Page "Cellular automaton" Paragraph 6

One way to simulate a two-dimensional cellular automaton is with an infinite sheet of graph paper along with a set of rules for the cells to follow.

Each square is called a " cell " and each cell has two possible states, black and white.

The neighborhood of a cell is the nearby, usually adjacent, cells.

The two most common types of neighborhoods are the von Neumann neighborhood and the Moore neighborhood.

The former, named after the founding CA theorist, consists the four orthogonally adjacent cells.

The latter includes the von Neumann neighborhood as well as the four remaining cells surrounding the cell whose state is to be calculated.

For such a cell and its Moore neighborhood, there are 512 (= 2 < sup > 9 </ sup >) possible patterns.

For each of the 512 possible patterns, the rule table would state whether the center cell will be black or white on the next time interval.

Conway's Game of Life is a popular version of this model.

Another common neighborhood type is the extended von Neumann neighborhood, which includes the two closest cells in each orthogonal direction, for a total of eight.

The general equation for such a system of rules is k < sup > k < sup > s </ sup ></ sup >, where k is the number of possible states for a cell, and s is the number of neighboring cells ( including the cell to be calculated itself ) used to determine the cell's next state.

Thus, in the two dimensional system with a Moore neighborhood, the total number of automata possible would be 2 < sup > 2 < sup > 9 </ sup ></ sup >, or.