Calculating growth rates and moments for additive cellular automata

Calculating growth rates and moments for additive cellular automata

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Article ID: iaor19921408
Country: Netherlands
Volume: 35
Issue: 1
Start Page Number: 47
End Page Number: 65
Publication Date: Jan 1992
Journal: Discrete Applied Mathematics
Authors:
Keywords: cellular automata
Abstract:

Suppose that the cellular automation F is the graph of an additive rule modulo p. It is shown how to compute the growth rates of the numbers of each kind of finite block of symbols, if p is a power of a prime and the initial configuration is finite. All accessible blocks are then proved to have the same growth rate for a fixed F. If the modulus is not a power of a prime, different blocks may have different growth rates. These growth rates are identical with the Hausdorff dimensions of related fractals. The methods generalize further to yeild explicit computations of the centers of mass and higher moments for the fractals.

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