WOLFRAM|DEMONSTRATIONS PROJECT

Coupled Cellular Automata: Symbiotic Patterns and Synchronization

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zoom
seed
CA
1
96
CA
2
117
CA
3
172
CA
4
94
output
input
coupling
input
X =
CA
1
X
Y
F

+
CA
2
X
Y
Y =
CA
3
X
Y
G

+
CA
4
X
Y
X-output
Y-output
Modeling of cooperative behavior has great relevance to a wide range of scientific fields. Often trivial systems with primitive standalone behavior produce rich dynamics working in collaboration. This Demonstration allows you to couple up to four different one-dimensional elementary cellular automata (1D-eCA) and produce behaviors beyond those of single 1D-eCA. Patterns of these 1D-eCA in the standalone case are shown in four rectangles on the left. They can be compared to the two patterns of coupled evolution on the right (the rectangles labeled
X
-output and
Y
-output). Often, simple evolution of standalone 1D-eCAs results in rich coupled dynamics of
X
and
Y
. Such behavior is "symbiotic", since the coupled behavior of
X
and
Y
cannot be obtained from standalone 1D-eCA. Another feature of coupled behavior is "synchronization". Namely, the pattern of
X
is generally different from the pattern of
Y
, yet often similar "twin" sub-patterns can be noticed in
X
and
Y
. In all images, the time of evolution goes from top to bottom. The four images on the left are just samples of standard 1D-eCA Wolfram rules. These four images are not used directly to create
X
and
Y
patterns and are given only for comparison with
X
and
Y
. Browse the snapshots for interesting patterns. See the "Details" section for a more technical discussion of the implemented coupling.