Principles of Cellular Automata

Although there is the possibility of confusion in terminology when dealing with the applications of CA, since they are often applied to the simulation of processes that involve biological cells, we shall follow standard practice and refer to both the finite state automaton and the place in which it is located as a cell.  

Many individual finite state automata are joined together to form a regular array in one, two, or more dimensions this entire array is the cellular automaton. The CA evolve, as all cells in this array update their state synchronously. Into each cell is fed a small amount of input provided by its neighbors. Taking account of this input, the cell then generates some output, which determines the next state of the cell in deciding what its output should be, each cell consults its state, which consists of one piece, or a few pieces, of information stored within it. In the most elementary of automata, the state of the cell that comprises this finite state automaton is very simple, perhaps just 

A finite state automaton is also known as a finite state machine. 

The cells in a CA use transition rules to update their states. Every cell uses an identical set of rules, each of which is easy to express and is computationally simple. Even though transition rules are not difficult either to understand or to implement, it does not follow that they give rise to dull or pointless behavior, as the examples in this chapter illustrate. 

Suppose that several cells are placed in a line to form a one-dimensional CA. Every unit has an initial state of 0, apart from the central cell, which has a state of 1. 

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