Glider Syntheses in Other Rules

[Extrementhusiast]

In several rules, there are small spaceships, which could reasonably be called "gliders". This thread is for glider syntheses in other rules. To start, three spaceship syntheses in B36/S245:

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x = 126, y = 46, rule = B36/S245
98b3o$98b2o$98bo16$50b2o10b2o$49bo14bo$48bobo12bobo$48bo2bo10bo2bo2$
122bo2bo$123bobo$124bo$6bo2bo112b2o$6bobo40b2o12b2o$7bo40b4o10b4o$8b2o
40b2o10b2o$23bo26bo12bo$22bobo$21bo90b2o$22bo29bo6bo2bo51bo$51bobo6bob
o36bo2bo10bobo5bo2bo$54bo6bo37bobo10bo2bo6bobo$53bo5b2o39bo22bo$101b2o
18b2o$10b2o$9b4o$9b2o$10bo34bo2bo16bo2bo$4o41bobo18bobo39bo2bo$2obo42b
o20bo40bobo$2b2o43b2o16b2o42bo$2b2o106b2o!

[c0b0p0]

B35/S3478 seems to be promising for glider syntheses; here are some of mine.

My (incomplete) table of two-glider syntheses that do not simply disappear:

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x = 95, y = 15, rule = B35/S3478
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo2$o17bobo21bobo23bobo23bo$76bo$o2b2obo11bobo
21bobo23bobo3b2obo16bo$5bobo29bo10b2obo23b3o$o3b3o11bobo14b3o4bobo5bob
o10bo4bobo4b3o16bo$5bo8bo9b2obo7b2obo10b3o9b3o24bo$o11bobo3bobo5bobo6b
3o4bobo5bo10b2obo3bobo15bobo5bo$11b3o11b3o33b3o21b3o$o11bobo3bobo5bo
15bobo23bobo15bobo5bo$13bo73bo$o17bobo21bobo23bobo23bo2$obobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobo!

A 3-glider synthesis of probably the most common p4 around:

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x = 24, y = 9, rule = B35/S3478
2obo$2bobo$b3o$2bo2$4b2obo14bo$6bobo11b3o$5b3o12b2obo$6bo13b3o!

A 4-glider synthesis of the following flipper:

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x = 26, y = 23, rule = B35/S3478
2obo$2bobo$b3o$2bo2$4b2obo14bo$6bobo11b3o$5b3o12b2obo$6bo13b3o11$23bo$
22b3o$21bobo$22bob2o!

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OOO
O..
O..

A synthesis of a c/4 orthogonal spaceship from three gliders:

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x = 31, y = 10, rule = B35/S3478
bo28bo$b3o24bobo$ob2o23b3o$b3o24bobo$29bo2$2bo$2b3o$bob2o$2b3o!

14-glider synthesis of a p6:

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x = 35, y = 35, rule = B35/S3478
34bo$32bobo$31b3o$15b4o13bobo$16b2o15bo$15b4o$16b2o9$3bobo23bobo$3b4o
21b4o$3b4o21b4o$3bobo23bobo10$16b2o$15b4o$16b2o$2bo12b4o$b3o$2bobo$2ob
o!

8-glider synthesis of the 6-cell phoenix:

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x = 100, y = 64, rule = B35/S3478
99bo$97bobo$96b3o$97bobo$98bo40$37bo38bo$37b3o34bobo$36bob2o33b3o$37b
3o34bobo$75bo2$38bo$38b3o$37bob2o$38b3o$o18bo$obo14b3o$b3o13b2obo$obo
14b3o$bo2$18bo$16b3o$16b2obo$16b3o!

Here are the three oscillators which I would like to find a synthesis for.

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x = 37, y = 8, rule = B35/S3478
2bo$bobo$o2bo30bo$b3o20b2o8b3o$4b3o15b2obo7bo2bo$4bo2bo16b2o8b3o$4bobo
27bo$5bo!

[lukebradford]

Live Free or Die (s0/b2) has this fun one, using two small p1 spaceships (moons) to construct a p19 oscillator, the monster. The moon is only four cells and the only p1 spaceship in the rule. What I find cool about this reaction is that the evolution of the monster actually contains a few phases in which two moons reappear and collide in the center again.

