Explore Wolfram's 3-color totalistic cellular automata from "A New Kind of Science"
These rules use three colors (White=0, Gray=1, Black=2) with totalistic neighborhood averaging
Stephen Wolfram explored 3-color cellular automata in "A New Kind of Science" to understand how increasing the number of possible states affects computational complexity. These systems use totalistic rules, where the new color depends only on the average of neighboring cells.
With 3 colors (0=White, 1=Gray, 2=Black) and nearest-neighbor interactions, there are exactly 2,187 possible totalistic rules. Each rule can be represented by a lookup table showing the output for each possible neighborhood average (0, 1/3, 2/3, 1, 4/3, 5/3, 2).