When I first saw this type of cellular automata described by Gugubo on Reddit I was sure I must have implemented it and included it in Visions of Chaos before, but a quick check showed it wasn’t a CA I had covered. There is enough info in the Reddit thread for me to code it up and put it into Visions of Chaos.

This is a 1D Cellular Automaton that uses 5 cells from the previous generation (2 either side and the central cell) to update the new cell state. The larger neighborhood with 2 cells either side is why I called these “Extended Neighborhood” in Visions of Chaos.

There are 4,294,967,296 (2^32) possible “rules” or types in this CA. Each of the rule numbers can be converted into a 32 digit binary number. For example, rule 260 becomes;

00000000000000000000000100000100

To update a cell, use the following steps;

1. Convert the previous step’s left 2 cells, current cell, and right 2 cells into a binary value.

i.e LLCRR may have states 11010 which can be converted into decimal 26

2. Counting from right to left on the binary representation of the rule above, the 26th digit is a 0, so the new cell state is a 0.

The process is repeated for all cells and then repeated for all rows as long as the CA runs.

I also added the option for more than 2 states (alive or dead) per cell. This way, when a cell dies it does not turn instantly into a dead cell, but has a delayed dying period. If there are 4 states per cell then a living cell (state 1) that dies will first go to state 2, then state 3, then finally die (state 0). Only newly born state 1 cells are used in the rule. All other non state 1 cells are considered state 0 when updating the cell based on the binary string rule.

Jason.