Mathematica 9 is now available

Wolfram Library Archive

All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

A Catalog of Cellular Automata

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

Revision date


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 contains the main notebook along with the data files generated after several weeks of computationally-intensive sessions.

*Mathematics > Discrete Mathematics > Cellular Automata

totalistic, invertible, reversible, all-ones problem, powers of integers, fractals
Downloads Download Wolfram CDF Player

CAcatalog.nb (13.2 MB) - Mathematica notebook
Download (1.7 MB) - Zip archive
allOnes4 (110 KB) - data file
allOnes5 (208.3 KB) - data file
allOnes6 (208.8 KB) - data file
allRules2 (630 B) - data file
reversible2 (135 B) - data file
reversible4 (612 B) - data file
totalistic2 (80 B) - data file
totalistic3 (8.4 KB) - data file
totalistic4 (4.1 MB) - data file