COMPUTATIONAL MECHANICS OF CELLULAR-AUTOMATA - AN EXAMPLE

We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of e lementary one-dimensional cellular automaton rule 54. The dominant reg ular domain of the cellular automation is identified and a domain filt er is constructed to locate and classify defects in the domain. The pr imary particles are identified and a range of interparticle interactio ns is studied. The deterministic equation of motion of the filtered sp ace-time behavior is derived. Filters of increasing sophistication are constructed for the efficient gathering of particle statistics and fo r the identification of higher-level defects, particle interactions, a nd 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 techniqu es serve as the basis for the investigation of pattern evolution and s elf-organization in this representative system.