Some suggestions for patterns to explore with the CA Pattern Maker
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".
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.
|| 2D-4 neighbors
|| 2D-8 neighbors
|54_2 (try the Fibonacci series)
174 (try "Random by steps")
85507 and 85507_2
254 (try "Random by steps")
374 and 374_100
|110 (try NoWrap)
467(try "Random by steps")
|220 (try "Random by steps")
494 (try 494_100)
Other examples of CA patterns can be found here.