobo
347bobo115bobo117bo239b2ob2o115b2ob2o115b2ob2o$1086bo119bo117b2o3b2o
111b2o5b2o125bo99bo$602b3o6b2o107b2o6b3o592bobo3bobo109bobo5bobo123bo
101bo$602bo7b2o109b2o7bo598bo4b2o107bo5bo125b3o97b3o$603bo8bo107bo8bo
603b2o101b2o17b2o234b2o107b2o9b2o$1335bo101b2o15b2o234bobo107bobo7bobo
$1436bo19bo234bo92b3o14bo9bo14b3o$595b3o137b3o829bo117bo100bo39bo$597b
o137bo831b2o115b2o70b3o26bo41bo26b3o$596bo139bo829bobo115bobo71bo95bo$
1757bo97bo8$1780b2o49b2o$1781b2o11b2o34b2o$1780bo7b2o3bobo27b2o7bo$
1789b2o4bo26b2o$1788bo24b3o8bo$1813bo$1770b2o42bo$1769bobo$1771bo!

Continuous synthesis:

Code: Select all

x = 295, y = 271, rule = B3/S23
26bo241bo$27bo239bo$25b3o239b3o5$30bo233bo$31bo231bo$29b3o231b3o2$46bo
bo$41bo5b2o$39bobo5bo$22bo8bo8b2o221bo8bo$23bo8bo229bo8bo$21b3o6b3o
229b3o6b3o$18bo257bo$16bobo257bobo$17b2o257b2o3$22bo249bo$23bo247bo$
21b3o247b3o17$26bo241bo$24bobo241bobo$20bo4b2o241b2o4bo$21b2o249b2o$
20b2o251b2o7$41bo$42bo$40b3o3$53bo11bo163bo11bo6bo$51bobo12b2o159b2o
12bobo3bo$52b2o11b2o161b2o11b2o4b3o13$77bo139bo$78b2o135b2o$77b2o137b
2o5$70bo153bo$71b2o149b2o$70b2o5bo139bo5b2o$75bobo139bobo$76b2o139b2o
3$207bo$205b2o$206b2o3$92bo$93b2o94bo$92b2o93b2o$188b2o$119bo$120b2o$
110bo8b2o80bo$111b2o87bo$110b2o88b3o$170bo$168b2o$98bo70b2o$99bo90bo$
97b3o89bo$125bo63b3o3bobo$123bobo69b2o$124b2o70bo$109bo61bo$110bo58b2o
11bo$102bobo3b3o59b2o10bobo$103b2o77b2o$103bo2$117bo$115bobo$116b2o41$
111b2o$112b2o$93b3o15bo9b2o49b2o$95bo24bobo49bobo$94bo27bo49bo$187b2o$
186b2o$97b2o89bo15b3o$96bobo105bo$98bo17b3o86bo$118bo$117bo$201b2o$
201bobo$181b3o17bo$181bo$182bo3$181bo$104b2o74b2o$105b2o73bobo$104bo$
175b2o7bo$175bobo5b2o$175bo7bobo3$105b2o$104bobo$106bo6$78b2o135b2o$
79b2o133b2o$78bo15b2o112bo7bo$95b2o110b2o$94bo112bobo2$63bo27b2o6b3o
129bo$63b2o27b2o7bo128b2o$62bobo26bo8bo129bobo3$206b3o$206bo$207bo3$
71b2o$70bobo$72bo$75b2o$76b2o$75bo139b2o10b2o$215bobo9bobo$215bo11bo$
223b2o$222b2o$73b2o149bo$36bo35bobo$36b2o36bo$35bobo2$68b2o$69b2o155b
3o$68bo157bo5bo$227bo3b2o$231bobo8$55b3o179b3o$57bo179bo$50bo5bo181bo
5bo$50b2o191b2o$15b3o31bobo191bobo31b3o$17bo259bo$16bo261bo3$57bo$57b
2o$56bobo3$28b3o211bo21b3o$30bo210b2o21bo$3o26bo211bobo21bo26b3o$2bo
289bo$bo291bo8$24b2o243b2o$25b2o11b2o228b2o$24bo7b2o3bobo221b2o7bo$33b
2o4bo220b2o$32bo218b3o8bo$251bo$14b2o236bo$13bobo$15bo!