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x = 13, y = 4, rule = B2/S0
o11bo$bo9bo$bo9bo$o11bo!

[c0b0p0]

B35/S3478 seems to be promising for glider syntheses; here are some of mine.

B3678/S35678 is even more promising -- it looks like a cross between LongLife and Dimoeba, plus it has a natural glider and natural infinite growth! (I still have not been able to synthesize that.)

Here is a two-glider recipe for the natural p22 I call "the arrow".

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x = 23, y = 13, rule = B3678/S35678
2bo$b3o$4o$2b2o$2b2o$2bo$3bo16bo$19b3o$19b4o$19b2o$19b2o$20bo$19bo!

Based on that recipe, below is a synthesis of a common p20 that is generated from a 3x3 block.

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x = 28, y = 19, rule = B3678/S35678
2bo$b3o$4o$2b2o$2b2o$2bo$3bo16bo$19b3o$19b4o$19b2o$19b2o$20bo$19bo5bo$
24b3o$24b4o$24b2o$24b2o$25bo$24bo!

Here is the natural infinite growth

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x = 12, y = 12, rule = B3678/S35678
3bo$2b3o$b6o$7o$b8o$2b7o$2b9o$4b7o$4b8o$6b5o$6b5o$8bo!

... and a sparkier version.

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x = 14, y = 14, rule = B3678/S35678
2bo2$ob3o$2b3o3bo$2b7o$4b6o$4b8o$4b8o$3b11o$5b9o$6b6o$6b6o$8b2o$8b2o!

[c0b0p0]

Here is a glider synthesis (in B358/S135) of a block.

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x = 37, y = 181, rule = B358/S135
o2$bo30b2o$bobo27b2obo$bobo26bo3bo$bobo27b2obo$bo30b2o2$o52$10bo2$11bo
$11bobo17bo$11bobo16bo2b2o$11bobo17bo$11bo2$10bo54$33b2o$32b2o2$32b2o$
33b2o12$31b3o2$30b5o$28bo7bo30$12bo2$13bo$13bobo$13bobo$13bobo$13bo2$
12bo20b2o$32b2o!

A big band (the only p4 in the B3A0124/S1D02 rulespace) is two gliders from the first intermediate oscillator in the pattern above, as shown below.

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x = 49, y = 18, rule = B358/S135
45bo$44bo2b2o$45bo$24bo2$25bo$25bobo$25bobo$25bobo$o24bo2$bo22bo$bobo$
bobo$bobo$bo2$o!

This rule also has a simple 16-cell eater, shown below.

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x = 38, y = 15, rule = B358/S135
3bo3bo$4b3o2$37bo2$36bo$2o32bobo$2o32bobo$2o32bobo$36bo2$37bo2$4b3o$3b
o3bo!

[c0b0p0]

This rule also has a simple 16-cell eater, shown below.

Here is a 15-cell eater.

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x = 27, y = 17, rule = B358/S135
21b3o$20bo3bo3$o2$bo24bo$bobo21bo$bobo21bo$bobo21bo$bo24bo2$o3$20bo3bo
$21b3o!

[unname66609]

7-glider synthesis of the 6-cell phoenix :

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x = 106, y = 64, rule = B35/S3478
105bo$103bobo$102b3o$103bobo$104bo33$29bo52bo$29b3o48bobo$28bob2o47b3o
$29b3o48bobo$81bo2$30bo$30b3o$29bob2o$30b3o8$o18bo$obo14b3o$b3o13b2obo
$obo14b3o$bo2$18bo$16b3o$16b2obo$16b3o!

[John]

I'm still spending my time looking around in hexagonal rules...
(first row is 2 gliders, 2nd row is 3).

