Pattern types

An cellular automata (CA) is a pattern of individual cells (bits) that can exist in a number of different states that depends on the states of its neighboring cells. For elementary CA's the cells can exist in only one of two states (binary bits) such as [alive,dead] or, as is the case for this Pattern Maker (CAPM), [colored,white]. A pattern is generated by starting (at t=0) with a set of initial cells and then applying the existence rules through a series of time steps to the emerging pattern. A CAPM pattern is thus completely described by: 1) the position of the initial cells; 2) the existence rule that specifies the dependence on the state of the neighboring cells; and, 3) the number of time steps during which the rule is applied.

There are two fundamental types of patterns: one dimensional (1D) where neighbors exist only to the Left or Right of the initial cell(s); and, two dimensional (2D), where "4 neighbors" rules are applied to the neighbors to the N, E, S and W, or "8 neighbors" rules applied to neighbors to the N, NE, E, SE, S, SW, W, and NW of the initial cell(s).

The rules are specified using the Wolfram numbering scheme. For CAPM, the number of initial cells, n, is specified by appending "_n" to the Wolfram rule (this is entered in the "Rule number" box). We can further identify a CA pattern by appending to the "Rule number" "_steps" (entered in the "Number of steps" box). For example 2D pattern 494_2_50 means Wolfram rule 494 applied to 2 initial cells and run for 50 steps. The default is one center cell (n=1) so a Rule number with only one appended _number is "rule_steps".