The Mathematics of Sequential Dynamical Systems

Sequential Dynamical Systems are a generalization of cellular automata. They have been used for a variety of computer simulations: traffic modeling in large cities, the spread of diseases, packet traffic in data lines, capital flow on world markets. We will try to give a general definition of Sequential Dynamical Systems, show some of the simulations and then address the question of a mathematical theory behind these systems. One of the more interesting questions in this context is: what is a simulation and can there be optimal simulations. We will show how to approach these problems and give partial answers.