Behavior of Topological Cellular Automata
Paul Halpern
Gaetano Caltagirone
Department of Mathematics and Physics,
Philadelphia College of Pharmacy and Science,
43rd Street and Woodland Avenue, Philadelphia, PA 19104 USA
Abstract
We introduce a new type of cellular automaton, one in which the link structure is dynamically coupled to the site values. The automaton structures are altered using simple Boolean rules, while the sites themselves are assigned values based on the mod 2 rule. We compare these dynamics to those in which the link structure is altered randomly and find that in the former case stable structures of noninteger dimensionality emerge. Fully exploring this model, we observe the effects of value rule alteration, initial lattice structure alteration, and alteration in the initial value seeding and observe patterns of self-organization, growth, decay, and periodicity. Finally, we comment on the relationship between this model and randomly generated Kauffman nets.
