[Forum Game] CA Puzzles

[b-engine]

- Prove that the set of SLs in B3/S12 and B3/S124a are the same. (Easy)

S4a implies that at least 3 cells needs to have 3 to 4 neighbors, which the cells will die out in next generation. Hence, no still lifes with S4a region can exist without S3, means that still lifes set in B3/S12 and B3/S124a are the same:

Code: Select all

x = 3, y = 2, rule = B3/S12History
EC$2EA!

Code: Select all

x = 3, y = 2, rule = B3/S124aHistory
EC$2EA!

Spoiler: x = 3, y = 2, rule = B3-q4ew8/S2-e34c8 3o$bo! x = 3, y = 2, rule = B34w/S23-e bo$3o!
Next:
Easy: find an INT rule 2 transitions from Life which pre-traffic lights evolves into 4 (speed simplified) 2c/5 spaceships.

Hard: find an INT rule which this alien p2 is common.

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x = 6, y = 6, rule = B3/S238
2bo$bo2bo$obo$3bobo$bo2bo$3bo!














(Hint: B4w)

[hotcrystal0]

New puzzle: Find a way to synthesize the long boat in red without touching the blocks and canoe (assume that the blocks go down infinitely after the red arrow):

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x = 19, y = 47, rule = LifeHistory
$5.2A.2A.2A.2A$4.A.A.2A.2A.2A$3.A$2.A$2.2A6.D$9.D.D$2.2A4.D.D$2.2A4.2D
2$2.2A$2.2A2$2.2A$2.2A2$2.2A$2.2A2$2.2A$2.2A2$2.2A$2.2A2$2.D$2.D$D.D.
D$.3D$2.D!

[Citation needed]

Find three spaceships that work in both B3/S23 and B3468/S23.

[b-engine]

Find three spaceships that work in both B3/S23 and B3468/S23.

All xWSSes work in both rules:

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x = 7, y = 20, rule = B3/S23
b6o$o5bo$6bo$o4bo$2b2o4$2b5o$bo4bo$6bo$bo3bo$3bo4$3b4o$2bo3bo$6bo$2bo2bo!

Code: Select all

x = 7, y = 20, rule = B3468/S23
b6o$o5bo$6bo$o4bo$2b2o4$2b5o$bo4bo$6bo$bo3bo$3bo4$3b4o$2bo3bo$6bo$2bo2bo!

[confocaloid]

Are there any other CGoL spaceships (not counting LWSS, MWSS, HWSS and their combinations; especially other speeds) with the property that neither of cell conditions B4, B6, B8 occurs in any phase of the spaceship?

I ran a few searches using qfind, without finding anything interesting:

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./qfind -r B3~468/S23 -v c/2 -w 10 -s even
./qfind -r B3~468/S23 -v c/2 -w 10 -s odd
./qfind -r B3~468/S23 -v c/3 -w 10 -s even
./qfind -r B3~468/S23 -v c/3 -w 10 -s odd
./qfind -r B3~468/S23 -v c/4 -w 10 -s even
./qfind -r B3~468/S23 -v c/4 -w 10 -s odd
./qfind -r B3~468/S23 -v c/5 -w 10 -s even
./qfind -r B3~468/S23 -v c/5 -w 10 -s odd
./qfind -r B3~468/S23 -v 2c/5 -w 10 -s even
./qfind -r B3~468/S23 -v 2c/5 -w 10 -s odd
./qfind -r B3~468/S23 -v c/6 -w 10 -s even
./qfind -r B3~468/S23 -v c/6 -w 10 -s odd

and as expected, this search finds the LWSS (and wider searches find MWSS and HWSS too):

Code: Select all

./qfind -r B3~468/S23 -v 2c/4 -w 5 -s asymmetric

Find three spaceships that work in both B3/S23 and B3468/S23.

All xWSSes work [...]