The images from the hexagonal cellular automaton shown in “Basic parity rule – sample images ” and “Modified parity rule – sample images ” are only black and white. But I prefer color. To get similar images in color I modified the cellular automaton.

I want to have more than two colors. Thus each cell now has to have more than two states. The state of a cell is then an integer number, having a value of 0 or greater up to the number of colors minus 1. To find the state of a cell for the next generation I note that the parity rule sums the states of the cells in the neighborhood. Then the new state of the cell is simply the rest of the sum after dividing it by 2. Having more than two colors we calculate the rest of the sum for a division by the number of colors. This gives the number for the state of the cell in the next generation.

This results in rather pixellated pictures and I am smoothing them. Using smoothing on the red, green and blue components of the resulting colors is not a good idea because the colors would mix up, resulting in dull greyish colors. Instead, I am first smoothing the number values of the cells and the colors are determined afterwards.

Here I am showing results with the von Neumann neighborhood and using 8 different colors:

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