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x = 193, y = 30, rule = B2/S3H
70bobo58bo19bo10bo17bobo$bo29bo11bo30bo16bo38bo2bo19bo7bo21b2o$3bo29bo
8bo28bo2bo18bo37b2obo15bobo2bo4bo2bobo14bobo$obo2bo6bo17bobo2bo5bo2bob
o24bobo16bobo2bo25bo8b2ob4o44b2obobo$11bo49bo10bo2bo25bobo19bo8b2obo
15bobo2bo4bo2bobo14bo2bo$bobo2bo3bo2bobo15bobo2bo5bo2bobo15bo12bo14bob
o2bo3b2o18bobo2bo6bo2bo19bo7bo18bo2b2o$5bo29bo8bo15bobo2bo7bobo19bo4bo
b2obo28bo19bo10bo18b2o$4bo6bo2bobo17bo11bo47bo10bo15bobo2bo$13bo47bobo
2bo34bob2obo18bo$15bo49bo36b2o20bo62bo$64bo39bobo82bo$186bobo2bo2$187b
obo2bo$191bo$190bo5$bo39bo$3bo36bo$obo2bo3bo32bo$31bo11bo$bobo2bo2bobo
21bo$5bo4bo19bobo2bo7bo$4bo$31bobo2bo$35bo$34bo!

[danieldb]

2x2:

Duoplet from 2 gliders:

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x = 11, y = 6, rule = B36/S125
3bo$o2bo3bo$bobo3bo2bo$7bobo$bo$9bo!

[strake]

3-glider synthesis of duplex rake in B2o45/S2o45H:

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x = 30, y = 25, rule = B2o45.S2o45
24b2o$27bo$25b4o$25b3o$25b3obo$29bo11$o$ob3o$2b3o11b2o2bo$b4o11b2obo$
2bo13b2obo$4b2o11bob2o$19bo2$20bo!

[confocaloid]

3-glider synthesis of duplex rake in B2o45/S2o45H: [...]

Modified the header so that the pattern can be viewed in the current version of LifeViewer:

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x = 30, y = 25, rule = B2o45/S2o45H
24b2o$27bo$25b4o$25b3o$25b3obo$29bo11$o$ob3o$2b3o11b2o2bo$b4o11b2obo$
2bo13b2obo$4b2o11bob2o$19bo2$20bo!

There is a forum thread about B2o45/S2o45H: viewtopic.php?f=11&t=1579 "Hex rule B2o45/S2o45H"

Unrelated (but still related to glider syntheses), here is a CA where "checkerboard still lives" of all sizes are constructible.
The pattern includes

• a small p5 orthogonal 2c/5 spaceship,
• a small p50 orthogonal 2c/5 spaceship,
• an engineered p40 orthogonal 2c/5 puffer that incrementally constructs 5-by-3 "checkerboards",
• a p40 rake that removes the "checkerboards".

It looks plausible that all "checkerboards" are also glider-destructible, but I did not prove that.

