4. Cellular Automata and Fractal Evolution

Classifying Cellular Automaton Behavior

Stephen Wolfram observed four classes of CA behavior for patterns growing from an initial random distribution of live and dead cells.

Class I: Homogeneous Everything eventually dies (or eventually lives). Some initial transient behavior usually precedes this final state.

Class II: Periodic Perhaps after some initial transients, the pattern repeats itself exactly, in space (horizontally), in time (vertically), or both.

Class III: Chaotic Patterns grow in a chaotic fashion: short-lived islands of order and sensitivity to initial conditions. Here are two examples.

Class IV: Complex Patterns grow in a complicated way, with both local stable behavior (acting as memory) and long-range correlations (acting to transmit data). In the first, the checkerboard background pattern is the memory; in the second it is the background pattern of vertical lines.

Class IV are the most interesting, and the most rare. Here is a surprising new example.

Conway's Game of Life is a (two-dimensional) Class IV CA:

blocks are the local stable behavior,

gliders give long-range correlations.

Return to Examples of Cellular Automata Patterns.