[muzik]

18G for an alternative cordership which can absolutely be reduced:

Code: Select all

x = 125, y = 125, rule = B3/S23
40bo$41b2o$40b2o$48bo$48bobo$48b2o2$51b3o$51bo$52bo8$25bobo$26b2o$26bo
8bo$34bo$34b3o3$38b2o$17bo20bobo$18b2o18bo$17b2o7$20b2o$19bobo$21bo2$
24b3o$24bo$obo22bo$b2o$bo6$3b3o$5bo$4bo$7b2o$7bobo$7bo13$112b2o$111b2o
9b3o$113bo8bo$123bo8$110b2o$109b2o$111bo30$78bo$77b2o$67bo9bobo$66b2o$
66bobo9$67b2o$67bobo$67bo!

It's easily possible to modify this cordership into a 3-engine spaceship by taking one of the engines from halfway through its evolution cycle and superimposing it on the original to yield this, so a synthesis for this one may be possible as well:

Code: Select all

x = 40, y = 45, rule = B3/S23
34b3o$33bo$32bo4b2o$31bo3bo$31bo2bo4bo$31bo3bo3bo$32b2obob3o$35bo$36b
4o$38b2o7$37b3o$35b2o$20b3o12bo3bo$19bo3bo11b3obo$18bo4bo12b4o$18bo2bo
bo15bo$18b2obobo$20b2obo2bo$22b2o2bo$23b3o6$3b3o$2bo$bo4b2o$o3bo15b3o$
o2bo4bo4b2o$o3bo3bo4b3obo$b2obob3o$4bo$5b4o$7b2o11bob2o$20bo2bo$20b3o
5bo$28bo$28bo!

Simply delaying one engine by 48 generations and positioning it accordingly does not seem to work:

Code: Select all

x = 49, y = 57, rule = B3/S23
11bo$12b2o$11b2o$43bo$43bobo$43b2o23$17bo$18b2o$17b2o$46b3o$46bo$47bo
4$20b2o$19bobo$21bo2$24b3o$24bo$obo22bo$b2o$bo6$3b3o$5bo$4bo$7b2o$7bob
o$7bo!

Seems it was a rogue B, which I've now eliminated for a clean 18G:

Code: Select all

x = 120, y = 130, rule = B3/S23
70bo$68b2o$69b2o6$71bo$71bobo$71b2o3$80bo$80bobo$80b2o2$104bobo$104b2o
$105bo3$98bo$98bobo$98b2o$105bo$104bo$104b3o7$110bo$109bo$109b3o$117bo
bo$117b2o$118bo28$51bo$51bobo$51b2o4$7bo$7bobo$7b2o$4bo$5bo$3b3o6$bo$b
2o$obo22bo$24bo$24b3o2$21bo$19bobo$20b2o4$47bo$46bo$46b3o$17b2o$18b2o$
17bo23$43b2o$43bobo$43bo$11b2o$12b2o$11bo!

Here's a third variant of it skewed by one generation and one cell:

Code: Select all

x = 126, y = 125, rule = B3/S23
41bo$42b2o$41b2o$49bo$49bobo$49b2o2$52b3o$52bo$53bo8$26bobo$27b2o$27bo
8bo$35bo$35b3o3$18bo20b2o$16bobo20bobo$17b2o20bo7$20bo$20b2o$19bobo2$
25b2o$bo22b2o$2bo23bo$3o7$3b2o$4b2o$3bo$8bo$7b2o$7bobo14$113b2o$112b2o
9b3o$114bo8bo$124bo8$111b2o$110b2o$112bo30$79bo$78b2o$68bo9bobo$67b2o$
67bobo9$68b2o$68bobo$68bo!

[dvgrn]

18G for an alternative cordership which can absolutely be reduced...

