Approximating cellular automata by finite-dimensional maps
Cellular automata can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications, finite-dimensional approximations have been proposed. The most commonly used one is known as the local structure theory, developed by H. Gutowitz et al. in 1987. The main idea behind this approximation is maximization of entropy, and we will discuss both consequences and possible modification of this approach. We will also present examples of cellular automata for which the local structure maps exhibit "asymptotically correct" behaviour and, at the same time, are amenable to analysis by standard tools of dynamical systems theory.
From cellular automata to unconventional computers
Automata networks are fast discovery and prototyping tools efficient in designing future and emerging computing devices. We demonstrate this on examples of solitons propagation in actin filaments, waves in excitable medium and growing living structures. We show synergy between automaton models, partial differential equations and biophysical processes in experimental laboratory findings.
Modelling and Simulation of Road Traffic
The analysis of traffic systems using methods of statistical physics during the past twenty-five years gave many new and interesting insights into the complex dynamics of road networks. On the basis of data drawn from various detection devices together with assumptions about psychological aspects of the driver behaviour a vast number of models were formulated and accurately investigated. With the help of cellular automata the models became much simpler and more intuitive. Instead of complicated differential equations here only a few basic rules determine the motion of thousands of vehicles. Although many phenomena now are quite well understood there remain lots of open questions. The talk tries to give a survey of the current status of the research in this field.