# Pattern

In a cellular automaton, a pattern is any particular configuration of cells covering the infinite plane (or other backdrop) that the automaton operates on.

## Finiteness

Only those patterns that have finite complexity can be studied. Most typically this is accomplished by establishing a vacuum: requiring the existence of a cell type that, in a neighborhood of no other cells, will remain the same type. A finite pattern, then, is a pattern where infinitely many cells are in the vacuum state, and a finite number in all other states. The vacuum state cells will be known as dead cells, all others as live cells, or "plain" cells.

A bounding box can be defined for any finite pattern, as the smallest rectangular area that contains all the live cells of a pattern. By definition, all cells outside the bounding box are dead, and a simple finite description of a pattern is to enumerate the state of each cell within the bounding box.

A different approach that allows patterns of infinite population is the study of spatially periodic patterns, known as agars.

## Equivalence

Two patterns, finite or not, are normally considered the same, if they differ only by an isometry: a rotation, reflection or translation. For certain pattern types, other criteria may also be established: typically e.g. the phases of an oscillator or a spaceship are not considered different patterns entirely.

## Interestingness

Patterns are usually only considered interesting if they evolve in special ways. Certain families of patterns of interest include oscillators and spaceships.

For a field F = {1, 2, 3}2 with 2 states, there are 218 = 262,144 different patterns. With the addition of another state, there are 134,217,728 different patterns.