Computational Mechanics of Cellular Automata: An Example

J. E. Hanson
Santa Fe Instutute
1399 Hyde Park Rd.
Santa Fe, NM 87501, USA

and

J. P. Crutchfield
Physics Department
University of California
Berkeley, California 94720, USA

Abstract

We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of elementary one-dimensional cellular automaton rule 54. The CA's dominant regular domain is identified and a domain filter is constructed to locate and classify defects in the domain. The primary particles are identified and a range of interparticle interactions is studied. The deterministic equation of motion of the filtered space-time behavior is derived. Filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher-level defects, particle interactions, and secondary domains. We define the emergence time at which the space-time behavior condenses into configurations consisting only of domains, particles, and particle interactions. Taken together, these techniques serve as the basis for the investigation of pattern evolution and self-organization in this representative system.

Citation

J. E. Hanson and J. P. Crutchfield, Computational Mechanics of Cellular Automata: An Example, Santa Fe Institute Working Paper 95-10-95.

To transfer a copy of the entire paper click on its title.

Compressed (Uncompressed) size = 496 (2833) kb.

To transfer a copy consisting of smaller pieces
click on the following page ranges:

All files stored as Unix-`compress'ed PostScript.
Above, kb = kilobytes.
For FTP access to these files use ftp.santafe.edu:/pub/CompMech/papers.
Last modified: 18 October 1995, JEH