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A Strategy for Exploring k=2, r=2 Cellular Automata

random seed
32
number of flips
0
ECA rule
110
initial condition
random
steps
140
140
sharper image
color
B&W
110
1023163644
r
=1 neighborhoods
ECA rule in binary
110
r
=2 neighborhoods
110
110
110
The 256
r=1
elementary cellular automata (ECA) rules can all be found somewhere among the four billion rules of the
k=2
,
r=2
cellular automata (CA). To find this correspondence, associate each three-bit neighborhood of the ECA with the four specific five-bit neighborhoods of the
r=2
CA that have the same three middle bits as the ECA. The resulting pattern is determined solely by the inner three bits, exactly like an
r=1
rule. Essentially, the status of the outermost bits does not matter. But now, what about slight perturbations of this mapping? Will there be similarly shaped CA patterns or radically different patterns?
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