Self-similar functions generated by cellular automata (Q2714129)
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scientific article; zbMATH DE number 1603467
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Self-similar functions generated by cellular automata |
scientific article; zbMATH DE number 1603467 |
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11 June 2001
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cellular automata
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self-similarity
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Hausdorff dimension
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Self-similar functions generated by cellular automata (English)
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The authors deal with cellular automata (CA) on the lattice of natural numbers (one-sided CA) or the lattice of integers (two-sided CA). They observe self-similarity properties in a most transparent way in the evolution patterns obtained from finite initial configurations with respect to an additive (or linear) relation, whose state space is a finite field. Results about the Hausdorff dimension of the graphs corresponding to a so-called closed relation (a map) are obtained. Moreover, they also consider an obstruction to the additivity of CA on the two-sided shift space.
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