Some suggestions for patterns to explore with the CA Pattern Maker

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".

Coloring

After establishing a pattern, creativity with the coloring schemes comes into play. This involves applying a sequence of colors from a palette of colors. The default is that each color in the palette is sequentially applied to all the cells uniformly over a certain number of steps, the default is one step. For some patterns a random choice of colors for each step can be very interesting. The default palette can be displayed and used or you can pick your own palette using a supplied color wheel.

Some suggested patterns to explore.

All patterns are for 50 steps unless otherwise noted.

1D	2D-4 neighbors	2D-8 neighbors
30	54	494
54_2 (try the Fibonacci series)	174 (try "Random by steps")	85507 and 85507_2
73	254 (try "Random by steps")	93737_70
90 (Default)	374 and 374_100	135877
110 (try NoWrap)	467(try "Random by steps")	143954_2
220 (try "Random by steps")	481 (Default)	175850_7
	494 (try 494_100)

Other examples of CA patterns can be found here.