Using notation:
A-B, A = set of alive neighbors necessary for cell to survive
B = set of alive neighbors necessary for cell to appear 23-3 (Classical Life) | 2345-4567 (Walled Cities)| 0-2 (Seeds)| -234 (Serviettes)| 23-36 (High life)| 23-367 (Higher life)| 5-345 (Long life)||||| 5678-35678 (Diamonds)| 235678-3678 (Stains)| 345-368 (Move)| 34678-3678 (Fur)| 235678-378 (Invasion)| 012345678-3 (Flakes)| 1-1 (Gnarl)| 45678-3 (Coral)| 12354-3 (Maze)| 125-36 (LSD)| 1358-357 (Cancer)| 13-1 (Chaos)| 34678-123457 (Inverse Life)| 1357-1357 (Replicator)| 1357-2468 (Diffusion| 2-2 (Uncontrolled life| 2-1 (Highest life| 23-1 (Spots) | 23-2 (Another Chaos | 23-23 (Boundary) | 234-35 (Flowers)| 234-356 (Slow growth)| Sandpile| Boundary| Randomchoice| Random Diffusion| Pattern Form| Movecolors| |

(This text was updated July 18, 2015 after realizing the final structure):
This is a randomized cellular automaton, for which the equilibria are
rectangles (in each color frame). To investigate, please let it run for a while, then look close
at the structure (by enlarging the picture, you can actually save the canvas
picture on your computer). There is an interesting random percolation pattern. Each
color defines a one dimensional connected graph, but the components do not
percolate in general. The empty spots within
a rectangle in the equilibrium are always one-dimensional graphs.
It would be interesting to know about the statistics of the final patterns. How large
are these one dimensional pieces in average, what is the average Euler characteristic?
The Conway type evolution is as follows: pick a random cell o and look at the neighbors a,b,c,d
to the left to the right, up and down. If o is alive, then kill it, if 0 or 4 cells
neighboring cells are alive. If o is dead, then awake it if 2 or 3 neighboring
cells are alive. In this javascript animation, 20000 time steps are done until the
canvas is updated.
An example, where the evolution gets to a random noise.
An translation example.
Oliver Knill, 7/17/2015 |