Yeah, six gliders for cleanup is definitely a little bit painful to look at. Here's 14G for the same 4-engine Cordership:

Code: Select all

x = 89, y = 89, rule = B3/S23
40bo$41b2o$40b2o$48bo$48bobo$48b2o2$51b3o$51bo$52bo8$25bobo$26b2o$26bo
8bo$34bo$34b3o3$38b2o$17bo20bobo$18b2o18bo$17b2o7$20b2o$19bobo$21bo2$
24b3o$24bo$obo22bo$b2o$bo6$3b3o$5bo$4bo81b2o$7b2o77bobo$7bobo76bo$7bo
33$50b3o$50bo$51bo!

[muzik]

I'm probably wrong on this, but this could be the first ever synthesis of a period-64 spaceship assuming it rewinds properly:

Code: Select all

x = 619, y = 338, rule = B3/S23
218bo$219bo202bobo$217b3o202b2o79bo$423bo78bo$502b3o2$433bobo$433b2o$
434bo82$32bo$32bobo$32b2o$5bobo$5b2o$6bo3bobo$10b2o$11bo3$b2o$obo21b2o
8b2o$2bo20bobo7b2o$25bo9bo11$102bo9bo$100bobo7b2o$101b2o8b2o8$32bobo$
33b2o74b2o$33bo75bobo$109bo$40b3o$40bo$35b3o3bo$35bo$36bo75$420b3o$
420bo$421bo8$224b2o$225b2o213b3o$224bo215bo$441bo$216b2o$215bobo217b2o
$217bo217bobo$435bo21$249bo$249b2o$248bobo4$503b3o$503bo$504bo13$233bo
$233b2o301b2o$232bobo300b2o$537bo9$531b2o$531bobo$531bo14$558b2o$558bo
bo$558bo26$576b2o$576bobo$576bo2$605b2o$605bobo$605bo2$601b2o$601bobo$
601bo2$599bo$598b2o16b2o$598bobo15bobo$616bo!

[dvgrn]

I'm probably wrong on this, but this could be the first ever synthesis of a period-64 spaceship assuming it rewinds properly...

There's definitely no problem with the rewinding. Do you know about /can you run glider-rewinder.py? (though somebody really ought to write something better than that, for cases like this where rewinding one tick at a time is painfully slow).

A couple of the early cleanup gliders seem to be necessary, but the final cleanup could actually be done with just one glider:

Code: Select all

x = 409, y = 263, rule = B3/S23
151bo6$182bo$180b2o$181b2o$154bo$154bobo$151bo2b2o3bo$159bobo$159b2o4$
116bobo152bo$117b2o152bobo$117bo153b2o78bobo$351b2o$151bo200bo$282bo$
282bobo$282b2o5$101bo161bo$102b2o158bo$101b2o48bo110b3o9$33bo$31bobo
117bo$32b2o10$151bo10$151bo10$151bo10$151bo11$151bo10$151bo10$28bo9bo
9bo9bo10bo9bo9bo9bo10bo9bo9bo9bo10bo9bo9bo9bo10bo9bo9bo9bo10bo9bo9bo9b
o10bo10$151bo11$151bo10$151bo10$151bo10$151bo2$2o$b2o20b2o157b3o$o23b
2o156bo$23bo159bo3$270bo$269b2o$269bobo$151bo8$123b3o164bo$125bo163b2o
$124bo26bo137bobo2$115b2o$116b2o166b2o$115bo167b2o$285bo2$261b2o$190bo
69b2o$189b2o71bo$151bo33bo3bobo$184b2o$184bobo8$151bo6$148b2o$147bobo$
149bo3$151bo201bo$352b2o$352bobo8$151bo6$132b2o$131bobo250b3o$133bo
250bo$385bo$151bo8$114b3o$116bo$115bo35bo14$407b2o$406b2o$408bo!

The *WSS constructions have been tightened up a bit, though the left-hand group could no doubt be brought in quite a bit more if someone was interested.