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x = 589, y = 141, rule = B2cin3aijk4iqr5acir6aci78/S1c2-ik3ceq4c5y
357b2o$278b2o76b2o$30b2o245b2o78b2o$29b2o247b2o81bobo188b2o$30b2o250bo
bo75bobo4bo6bo176b2o$34bobo244bobo4bo6bo65bo4bobo5bo177b2o4bo$33bobo4b
o6bo234bo4bobo5bo32b2o35bobo6bo181b2ob2o$34bo4bobo5bo71b2o128b2o35bobo
6bo31b2o37bo68b2o118bobobo4bo$b2o35bobo6bo70b2o78b2o48b2o37bo40b2o104b
2o120bobo4bobo4bobo$2o37bo79b2o4bo71b2o50b2o81bobo5bo94b2o4bo81b2o32bo
4bobo$b2o120b2ob2o70b2o4bo48bobo5bo69bobo5b2o98b2ob2o78b2o39bo$5bobo5b
o108bobobo4bo70b2ob2o45bobo5b2o70bo5b2obo5b3o13b3o72bobobo4bo75b2o4bo$
4bobo5b2o109bobo4bobo4bobo61bobobo4bo42bo5b2obo5b3o13b3o52b3obo95bobo
4bobo4bobo71b2ob2o$5bo5b2obo5b3o13b3o51b2o32bo4bobo70bobo4bobo4bobo41b
3obo75b2obo11bo15bo15bo18b2o32bo4bobo78bobobo4bo9bo15bo$12b3obo72b2o
39bo38b2o32bo4bobo50b2obo11bo15bo15bo31bo2b2o60b2o39bo80bobo5bo$13b2ob
o11bo15bo15bo29b2o4bo71b2o39bo51bo2b2o71bo17bo15bo15bo18b2o4bo115bo4bo
bo9bo15bo$13bo2b2o76b2ob2o70b2o4bo82bo17bo15bo15bo101b2ob2o$10bo17bo
15bo15bo32bobobo4bo9bo15bo44b2ob2o161b2o68bobobo4bo9bo15bo90b2obo12b3o
13b3o13b3o$94bobo5bo69bobobo4bo9bo15bo52b2o76b2o70bobo5bo117b3o$12b2o
81bo4bobo9bo15bo44bobo5bo77b2o76bo51bo21bo4bobo9bo15bo92bo$11b2o161bo
4bobo9bo15bo50bo51bo25b2o45bo4bobo191bobo$10bo51bo39b2obo12b3o13b3o13b
3o104b2o45bo4bobo19bo4bobob2o40bobo4bobo26b2obo12b3o13b3o13b3o111b3ob
3o$9b2o45bo4bobo39b3o75b2obo12b3o13b3o13b3o20bo4bobob2o40bobo4bobo19bo
4b3o41b2o2b2o3bo28b3o158b3ob3o$4bo4bobob2o40bobo4bobo39bo77b3o68bo4b3o
41b2o2b2o3bo16b2o8bo4bo36bo5bo33bo106bo51bobo2bo2bo$5bo4b3o41b2o2b2o3b
o85bobo31bo65b2o8bo4bo36bo5bo19b2o48bobo3b3o79bobo58bobo9bo41b2o4bobo$
b2o8bo4bo36bo5bo87b3ob3o74bobo17b2o48bobo3b3o21b2o48b3o82b3ob3o57bobo
7b3o36bo3b2o5bo$2o48bobo3b3o88b3ob3o72b3ob3o16b2o48b3o75bobo83b3ob3o
53b2o50bobo4bo$b2o48b3o40bo51bobo2bo2bo71b3ob3o65bobo109bo51bobo2bo2bo
51b2o48bobo$50bobo40bobo9bo41b2o4bobo17bo51bobo2bo2bo175bobo9bo41b2o4b
obo51b2o48b3o$94bobo7b3o36bo3b2o5bo17bobo9bo41b2o4bobo175bobo7b3o36bo
3b2o5bo101bobo$90b2o50bobo4bo23bobo7b3o36bo3b2o5bo172b2o50bobo4bo$89b
2o48bobo27b2o50bobo4bo176b2o48bobo$90b2o48b3o25b2o48bobo185b2o48b3o$
139bobo27b2o48b3o233bobo$218bobo$357bo$278bo77b3o$30bo246b3o$29b3o2$
554bo$553b3o3$121bo315bo$120b3o77bo235b3o$199b3o5$b2o370bo$2o292bo77b
3o$b2o43bo246b3o$45b3o2$570bo$569b3o3$137bo251bo63bo$136b3o77bo93bo76b
o64b3o$215b3o90bo$387b2o$308b2o2$413bo15bo15bo15bo15bo15bo15bo15bo15bo
15bo15bo$b2o331bo15bo15bo15bo8b2o5bo13bobo13bobo13bobo13bobo13bobo13bo
bo13bobo13bobo13bobo13bobo13bobo$2o61bo15bo15bo15bo15bo15bo15bo15bo15b
o15bo15bo15bo15bo15bo15bo15bo8b2o5bo13bobo13bobo13bobo13bobo13bobo11bo
