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Description of Life

Life requires a two-dimensional binary Moore neighborhood; therefore neighborhoods containing a central cell with eight additional neighbors. The rule is semitotalistic, meaning that the state of the central cell together with the number of remaining live cells determines the evolution. In these terms a live cell (binary state 1) lives in the next generation whenever it has two or three live neighbors. The quiescent state (0, also called dead) becomes live (a new cell is born) whenever it has exactly three live neighbors. All other cells die (or remain quiescent).

This automaton is remarkable for the fact that an initial population of randomly chosen live cells eventually settles down into a collection of visibly separated objects which run through short cycles of evolution. The most common cycle, of period 1, is called a ``still life'' but there are ``oscillators'' and ``alternators,'' mostly of period 2. Period 3 objects are quite rare; occasionally others are found with longer periods.

One especially striking five-cell object, called a glider, translates itself diagonally by a single cell every four generations. Its phases comprise two pairs of mirror symmetric figures; the name is therefore a pun on the crystallographic concept of a glide plane.

After a long evolution, small residual objects are the most common; a graph of frequency versus size is instructive. Automata other than Life tend to evolve into uniform chaotic fields of a fixed density, or to dwindle away altogether. Life -like rules are merely uncommon, not unknown; hard it is, however, to find another rule exhibiting the organized behavior discovered within Life --- certainly none governed by a rule of equal simplicity.

Harold V. McIntosh