[muzik]

I recently expanded the wiki page on c/3 orthogonal spaceships to account for everything up to 50 cells. In the process of doing this, I noticed a bunch of commonalities between some of the smaller spaceships as follows:

If we look at four of the five smallest synthesizable spaceships so far, it turns out that they can be broken down into multiple constituent components, which I've color coded below. For the sake of convenience, I've decided to name these "ragged" (white), "crotchet" (red) and "saucer" (orange):

Code: Select all

x = 68, y = 19, rule = LifeSuper
2.M20.Q23.Q15.Q$.M.M18.Q.Q21.Q.Q13.Q.Q$2M20.Q.Q21.Q.Q13.Q.Q$2.M19.Q
23.Q15.Q$2M19.2Q22.2Q14.2Q$3M18.Q.Q21.Q.Q13.Q.Q2$.M.M16.3Q21.3Q13.3Q$
.3M16.3Q21.3Q13.3Q2$4.3O16.3O15.3M19.3Q$4.3O16.3O15.M.M19.3Q2$3.2O17.
2O16.3M21.Q.Q$3.2O17.2O16.2M22.2Q$5.O18.O17.M22.Q$40.2M23.Q.Q$41.M.M
21.Q.Q$42.M23.Q!

If we now look at the two smallest c/3 orthogonal spaceships, we can see that they also can be broken down into these components, but that there also exist an inner c/3 orthogonal wave (cyan) which can be stabilised at both sides by these accordingly:

Code: Select all

x = 28, y = 22, rule = LifeSuper
2.M20.Q$.M.M18.Q.Q$2M20.Q.Q$2.M19.Q$2M19.2Q$3M18.Q.Q2$.M.M16.3Q$.3M
16.3Q2$4.3S16.3S$4.3S16.3S2$3.2S17.2S$3.3S16.3S2$6.3O16.3O$6.3O16.3O
2$5.2O17.2O$5.2O17.2O$7.O18.O!

And this wave can be extended indefinitely:

Code: Select all

x = 47, y = 18, rule = B3/S23
3b2o$o2b2o$2ob2o4b2o$2o4bo2b2o$6b2ob2o4b2o$6b2o4bo2b2o$12b2ob2o4b2o$
12b2o4bo2b2o$18b2ob2o4b2o$18b2o4bo2b2o$24b2ob2o4b2o$24b2o4bo2b2o$30b2o
b2o4b2o$30b2o4bo2b2o$36b2ob2o4b2o$36b2o4bo2b2o$42b2ob2o$42b2o!

The following four spaceships can be derived through similar means, three of which I didn't even see in the updated jslife moving collection:

Code: Select all

x = 59, y = 64, rule = B3/S23
2$30bo$29bobo$28b2o$30bo$28b2o$28b3o2$4bo24bobo$3bobo23b3o$2b2o$4bo27b
3o$2b2o28b3o$2b3o$31b2o$3bobo25b3o$3b3o49bo$34b3o17bobo$6b3o25b3o17bob
o$6b3o45bo$35bobo15b2o$5b2o28b2o16bobo$5b3o28bo$36bobo13b3o$2b3o31bobo
13b3o$2bobo32bo$55b3o$b3o51b3o$b2o$3bo50b2o$b2o25bo25b3o$2bobo22bobo$
3bo23bobo21b3o$27bo23bobo$26b2o$26bobo21b3o$50b2o$25b3o24bo$25b3o22b2o
$51bobo$28b3o21bo$28b3o2$27b2o$27b3o2$30b3o$30b3o2$31bobo$31b2o$32bo$
32bobo$32bobo$33bo!

If we can find a way to insert fragments of this wave within the three fenceposts that we can already synthesize, then this should trivially allow for not only all seven of the smallest c/3 orthogonal spaceships to be synthesized, but for arbitrarily large syntheses as well.

I'm almost certain that I'm not the first one who has noticed this given the large existing collections of c/3 orthogonal technology, but I felt this fit here, could be of use for future syntheses, and didn't really know what to search for (especially since the forum forbids searching for "c/3").

