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A Catalog of Cellular Automata
Author

Jaime Rangel-Mondragón
Organization: Universidad Autonoma de Querétaro
Department: Facultad de Informatica
Old MathSource #

0211-521
Revision date

2000-11-29
Description

Cellular automata (CA) comprise rules encapsulating mechanisms of evolution that model highly complex behavior. Systematic interest in CA has received considerable impetus from the continuous work of Stephen Wolfram since 1983 (who undertook a computer-based search on the properties of one-dimensional CA) up to the worldwide interest in his book A New Kind of Science.

A one-dimensional CA processes in parallel the simultaneous change of state of each individual cell forming a collection arranged in a line. These individual changes are performed in accordance to the states of each one of their neighbors including itself through the application of a local transition rule. It is remarkable the fact that from such a simple mechanism we are able to generate a behavior of profoundly intrincate complexity, all this in contrast to the general impression that effects are always preceded by causes of at least comparable complexity.

In this work we assume only two possible states and the allotted set of states to be Range[0, b-1], where b varies from 2 to 4 calling such CA dyadic, triadic and tetradic respectively. This work comprises the generation and display of catalogs of families of these CA covering irreducible, totalistic and reversible ones.

The file CAcatlog.zip contains the main notebook along with the data files generated after several weeks of computationally-intensive sessions.
Subject

*Mathematics > Discrete Mathematics > Cellular Automata
Keywords

totalistic, invertible, reversible, all-ones problem, powers of integers, fractals
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CAcatalog.nb (13.2 MB) - Mathematica notebook
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CAcatalog.zip (1.7 MB) - Zip archive
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allOnes4 (110 KB) - data file
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allOnes5 (208.3 KB) - data file
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allOnes6 (208.8 KB) - data file
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allRules2 (630 B) - data file
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reversible2 (135 B) - data file
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reversible4 (612 B) - data file
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totalistic2 (80 B) - data file
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totalistic3 (8.4 KB) - data file
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totalistic4 (4.1 MB) - data file