4. Cellular Automata and Fractal Evolution

Two-Dimensional CA Examples

Here are a few examples of patterns grown by two-dimensional CA.

Here is a von Neumann CA that generates gaskets. Click the picture for a larger view, and the CA rule.
Here is an outer totalistic von Neumann CA that does not generate gaskets, but its cross-sections are.
Here is another outer totalistic von Neumann CA. Again we consider the pattern growing from a single cell.
Here are the patterns grown from a single live cell for three Moore outer totalistic CA.
Here is another von Neumann outer totalistic CA, and pattern evolving form a single cell.
A minor change in the preovious CA gives an example of sensitivity to initial conditions for 2D CA.
Next we inverstigate how random initial patterns evolve under the majority rules 2D CA.
Here is another pattern evolving from a random initial distribution of live and dead cells.
Here is another CA exhibiting self-organization. We show the patterns that evolve from two different random initial configurations.

Return to Examples of Cellular Automaton Patterns.