I continue to pursue my main interest – to create geometric images. Thus I have tried new recipes for cellular automatons on the hexagonal lattice. The cells have either state 1 or 0. To get symmetric images we start with only one cell of state 1 in the center.
A simple rule uses the von Neumann neighborhood of the hexagonal lattice. A cell of state 1 will stay in state 1 if it has exactly two neighboring cells of state 1 and else it will have state 0. A cell of state 0 will have state 1 if it has exactly one cell of state 1 in its neighborhood. The resulting images have an outline that seems to be a fractal snowflake, see the images at the left and below. The inside has a symmetric, but rather random decoration of not much interest.
More interesting images result from another rule. It uses the Moore neighborhood. A cell of state 1 remains in state 1 if it has either 2 or 4 neighbor of state 1. A cell of state 0 will be of state 1 in the next generation if it has 1 or 3 neighbors of state 1. Results are shown at the left and below. There are many similar rules one can experiment with. Some give quite interesting results but in general they are too much pixellated. Thus extra image processing is needed to get satisfying results.