Fractal and Recurrent Behavior of Cellular Automata
Karel Culik II
Simant Dube
Department of Computer Science, University of South Carolina
Columbia, S.C. 29208
Abstract
In recent years, cellular automata (CA) have been found capable of producing complex behavior. Some examples of cellular automata show remarkably regular behavior on finite configurations. On simple initial configurations, the generated pattern might be fractal or self-similar. In this paper, regular evolution of totalistic linear CA is investigated. In particular, it is shown that additive CA will always produce a highly regular behavior on an arbitrary finite configuration as the initial seed. Totalistic CA with binary function code of the form 
are also studied. The results are extended to trellis automata.
