Roger Eugene Hill
The life, career, scientific and spiritual insights of a physicist plus a few excursions into Complexity Science and Art.

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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).
CA 494_2_50

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".


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.

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