[mniemiec]

If we now look at the two smallest c/3 orthogonal spaceships, we can see that they also can be broken down into these components ... I'm almost certain that I'm not the first one who has noticed this given the large existing collections of c/3 orthogonal technology, but I felt this fit here, could be of use for future syntheses, and didn't really know what to search for (especially since the forum forbids searching for "c/3").

Dean Hickerson once created a grammar for putting together small c/3 spaceships out of smaller component parts like this. I'm not sure if there is any mention of it on the forums or the wiki, however. A cursory search of the forums couldn't find it.

[w33z8kqrqk8zzzw33]

Heres the relevant text from life3.zip in David Bell's six part article:

Code: Select all

In Dean's grammar, the components are labeled using letters, or letters
followed by either a single quote or a double quote (e.g., A, A', and A").
Any three components with the same letter are related, and represent the
same section of a period 3 spaceship in three successive generations.
Therefore, if component A appears in generation 0 of a spaceship, then
component A' must appear in the same location in generation 1, and
component A" must appear in the same location in generation 2.

A component name followed by a dash represents the mirror image of a
component.  The mirroring is done by reflecting the component across a
horizontal line.  For example, component B"- is the mirror image of
component B".

The components in Dean's grammar are the following.

 [A]     [A']    [A"]   [B]     [B']    [B"]     [C]       [C']       [C"]
 ..O.    ..O.    ..O    ..O.    ..O.    ..O    ...O...    .......    ...O...
 .O.O    .O.O    OO.    .O.O    .O.O    OO.    ..O....    .OOO...    ..O.O..
 .O.O    OO..    OO.    .O.O    OO..    OO.    .OO....    .OOO...    ..O....
 .O..    ..O.    ..O    .O..    .O..    ..O    ...O.O.    ...OO..    ..O...O
 ....    OO..    O..    OO..    O.O.    O..    .OOO..O    .O.O.OO    ....O.O
 OO..    OOO.    O.O     X       X      X      .OO..O.    .O.O...    .OO..O.
  X       X      X                             .......    O......    .O.....
                                               OOO....    OOO....    OO.....
                                               .O.....    O......    .O.....
                                                 X          X          X


  [D]      [D']     [D"]     [E]     [E']    [E"]     [F]     [F']    [F"]
   X         X        X       X       X       X        X        X       X
 ..O.O    ......    ..O..    .O.O    ....    .O.O    .OO..    .O.O    ..O..
 ..OO.    ...OO.    ...OO    O.O.    O..O    ..O.    ..O..    ..O.    ....O
 .....    ..O..O    .O...    OOO.    O.O.    OO..    ..O.O    .OO.    ..OO.
 OO.OO    .OOO..    .O.OO    ....    O...    .O..    ..OO.    ....    ..OO.
 OO...    O..O..    O..OO    .O.O    .O..    .OOO    .OO..    O..O    .....
 O....    O..O..    O..O.      X       X       X     OO...    O...    OO...
 OO.O.    .OO...    .OOO.                            X        X        X
 .O.O.    ....O.    .O...
   X        X         X


 [G]     [G']    [G"]    [H]       [H']      [H"]      [I]     [I']      [I"]
  X       X       X        X          X        X        X        X        X
 O..O    O...    O.O    ..OO..    ...O.O    ...O..    .O.O.    .O...    .OOO..
 OO..    OOO.    OO.    ...O..    ....O.    .....O    .....    O....    .O....
 .O..    ....    O..    ...O.O    ...OO.    ...OO.    OOO..    O.O..    OO....
 .OOO    .O.O    .O.    ...OO.    ......    ...OO.    OO...    O.O..    .O....
   X       X       X    .OOO..    ..O..O    ......    .....    .OOO.    ......
                        O.O...    .O....    OOO...    ..OOO    ..O.O    .....O
                        O.O...    OO....    OOO...    .O.OO    .O..O    .OOOO.
                        O.....    .O....    ......    .O...    OO...    .OO...
                        .O....    .OOO..    .O.O..    .O...    .....    ......
                          X         X         X       .....    OO...    .O.O..
                                                      OO...    OOO..    .O.O..
                                                       X        X        X


