Simple Basic Comments on the Growth of Cellular Automata Boundaries
Richard Phillips Wolfram Research
Even some of the simplest cellular automaton rules can produce patterns as intricate as any pattern we expect to be possible in nature. Here we look at how the overall shapes produced by these simple rules grow. There are many possibilities besides the familiar triangular shape.
We include investigations of many initial states, such as those that are made by changing a small group of cells on a periodic background pattern. We will also look at the more specific question of what boundary growths are possible in theory, and find some useful answers.