bobo11bobobo11bobobo11bobobo11bobobo11bobobo11bobobo11bobobo11bobobo
11bobobo11bobobo$b2o59bo15bo15bo15bo15bo15bo10bo4bo15bo15bo15bo15bo15b
o15bo15bo15bo15bo15bo13bobo13bobo13bobo13bobo9bo3bobo11bobobo11bobobo
11bobobo11bobobo6bo4bobobo11bobobo11bobobo11bobobo11bobobo11bobobo11bo
bobo$5bo7b2o140bo17bo15bo15bo15bo10bo4bo15bo15bo15bo15bo11bo3bo13bobo
13bobo13bobo13bobo8bo4bobo13bobo13bobo13bobo13bobo9bo3bobo11bobobo11bo
bobo11bobobo11bobobo11bobobo11bobobo$4bo4bobo3bo218bo17bo15bo15bo15bo
10bo4bo15bo15bo15bo15bo15bo15bo15bo15bo15bo15bo13bobo13bobo13bobo13bob
o13bobo13bobo$8b2o4bobo137b2o314b2o19bo15bo15bo15bo15bo15bo$7bo7bo217b
2o$8b2obob2o$9bobobo$150b2o314b2o$229b2o$9bobobo136bo222b3o90bo$8b2obo
b2o137bo76bo64b3o77bo93bo$7bo7bo215bo63bo$8b2o4bobo$4bo4bobo3bo$5bo7b
2o31b3o$b2o44bo$2o$b2o$135b3o313b3o$136bo77b3o235bo$215bo5$357b3o$278b
3o77bo$279bo3$30b3o$31bo3$119b3o313b3o$120bo77b3o235bo$199bo$376bobo$
297bobo27b2o48b3o$248b2o48b3o25b2o48bobo$51bobo193b2o48bobo27b2o50bobo
4bo$2b2o48b3o193b2o50bobo4bo23bobo7b3o36bo3b2o5bo$b2o48bobo3b3o192bobo
7b3o36bo3b2o5bo17bobo9bo41b2o4bobo$2b2o8bo4bo36bo5bo190bobo9bo41b2o4bo
bo17bo51bobo2bo2bo$6bo4b3o41b2o2b2o3bo75bobo109bo51bobo2bo2bo71b3ob3o
65bobo$5bo4bobob2o40bobo4bobo25b2o48b3o75bobo83b3ob3o72b3ob3o16b2o48b
3o$10b2o45bo4bobo25b2o48bobo3b3o21b2o48b3o82b3ob3o74bobo17b2o48bobo3b
3o$11bo51bo27b2o8bo4bo36bo5bo19b2o48bobo3b3o79bobo31bo65b2o8bo4bo36bo
5bo$12b2o81bo4b3o41b2o2b2o3bo16b2o8bo4bo36bo5bo33bo77b3o68bo4b3o41b2o
2b2o3bo$13b2o79bo4bobob2o40bobo4bobo19bo4b3o41b2o2b2o3bo28b3o75b2obo
12b3o13b3o13b3o20bo4bobob2o40bobo4bobo$99b2o45bo4bobo19bo4bobob2o40bob
o4bobo26b2obo12b3o13b3o13b3o104b2o45bo4bobo$11bo17bo15bo15bo38bo51bo
25b2o45bo4bobo99bo4bobo9bo15bo50bo51bo$14bo2b2o82b2o76bo51bo21bo4bobo
9bo15bo44bobo5bo77b2o$14b2obo11bo15bo15bo40b2o76b2o70bobo5bo69bobobo4b
o9bo15bo52b2o$13b3obo163b2o68bobobo4bo9bo15bo44b2ob2o$6bo5b2obo5b3o13b
3o60bo17bo15bo15bo101b2ob2o70b2o4bo82bo17bo15bo15bo$5bobo5b2o88bo2b2o
71bo17bo15bo15bo18b2o4bo71b2o39bo51bo2b2o$6bobo5bo88b2obo11bo15bo15bo
31bo2b2o60b2o39bo38b2o32bo4bobo50b2obo11bo15bo15bo$2b2o98b3obo75b2obo
11bo15bo15bo18b2o32bo4bobo70bobo4bobo4bobo41b3obo$b2o37bo54bo5b2obo5b
3o13b3o52b3obo95bobo4bobo4bobo61bobobo4bo42bo5b2obo5b3o13b3o$2b2o35bob
o6bo45bobo5b2o70bo5b2obo5b3o13b3o72bobobo4bo70b2ob2o45bobo5b2o$35bo4bo
bo5bo46bobo5bo69bobo5b2o98b2ob2o70b2o4bo48bobo5bo$34bobo4bo6bo42b2o81b
obo5bo94b2o4bo71b2o50b2o$35bobo52b2o37bo40b2o104b2o78b2o48b2o37bo$31b
2o58b2o35bobo6bo31b2o37bo68b2o128b2o35bobo6bo$30b2o92bo4bobo5bo32b2o
35bobo6bo223bo4bobo5bo$31b2o90bobo4bo6bo65bo4bobo5bo222bobo4bo6bo$124b
obo75bobo4bo6bo223bobo$120b2o81bobo230b2o$119b2o78b2o234b2o$120b2o76b
2o236b2o$199b2o!