   [J]         [J']        [J"]       [K]     [K']      [K"]
   X            X          X           X        X        X
 ..O.....    ..OO....    .O.O....    .O.O.    .O...    .OOO..
 ..OOO...    ..OO....    ....O...    .....    O....    .O....
 ..O.....    ...O....    ...O....    OOO..    O.O..    OO....
 ........    ..O.....    ..OOO...    OO...    O.O..    .O....
 OO...O..    .O..OO..    .O.OO...    .....    .OOO.    ......
 OOOOO...    O...OOOO    OO..O..O    ..OOO    ..O.O    .....O
 OO...O.O    .O....O.    ........    .O.OO    .O..O    .OOOO.
 ..O..OO.    ...O.OOO    .O...OOO    O....    OO...    .OO...
 OO.O....    .OO.....    .O.OOO..    O....    .....    .OO...
 .O......    .OO..O..    .O..O...    .....    O....    .O....
 ..OOO...    ...OO...    ..OOO...    OOO..    OOO..    OO....
 ........    ........    ........    .O...    O....    .O....
 ..OOO...    ...OO...    ..OOO...      X        X        X
 .O......    .OO..O..    .O..O...
 OO.O....    .OO.....    .O.OOO..
 ..O..OO.    ...O.OOO    .O...OOO
 OO...O.O    .O....O.    ........
 OOOOO...    O...OOOO    OO..O..O
 OO...O..    .O..OO..    .O.OO...
 ........    ..O.....    ..OOO...
 ..O.....    ...O....    ...O....
 ..OOO...    ..OO....    ....O...
 ..O.....    ..OO....    .O.O....
   X            X          X


The components are strung together by stacking them above each other,
similarly to the way that period 2 components are stacked.  (The X's
indicate the horizontal alignment of components, and should be removed.)

The rules which give the allowed sequences of components to make a valid
spaceship are the following.

The sequence must begin with A, A', A", B, B', B", C, C', or C".

The sequence must end with A-, A'-, A"-, B-, B'-, B"-, C-, C'-, or C"-.

Each pair of adjacent symbols must appear in one line of the following table,
with the first symbol found before the vertical bar, and the second symbol
found after the vertical bar.

                        A    |  D    E
                        A'   |  D'   E'
                        A"   |  D"   E"
                        I    |  D
                        I'   |  D'
                        I"   |  D"
                        D-   |  A-   I-
                        D'-  |  A'-  I'-
                        D"-  |  A"-  I"-
                        E-   |  A-
                        E'-  |  A'-
                        E"-  |  A"-
              B    F-   H-   |  E-   G'-  H"-  I    K
              B'   F'-  H'-  |  E'-  G"-  H-   I'   K'
              B"   F"-  H"-  |  E"-  G-   H'-  I"   K"
    E    G'   H"   I-   K-   |  B-   F    H
    E'   G"   H    I'-  K'-  |  B'-  F'   H'
    E"   G    H'   I"-  K"-  |  B"-  F"   H"
                   C    K    |  J
                   C'   K'   |  J'
                   C"   K"   |  J"
                        J    |  C-   K-
                        J'   |  C'-  K'-
                        J"   |  C"-  K"-
                   D'   G-   |  F-
                   D"   G'-  |  F'-
                   D    G"-  |  F"-
                        F    |  D'-  G
                        F'   |  D"-  G'
                        F"   |  D-   G"


The simplest spaceship which can be constructed by these rules is A E B-,
which is shown below.  This spaceship has 25 ON cells in every generation.
There is no known period 3 spaceship which has fewer ON cells than 25.
(Any such spaceship must be spread out very thinly.)

[Smallest known period 3 spaceship (speed c/3)]
 ..O..
 .O.O.
 .O.O.
 .O...
 .....
 OO...
 .O.O.
 O.O..
 OOO..
 .....
 .O.O.
 .OO..
 ..O..
 ..O.O
 ..O.O
 ...O.


Another example spaceship created using these rules is C J C-, which
represents the following symmetrical spaceship.

