This was a quick experiment with an idea I had.
Update a cellular automata using different neighborhoods and rules every second step. Green is the current cell. Red are the cells checked each step. The first step uses the 4 neighbor cells north, south, east and west. The second step uses the 4 diagonal neighbors. Then they alternate each step of the CA. Each neighborhood has its own set of rules for birth and survival.
There are a total of 2^20 or 1,048,576 possible rules using this method. 9*2^20 (9,437,184) if you take into account a maximum state value of between 2 and 10 for each cell.
Click the following to open a short GIF animation of each of the rules. The thumbnails are a mess.
Walkers and Spinners
Extending the possible maximum states of each cell up to 10 shows potential with some more interesting structures.
My next idea was to extend the neighborhoods as follows
The settings are extended to handle the larger neighborhood.
This gives 2^52 or 4 quadrillion (4,503,599,627,370,496 to be exact) possible rules (and that is only for 2 state rules). A maximum cell state of 10 gives 9*2^52 or 40 quadrillion (40,532,396,646,334,464) possible rules. Finding those sweet spots of interest between dying out and total chaos becomes even more daunting.
I wasn’t confident that those neighborhoods would give any interesting results beyond chaotic noise, but they are showing potential so far from random searches and mutations of rules.
The Alternating Neighborhood Cellular Automata are now available as part of the latest version of Visions of Chaos.