Registered: Jan 2004
Posts: 350

On page 1129 of the NKS book there is a discussion of the difficulty in emulating discrete systems with continuous systems.

Here is an example of a cellular automaton that uses the cosine function to emulate randomness similar to that in elementary rule 30.

The rule is: Cos[Apply[Plus, Flatten[ {neighborhood} ]]], where neighborhood is the cell and its left and right neighbors.

Initial conditions are the reals: Flatten[ { Table[ 0., {255} ], {1.}, Table[ 0., {255}]}].

Both elementary rule 30 and this cosine function are shown in the attached graphic.

Lawrence J. Thaden has attached this image:

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L. J. Thaden

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Registered: Aug 2003
Posts: 712

Just a Mathematica simplification - you can just use Cos[Total[#]]& of the neighborhood list you get from Paritition. You don't need to Flatten a first level list, and the Apply with Plus construction can be simplifed to Total.

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