[confocaloid]

There are three different two-glider collisions that emit a glider 3736:

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#C Weights of neighbours (in hexadecimal):
#C 7D 7D -- -- -- 7D 7D
#C 7D 7D 7D 01 7D 7D 7D
#C -- 7D 05 19 05 7D --
#C -- 01 19 -- 19 01 --
#C -- 7D 05 19 05 7D --
#C 7D 7D 7D 01 7D 7D 7D
#C 7D 7D -- -- -- 7D 7D
x = 101, y = 106, rule = R3,C0,S11-12,30-56,122,127-137,156-181,260-262,280-305,371,386,406-431,510-516,530-557,621,636,656-682,760-761,780-808,827-828,905-911,930-931,1011,1035-1057,1162,1326,B25,35-36,55,86,160-161,180-181,252,262,285-286,305-307,327-338,410-411,430-432,440-461,535-546,555-557,566-596,660-662,680-722,785-787,806-807,825-835,911-912,931-932,942,1035-1047,1056,1087,1160-1182,1191,1586,NW7D7D0000007D7D7D7D7D017D7D7D007D0519057D0000011900190100007D0519057D007D7D7D017D7D7D7D7D0000007D7D
35bobo$37bo3$68bo14b2o9bo$67bobo12bo2bo7bobo$68bo12bob2obo7bo$82bo2bo$
83b2o4$18b2o4bo$7bo7bo3bo$6b3o6bo8b2o$2b2o11bo$obo2bo17bo2bo$4bo19b2o
16bo2$39bobo$41bo$4bo$obo2bo$2b2o11b2o$6b3o5bo2bo77bo$7bo6bo2bo51b2ob
2o21b2o$15b2o51bo5bo$69b2ob2o2$15b2o$7bo6bo2bo$6b3o5bo2bo$2b2o11b2o$ob
o2bo$4bo$41bo$39bobo2$4bo19b2o16bo$obo2bo17bo2bo$2b2o11bo$6b3o6bo8b2o$
7bo7bo3bo$18b2o4bo3$69bo$67bo3bo$66bo$66bo4bo$66b5o4$37bo$35bobo23$81b
o$38bo43bo$39bo40b3o$6bo30b3o$4bobo$5b2o92bo$98bo$57bo40b3o$55b2o$56b
2o16$4b2o$3bobo$5bo!

In addition, there are spaceships (p20 orthogonal c/1, p1 orthogonal c/1, the p4 orthogonal c/2 MWSS) and oscillators (p12 mod-6 oscillator and p88 mod-44 shuttle). Unfortunately so far I can't seem to be able to tweak the rules of this CA to make soups/collisions evolve in a more interesting way. Probably there is something to be found in the space (2^5421 cellular automata with the same fully-symmetric weighted range-3 neighbourhood):

