Complex Systems

Mechanisms for Pattern Generation Download PDF

Karel Culik II
Department of Computer Science,
University of South Carolina, Columbia, SC 29208, USA

Jarkko Kari
Academy of Finland
Mathematics Department,
University of Turku, 20500 Turku, Finland


Three mechanisms---cellular automata, finite automata, and L-systems---for generating static patterns are compared. Matrix substitution systems, nondeterministic extensions of iterative matrix homomorphisms, are also introduced and shown to be equivalent to finite automata. Two different ways for taking the limit of a sequence of finite resolution patterns produced by any of the mechanisms are studied: one gives an infinite resolution pattern on the unit square, the other one a pattern of infinite size.