Cellular automaton

A two-dimensional cyclic cellular automaton with 16 states, on a 300×300 torus, after 400 steps starting from a random initial configuration. At this stage in the automaton's evolution, three different types of pattern can be seen: random fields similar to the starting configuration, large blocks of color, and spirals. Eventually the spirals will take over the entire field.

A cellular automaton is a 4-tuple $\left(Z,S,N,f\right)$, where:

• $Z$ is a lattice.
• $S$ is a finite set of cell states or values.
• $I$ is the finite neighborhood.
• $f$ is the transition function.

The lattice is a grid filled with cells, each cell is uniquely identified by its coordinates and value. The cellular automaton evolves via the transition function with respect to the discrete time variable.

Lattice-Gas Cellular Automatons can be used to model physical systems such as fluid and biological systems. Mathematica uses a cellular automatons as a random number generator.

Further Readings

Cellular Automaton Fluids: Basic Theory, Stephen Wolfram, 1986.

Random Sequence Generation by Cellular Automata, Stephen Wolfram, 1986.

Thermodynamics and Hydrodynamics of Cellular Automata, Stephen Wolfram, 1985.

Cryptography with Cellular Automata, Stephen Wolfram, 1986.