Cellular Automata: Wolfram’s Metaphors for Complex Systems

In the late 1940’s while he was trying to construct a model for self-reproduction, a machine equivalent to biological systems, von Neumann invented a class of discrete mathematical systems called cellular automata [1]. Almost thirty years after the invention cellular automata underwent a radical reformation when, in the early 1980’s, Wolfram considered them as general mathematical representations of complex systems in nature [2, 3]. His investigations on cellular automata led him to the conviction that the laws for complex systems cannot be formulated as conventional mathematical equations; he proposed that the evolution of these systems can be correctly described only in the form of algorithms, the kind that are used in computer programs. It was the beginning of a new branch of science which Wolfram originally called the science of complexity. This new branch of science is based on the notion of computation [4]. According to Wolfram the evolution of any system, natural or artificial, can be viewed as a computation for which the initial state of the system is the input and the state that emerges after a given interval of time is the output. Cellular automata provided the ground for the discovery and the development of this new science.