Code: Select all

optional birth conditions (2671): 3-4, 8-9, 13-24, 29, 33-34, 38-40, 42-49, 53-54, 58-59, 63-65, 67-71, 73-74, 78-80, 82-84, 87-99, 101-109, 111, 113-123, 128-129, 133-134, 138-149, 153-154, 159, 163-164, 167, 169-174, 178-179, 183-184, 188-190, 192-199, 202-204, 208-209, 213-224, 226-234, 236, 238-240, 242-249, 253, 258-259, 264-274, 278-279, 283-284, 289-291, 293-296, 298-299, 303-304, 308-309, 314, 318-321, 323-325, 328-329, 332-334, 336-337, 339, 343-349, 352-354, 356-357, 359-360, 362-374, 378-379, 383-384, 389-399, 404, 409, 414, 417, 419-424, 429, 434, 438-439, 442-446, 448-450, 452-454, 457-459, 463-464, 467-484, 486-492, 494-499, 504, 509, 515, 517-519, 521-524, 528-529, 534, 539-541, 543-545, 547, 549, 553-554, 558-559, 564-565, 567-574, 579, 584, 588-593, 595, 597-598, 603-605, 607, 609, 612-617, 619-624, 629, 633-634, 638-639, 641-649, 653-654, 658-659, 663-665, 667-668, 670-672, 674, 679, 683-685, 689-690, 693-697, 699, 702-704, 708-711, 713-714, 716, 718-719, 721, 723-740, 742-749, 754, 758-759, 764-774, 779, 783-784, 789, 792-799, 804, 808-809, 813-815, 819-820, 822, 824, 829-834, 837, 839-840, 843-850, 852-855, 857-860, 862-863, 865-872, 874, 878-879, 883-884, 888-899, 903-904, 908-909, 913-914, 917-924, 928-929, 934, 939-940, 943-950, 952-955, 957, 959-999, 1002-1004, 1007-1010, 1012, 1014-1024, 1028-1029, 1033-1034, 1039-1045, 1048-1049, 1052-1054, 1058-1059, 1061, 1064-1079, 1082-1086, 1088-1100, 1102-1111, 1113-1124, 1128-1129, 1132-1149, 1152-1154, 1157-1159, 1162-1180, 1183-1185, 1188-1190, 1192-1195, 1197-1249, 1252-1254, 1256, 1258-1275, 1277-1279, 1281-1285, 1288-1305, 1307-1312, 1315-1374, 1376-1406, 1408-1499, 1502-1509, 1512-1531, 1533-1585, 1587-1609, 1611-1749, 1752-2010, 2012-3124
optional survival conditions (2750): 2-4, 7-9, 13-16, 18-21, 23-24, 28-29, 32-34, 38-49, 53-54, 57-59, 62-75, 77-79, 81-84, 86-89, 92-96, 98-110, 112-121, 123-124, 128-129, 133-134, 138-141, 143-149, 153-154, 158-159, 163-164, 166-174, 178-179, 183-184, 188-191, 193-204, 206, 208-209, 212-214, 216-230, 232-235, 237-249, 253-254, 258-259, 264-265, 267-274, 279, 283-284, 289-290, 294, 296-297, 299, 303-304, 308-309, 313-315, 318-324, 326, 328-329, 332-334, 337, 339-345, 347-355, 357-362, 364-370, 372-374, 378-379, 383-384, 387-399, 403-404, 408-409, 413-414, 418-424, 428-429, 434, 438-439, 441, 443-445, 447-454, 457-459, 463-465, 469-481, 483-485, 488-490, 492-499, 503-504, 508-509, 513-515, 517-524, 529, 533-534, 539-540, 543-549, 553-554, 558-559, 564, 569-572, 574, 578-579, 583-584, 589-590, 594-595, 597, 599-604, 606-609, 613-616, 618-620, 622-624, 627-629, 633-634, 638-641, 643-649, 653-654, 658-659, 663-665, 668-674, 677-679, 684, 688-690, 692, 694-699, 702-704, 708-709, 713-714, 716, 718-732, 734, 737-739, 741-744, 747-749, 752-753, 759, 763-769, 771-774, 778-779, 782-784, 789-791, 793-799, 803-804, 809, 814, 818-821, 823-824, 829, 833-834, 839-840, 842-854, 856-865, 867-879, 882-885, 887-904, 907-909, 913-916, 918-929, 933-934, 939-940, 942-955, 959, 964-965, 967-1010, 1012-1025, 1027-1030, 1032-1034, 1039-1049, 1053-1054, 1058-1060, 1064-1072, 1074-1075, 1077-1081, 1083-1085, 1088-1099, 1101-1105, 1107-1115, 1117-1155, 1157-1161, 1163-1209, 1211-1256, 1258-1313, 1315-1325, 1327-1527, 1529-3124

[confocaloid]

[...] here is a CA where "checkerboard still lives" of all sizes are constructible. [...]