[One of many period 3 spaceships constructed by the above grammar (speed c/3)]
 ...O....
 ..O.....
 .OO.....
 ...O.O..
 .OOO..O.
 .OO..O..
 ........
 OOO.....
 .O......
 ..O.....
 ..OOO...
 ..O.....
 ........
 OO...O..
 OOOOO...
 OO...O.O
 ..O..OO.
 OO.O....
 .O......
 ..OOO...
 ........
 ..OOO...
 .O......
 OO.O....
 ..O..OO.
 OO...O.O
 OOOOO...
 OO...O..
 ........
 ..O.....
 ..OOO...
 ..O.....
 .O......
 OOO.....
 ........
 .OO..O..
 .OOO..O.
 ...O.O..
 .OO.....
 ..O.....
 ...O....

[dvgrn]

If we can find a way to insert fragments of this wave within the three fenceposts that we can already synthesize, then this should trivially allow for not only all seven of the smallest c/3 orthogonal spaceships to be synthesized, but for arbitrarily large syntheses as well.

"Trivially allow" is probably a bit of a stretch. There's maybe a good analogy here to the idea about synthesizing signal conduits that came up recently. The problem is that if you synthesize Conduit A in isolation, and Conduit B in isolation, that really doesn't necessarily end up being a lot of help when you're trying to synthesize Conduit A connected to Conduit B. More often than not you end up having to build more than half of the pieces in a completely different order, with completely different recipes, because the two separate recipes just weren't designed to fit together.

There are some differences between conduit syntheses and spaceship-part syntheses, but they all just make things worse. As soon as you finish building a piece of a spaceship it starts to try to move (or explode, or implode). So all the pieces have to be brought into existence at exactly the same time, and rightupnexttoeachotherwithnospacebetweenthepieces.

That's not to say that it will be impossible to find a synthesis for any given one of those spaceships -- just that it seems like the lessons we can carry over from one synthesis to another will be fairly limited. It might not be necessary to start completely from scratch to assemble each new variant, but then again it's a long way from a foregone conclusion that a recipe for any given combination will be findable, just because we know how to assemble all of the pieces in other contexts.

EDIT: I had a sneaking suspicion while posting the above, that the general rule of thumb I was looking for would quickly be proved wrong, at least in some specific cases. It's nice to see that I was right about that, at least!

[Goldtiger997]

Speaking of infinite sequences, I suspect the following sequence of wormy c/3 ships should be within reach of current techniques:

Code: Select all

x = 28, y = 52, rule = B3/S23
5bo$b3ob3o$o6b2o$b2o3bo2bo3bo$11b4o$11bo3bo$9bo2bobo$10bo13$5bo$b3ob3o
$o6b2o$b2o3bo2bo3bo$11b4o$11bo3bo3bo$9bo2bo4b4o$10bo6bo3bo$15bo2bobo$
16bo11$5bo$b3ob3o$o6b2o$b2o3bo2bo3bo$11b4o$11bo3bo3bo$9bo2bo4b4o$10bo
6bo3bo3bo$15bo2bo4b4o$16bo6bo3bo$21bo2bobo$22bo!

I found a way of adding that small component (muzik called it a "crotchet" a few posts up) onto the edge of an appropriate c/3 spaceship, so that entire family of c/3 ships should now have syntheses:

Code: Select all

x = 53, y = 39, rule = B3/S23
41bo$39b2o$39b2o$41bo$39bo$38b3o$38bo$37b2o$38bo$39bo2bo$43bo$bo38b2o$
2bo5bo31bobo$3o3bobo30b2o$7b2o31bo$41bo2bo$45bo$42b2o$42bobo$41b2o$42b
obo$43bo$24b2o$23bobo13bo$24bo13bobo$38b2o2$27bo$26bobo$26bobo$6bo20bo
$6b2o42b2o$5bobo42bobo$50bo3$34bo$33b2o$33bobo!

[HartmutHolzwart]

Great! Would you add some of the extensions to catagolue?

