Computational Materials Engineering

4

Cellular Automata

Koen Janssens

4.1 A Definition

In a generalized form cellular automata are defined by the following minimal description:

1. n-dimensional space is partitioned into a discrete subset of finite n-dimensional volumes, which are named cells.

2. A state is assigned to each cell.

3. At every time step, a local neighborhood is defined for each cell.

4. A state change rule is defined, which computes the new state of a cell as a function of the state(s) of all cell(s) in the local neighborhood of that cell.

5. A cellular automata simulation proceeds by discrete simulation steps—hence discrete time steps—consisting of the computation of the new states of all cells based on their current states.

Note that this definition is less ...