Here is a two-state isotropic cellular automaton where M-by-N block arrays of all sizes are glider-constructible:

Code: Select all

x = 274, y = 202, rule = R3,C0,S154,156-487,B6,30,33,58,156,181,277,279,283,304-378,402-406,NW190001010100190000010101000001017D7D7D010101017D007D010101017D7D7D01010000010101000019000101010019
242bo$240bobo$241b2o$192bo$190bobo$191b2o$142bo$140bobo$141b2o$92bo$
90bobo$91b2o3$268bo$268bobo$250bo17b2o$218bo29bobo$218bobo28b2o$200bo
17b2o$168bo29bobo$168bobo28b2o$150bo17b2o$118bo29bobo$118bobo28b2o$
100bo17b2o$2o9b2o11b3o71bobo$2o8bo2bo85b2o$10bobo$11bo$269b2o$269bobo$
258b2o9bo$219b2o37b2o$219bobo$bo206b2o9bo38b2o$obo8bo12b2o30bo112b2o
37b2o48b2o$bo8bobo11bo29bobo112bobo$11bobo13bo27b2o101b2o9bo38b2o48b2o
$12bo13b2o91b2o37b2o48b2o48b2o$119bobo$108b2o9bo38b2o48b2o48b2o$108b2o
48b2o48b2o48b2o2$108b2o48b2o48b2o48b2o$108b2o48b2o48b2o48b2o$2o9bo$obo
7bobo$bo9bobo41b2o$12bobo39bobo$13bo42bo$25bobo$23bo3bo$25bobo3$2o9b2o
$obo7bo2bo$b2o7bo2bo$11b2o7$2o$o2bo$2b2o5$21bo$22bo$20b3o$2obo$ob2o2$
258b2o$258b2o2$208b2o48b2o$208b2o48b2o2$158b2o48b2o48b2o$b2o155b2o48b
2o48b2o$o2bo68bo49bo49bo49bo49bo$b2o16b3o49bo36b2o11bo36b2o11bo36b2o
11bo36b2o11bo$21bo49b3o34b2o11b3o34b2o11b3o34b2o11b3o34b2o11b3o$20bo$
58b2o48b2o48b2o48b2o48b2o$58b2o48b2o48b2o48b2o48b2o2$58b2o48b2o48b2o
48b2o48b2o$58b2o48b2o48b2o48b2o48b2o4$69b2o48b2o48b2o48b2o48b2o$69bobo
47bobo47bobo47bobo47bobo$69bo49bo49bo49bo49bo28$255b2ob2o$255b2ob2o2$
205b2ob2o45b2ob2o$205b2ob2o45b2ob2o2$155b2ob2o45b2ob2o45b2ob2o$155b2ob
2o45b2ob2o45b2ob2o$72bo49bo49bo49bo49bo$71bo33b2ob2o11bo33b2ob2o11bo
33b2ob2o11bo33b2ob2o11bo$71b3o31b2ob2o11b3o31b2ob2o11b3o31b2ob2o11b3o
31b2ob2o11b3o2$55b2ob2o45b2ob2o45b2ob2o45b2ob2o45b2ob2o$55b2ob2o45b2ob
2o45b2ob2o45b2ob2o45b2ob2o2$55b2ob2o45b2ob2o45b2ob2o45b2ob2o45b2ob2o$
55b2ob2o45b2ob2o45b2ob2o45b2ob2o45b2ob2o4$69b2o48b2o48b2o48b2o48b2o$
69bobo47bobo47bobo47bobo47bobo$69bo49bo49bo49bo49bo28$252b2ob2ob2o$
252b2ob2ob2o2$202b2ob2ob2o42b2ob2ob2o$202b2ob2ob2o42b2ob2ob2o2$152b2ob
2ob2o42b2ob2ob2o42b2ob2ob2o$152b2ob2ob2o42b2ob2ob2o42b2ob2ob2o$72bo49b
o49bo49bo49bo$71bo30b2ob2ob2o11bo30b2ob2ob2o11bo30b2ob2ob2o11bo30b2ob
2ob2o11bo$71b3o28b2ob2ob2o11b3o28b2ob2ob2o11b3o28b2ob2ob2o11b3o28b2ob
2ob2o11b3o2$52b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o$
52b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o2$52b2ob2ob2o
42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o$52b2ob2ob2o42b2ob2ob2o42b
2ob2ob2o42b2ob2ob2o42b2ob2ob2o4$69b2o48b2o48b2o48b2o48b2o$69bobo47bobo
47bobo47bobo47bobo$69bo49bo49bo49bo49bo!

There is probably a simpler way; the above is just the first thing that worked at all.