In Wolfram’s book “A New Kind of Science” he studies cellular automata. What is also interesting is the approach he is taking. Rather than take something we know and try to figure out the rules, he tries different rules to see what they will create. While his book was badly received when it came out, other’s have found great success using this approach recently.
Wolfram was hardly the first to use cellular automata to mimick real life. Martin Gerhardt and Heike Schuster created ‘HodgePodge’ a cellular automata to mimic a chemical reaction. They explained it as using a discrete form of a differential equation. Since we have described most natural phenomena with differential equations that may explain why we have not done more with cellular automata. We just haven’t needed it. We may find use for it in things we can not yet easily describe with differential equations.
For example, cellular automata has found success in artificial intelligence in solving echohydraulics modeling problems. Cellular automata is also being used in pattern recognition, image processing, fluid mechanics and bioinformatics.
Cellular automata is simple rules repeated over and over. While one would expect simple patterns to emerge and repetitive patterns to emerge, non-repetitive and complex patterns also emerge in some cases. The two examples shown use only two colors and simple rules. Three colors leads to many more complex designs.
Nested: If either neighbor but not both neighbors in previous row are black-> color this cell black else color it white.
Irregular: If self and right neighbor in previous row are white then self is same color as left neighbor in previous row. If self and right neighbor are not both white then self is opposite color of left neighbor in previous row.
Java automata examples
A New Kind of Science, Talk at US by Stephen Wolfram
CelLab, Cellular Automata Laboratory
A New Kind of Science ( book is available online and free)
Some of the recent controversy about Wolfram’s book
Cellular Automata Links
An Introduction to Lindenman Systems ( related subject )
The Primordial Soup Kitchen
One dimensional cellular automata Java applet
A weakly universal cellular automaton in the hyperbolic 3D space with three states
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