Registered: Apr 2005
Posts: 11

The Squaring and Primes cellular automata constructions described on page 1109 and illustrated on pages 639 and 640 are intriguing. Is there a collection of such 1D CA constructions in the public domain somewhere?

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Registered: Jul 2004
Posts: 4

Some 1D CA constructions that perform some simple arithmetical functions can be found at:

http://www.stetson.edu/~efriedma/mathmagic/0103.html

Although small, to my knowledge, this is the only collection of arithmetical CA in the public domain.

I have been working with arithmetical CA for some time now and have found, by mixing two different methods (see http://forum.wolframscience.com/sho...s=&threadid=771), thousands of different rules that can perform all types of simple arithmetical calculations. Right now I am in the process of summarizing all these different families of CA and refining a new method for doing searches in rule spaces with many colors.

The book "Collision-Based Computing" edited by Andrew Adamatzky contains a collection of papers related to the particle based approach of computing with 1D and 2D CA. There is also a review paper (although a bit dated now) "Computation in Celllular Automata: A Selected Review" by Melanie Mitchell which can be found at:

http://www.cs.pdx.edu/~mm/ca-review.pdf

These two references deal with more general subjects and focus on the density classification task and the firing squad synchronization problem as examples of computations, rather than the more specific type of CA that you are asking for, but maybe you'll find them interesting.

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