On the Iota-Delta Function: Universality in Cellular Automata's Representation

Abstract

Universality has always played a major role in every branch of science. Since the advent of cellular automata (CAs), this type of model has been widely applicable to the modeling of physical phenomena. On the other hand, the way the evolution rules were described lacked a unified formulation in terms of mathematical functions. In the present paper, a general formulation that is able to describe every elementary CA is derived. The new representation is given in terms of a new function hereby defined: the iota-delta function.