ConwayLife.com

As you likely know, there are exactly 2^18 outer-totalistic CA on the 1-Moore neighbourhood -- 9 transitions of quantity (012345678) independently in Birth and Survival.

Suppose you have a 4-state Von Neumann automaton with the restriction that it must be isotropic on the grid and that all 24 ...

A 2-state cellular automaton has exactly two types of colour invariance: none (as in Life) and self-complement (as in Day and Night ).

3-state CA admit four types of colour invariance, corresponding to the subgroups of the group of permutations on 3 elements up to conjugacy (so that 1<->2 and 1<->3 ...

B/S01 has three still-lives: the dot, domino and duoplet.

Out of all INT rules that have only finitely many still-lives of finite population, do any of them have more finite SLs?

Which is the closest INT rule to Life (by transitions different from B3/S23) where a two-glider SMOS is known to exist and the glider otherwise moves identically to Life?

On behalf of Leriendil/majestaz, a (10,3)c/149 puffer that should be corderisable:

[catagolue][/catagolue]
The pre-block is a counterexample for both conjectures:
x = 2, y = 2, rule = B3/S23
2A$.A!


You've done it! And of course the reward of a taskmaster to his subjects is to set them another task.

A spirited pattern in Life is a pattern where all live cells have 2 or 3 ...

A lively pattern in Life is a pattern where every live cell survives to the next generation (because they all have 2 or 3 live neighbours). By this definition, still-lives are the lively patterns where no dead cell has exactly 3 neighbours so no birth can occur.

The above describes 1-lively ...

A lively pattern in a no-B0 MAP CA is one whose live cells will all stay live in the next generation, although some may be born. As all still lives are lively by this definition, we will write them out of it by fiat: inductees in Life are thus the only "lively" patterns Life is considered to have ...

B468S02357 wrote: February 18th, 2026, 5:40 pm What type of pattern is this?

Code: Select all

x = 19, y = 23, rule = R3,C2,S8-10,18,20-24,B4,10-13,NN
bo$o$o2b2o$o3bo$4bobo$o5b2o$6bo$2bo2bo$bo2bo9$14bo$17bo2$13bo4bo$13b3o
b2o$17bo!

Seems to be a replicator with many diferent copies out of phase with each other.

I think the quotation marks around "soup" were important in the original definition.

Predecessors that aren't randomly generated are not really soups. So there can't be a soup that not's randomly generated -- but there can be a "soup" that's not randomly generated (because it looks just like a ...

The fully universal Turing machine, demonstrating that the evolution of finite patterns in Life was as hard as the halting problem, was finished on March 23rd aka 23/3 (or 3/23 with missing B and S).

I think I solved the bonus.

2c/127d which has both a u-pentomino ship and the t-ship from traveling ts.
x = 7, y = 7, rule = B2ei3-ckry4enqr6aei8/S2-n3eiry4nwyz5acin6akn7c
2o$bo$2o3$4b3o$4bobo!
x = 8, y = 8, rule = B2ei3-ckry4enqr6aei8/S2-n3eiry4nwyz5acin6akn7c
bo$2o$bo4$5b3o$6bo!



This ...

Has this dirty replicator been discovered?
As it turns out yes, it's in the titanic toroidal traveler.

One can formalise a shooter to be any finite periodic pattern for which Generation N is identical to G0 except that some periodic debris is present at generation N, with catapults being those shooters whose cores undergo 0 displacement from shot to shot, and firearms undergoing some displacement ...

Elaborating existing terminology:

Minimal definition of SMOS: a spaceship which is decomposable as "made of spaceships" and vacuum in at least one phase, and isn't MOS+vacuum in some other phase,

Restrictions on decomposability give increasingly specific and "natural" SMOSes within 2-state ...

INT's most supported...

• still-life: the dot (2^98 rules: forced S0 and no B0, B1e, B1c)

• oscillator: the duoplet (2^97 rules: forced B2e and no B0, B1e, B1c, S1c)

• spaceship: the p1 moon (2^94 rules: forced B2a, B2e and no B0, B1e, B1c, S1c, S2k)

What is INT's most supported gun?

Is there a pattern which:

• fits in a finite bounding box

• is rotationally asymmetric

• is never a spaceship when run in any INT CA?

Or is there a proof against the existence of such a pattern?

PK22 wrote: August 23rd, 2025, 1:12 pm

Resu wrote: August 23rd, 2025, 11:19 am How do you find the maximum speed of spaceships in each rule?

[...]contains B3 and (rule contains S4 or S5): Maximum speed is (x, y)c/2*max(x, y) + min(x, y).[...]

Is this speed accurately represented as (x,y)c/(2*max(x,y) + min(x,y))? <note extra brackets>

What types of pattern are known to exist in CGoL thanks to universal construction/0E0P emulation, but have not been explicitly constructed?


Any pattern in INT also exists in Life at a step-size of 2^36 thanks to 0E0P -- including any type of SMOSMOS, replicator, binary counter, Rule 110 or ...

1) Does a two-recipe SMOS exist?

2) Do n-recipe SMOSes exist for n > 2?


NimbleRogue has exhibited an isotropic rule with a 79c/13756 pi-only SMOS evolving into at least four recipes: arrangements of two, four, seven, four pis respectively, both "four" arrangements different in their ...

I saw Michael Stevens of Vsauce mention it, played with it for some years then got into it seriously in 2019 with Golly and this site.

1) Does a two-recipe SMOS exist?

2) Do n-recipe SMOSes exist for n > 2?

bonus: Is there a two-recipe SMOS where no spaceship in the first recipe appears in the second?

In which types of CA?


Two state INT.
Example of the bonus; a two-glider collision for which the crash creates a two ...

1) Does a two-recipe SMOS exist?

Is "two-recipe SMOS" means a spaceship made of two different ship?


A spaceship which has two different phases at which there are two recipes. For example if you can find a SMOS with 3-glider and 5-glider phases in its evolution, or a glider+glider -> glider ...

They are engineered spaceships, e.g. the c/18 in HighLife:[...]


This isn't a SMOI, because there's no small phase that becomes two of itself at any point. (actual SMOI by macbi for comparison)

I suspect universal construction allows arbitrary k-SMOSes, because self-making constructors could be ...

A SMOS' recipe is the multiset of spaceships that make it up in its MOS phase, strictly defined as a phase with suitably separated spaceships and no other debris. Two recipes are different if they have different quantities (4 vs 7 gliders) or different types of spaceship.

A two-recipe SMOS has two ...