As I have explored the Cellular Automata phenomenon (see previous posts), I have tried to quantify the variability of their outputs, their periodicity via graphs. Some of these have turned out to be quite aesthetically pleasing in addition to elucidating the richness of CA versatility.
See for yourself!
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This is a phase space diagram - it maps transitions from some state mapped at time t to time t+1.
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This is also a phase space diagram but with much fewer phase states and fewer transitions. Amazingly, it is quite possible for the same CA to generate both of the above graphs - the variability arising purely from different initial conditions.
A few more to drive the point home - all of these were from a single CA (same rules) but with different initial conditions.
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(initial condition bitmask: 57)
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(initial condition bitmask: 109)
The one below is "Rule 90" CA - the short version and then a few variations - projections onto a torus and a sphere.
Finally, rule 30 CA:
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