Cellular Automaton Rules on Dendrites
This is an exploration of cellular automaton rules in fractal spaces. It is a simple example using dendrites to generate fractal spaces, where each cell has either one, two, or three neighbors. At the intersections (three neighbors) the standard enumerated (0-255) rules are combined to take a best two out of three to assign that cell. For the most part, the sequences on the dendritic spaces converge to order more quickly than those on the linear spaces. There are some interesting discrepancies in long-term averages and variances of cell values.
Note that the cellular automaton rules are applied using the CellularAutomaton function, but in a nonperiodic form. The ends are padded with zeros on both ends and then the padding cells are dropped. So the rules are applied with a kind of absorbing barrier for the cells with one neighbor (end cells).