4. Cellular Automata and Fractal Evolution

4.B. Cellular Automaton Basics

A cellular automaton (CA) is defined by four attributes:
1. The state space, the model of the world, a collection of cells.
2. The neighborhood (nbhd) of a cell. Those cells whose current states affect the next state of a cell.
3. The number of states a cell can assume. This measures the level of detail at which we view the cells.
4. The rule of the CA: how the current states of the cells in the nbhd determine the next state of a cell.
This seems awfully simple, especially if the number of states is few and the neighborhood size small. As a hint of the possible richness involved, we calculate the number of CA rules.
Cellular automata are used to model physical, chemical, biological, and social interactions.
For many of these applications, the exact positions of live cells in the neighborhood is not as important as the number of live cells.
Such CA are called totalistic.
We are interested in an extension of this notion called outer totalistic.