[dbell]

>> I found a way of adding that small component (muzik called it a "crotchet" a few posts up) onto the edge of an appropriate c/3 spaceship, so that entire family of c/3 ships should now have syntheses:

That is great! I had asked several times in the past for such a reaction, and it's nice to see it finally done.

BCNU,
-dbell

[dvgrn]

I found a way of adding that small component (muzik called it a "crotchet" a few posts up)...

That name seems like it might stick, given that a synthesis has been found. Can we get an official pronouncement (heh) on how the term was intended to be spelled?

crotchet (ˈkrɒtʃ ɪt ):
1. a note having the time value of a quarter of a whole note or half a half note, represented by a large solid dot with a plain stem; a quarter note.
2. a perverse or unfounded belief or notion.

It seems possible that crochet (kroʊˈʃeɪ; British ˈkroʊ ʃeɪ, -ʃi) was intended. (?)

[muzik]

crotchet (ˈkrɒtʃ ɪt ):
1. a note having the time value of a quarter of a whole note or half a half note, represented by a large solid dot with a plain stem; a quarter note.

The morphology of the component, with a dense component hanging from a single cell near the top, distantly reminded me of a quarter note:

Code: Select all

x = 4, y = 6, rule = B3/S23
bo$2b2o$2b2o2$3o$3o!
[[ LABELSIZE 128 LABEL -5 2 16 "♩" ]]

Granted, however, one of the 5-cell (and, to my knowledge, still unnamed for 53 years discounting systematic pentomino naming) sparks present within the wave resembles it even more so ("crotchet spark", anyone?)

Code: Select all

x = 2, y = 3, rule = B3/S23
bo$2o$2o!
[[ LABELSIZE 64 LABEL -5 1 16 "♩" ]]

So maybe it might be worth calling the 5-cell spark itself "crotchet", the c/3 wave that contains them something relating to bars in Western music notation (perhaps "waltz" to tie into the threeyness of it), and the c/3 fencepost component that one unprotected side of the wave evolves into "anacrusis", since it begins those bars?

EDIT: definitely getting off the rails of "synthesising spaceships" here, but this name conveniently enough also permits a similar 6-cell spark to be named "quaver" due to resembling an eighth note, if it is ever deemed notable enough for documentation:

Code: Select all

x = 3, y = 3, rule = B3/S23
b2o$2o$2o!
[[ LABELSIZE 64 LABEL -5 1 16 "♪" ]]

Any percieved influence my username may have on this proposed naming scheme is entirely coincidental.

[muzik]

Hey, this works:

Code: Select all

x = 54, y = 50, rule = B3/S23
53bo$51b2o$52b2o6$4bo$3bobo$5b2o$4bo$5b2o$4b3o2$3bobo$3b3o32bobo$38b2o
$3o36bo$3o$36bo$2b2o31bo$2b2o31b3o$bo$17b2o$17bo16bo$19bo13b2o$18b2o
13bobo$17bo$17bo$18b2o$16bobobo$16b2o3bo$22bo$21b2o6$23b2o13b2o$22bobo
12b2o$5b2o17bo14bo$4bobo$6bo$31bo$11b2o17b2o$10bobo17bobo8bo$12bo27b2o
$40bobo!

[dbell]

There are lots of ways that incoming spaceships can react with the end crotchet on a c/3 ship, to either cleanly delete it or else create something else while deleting it.

For example, here is a reaction where a LWSS coming from behind leaves a block.

Code: Select all

x = 28, y = 19
20bo$19b4o$14bo3bo3booboo$13b4o5bobboo$8bo3bo3bo7bobbo$7b4o4bobbo$6bo
3bo6bo$7bobobbo$11bo6$b3o$obbo$3bo$3bo$obo!

This gives me the idea that you could rebuild a crotchet from behind using a large swarm of upward moving spaceships.
The first one hits the block from the above reaction, and then many more spaceships push the result far ahead of the c/3 ship using reactions similar to the helix in a caterpillar. Then a final set of spaceships turns that result into the recipe for building the new crotchet just in time to meet the arriving c/3 ship.

I think it would be interesting to see this work, but I'm not going to try building it.

BCNU,
-dbell