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Prospecting for Complexity in k=3, r=1 Cellular Automata

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generate random rule
generate the identity rule
presets
all 3-cycles
all 2-cycles
all 1-attractors
all 2-attractors
●
prior rule
add complexity
shuffle
add simplicity
display
CA
finite state graphs
initial condition
single 1
single 2
de Bruijn
random
​
color scheme
SunsetColors
color map
colorize horizontal runs
colorize this digit
0
1
2
color treatment of other digits
normal
make all white
make all black
conflate
steps
124
pixel constrained
6161507679144
​
​
0
3-cycle
1
2-cycle
4
2-attractors
4
1-attractor
0
identity
​
​
Exploring the
k=3
,
r=1
one-dimensional cellular automata (CA) with over 7 trillion rules is daunting. This rule explorer attempts to collect rules with similar behavior together, and furthermore, to create a feeling of control when prospecting for simple or complex behavior.
You do not specify a specific rule number with this widget, but rather choose one of the preset starting positions and then apply small perturbations to the rule specification. The initial presets include "generate random rule", "generate the identity rule", and four other presets with strange names like "all 3-cycles" or "all 1-attractors". From one of these starting positions click the "add complexity" or "add simplicity" button to move in the desired direction of more or less complexity, or click the "shuffle" button to transition laterally to another equally complex rule.
See the Details section for a complete description of all the controls and a discussion of the underlying methodology, which is framed around the notion of finite state machines.
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