This book addresses two disciplines that have traditionally occupied completely different realms: quantum information and computation, and game theory. Helping readers connect these fields, it appeals to a wide audience, including computer scientists, engineers, mathematicians, physicists, biologists or economists. The book is richly illustrated and basic concepts are accessible to readers with basic training in science. As such it is useful for undergraduate students as well as established academicians and researchers. Further, the didactic and tutorial-like style makes it ideal supplementary reading for courses on quantum information and computation, game theory, cellular automata and simulation.

Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian: only the actual configuration is taken into account to generate the next one. Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced. The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects.

This book addresses two disciplines that have traditionally occupied completely different realms: quantum information and computation, and game theory. Helping readers connect these fields, it appeals to a wide audience, including computer scientists, engineers, mathematicians, physicists, biologists or economists. The book is richly illustrated and basic concepts are accessible to readers with basic training in science. As such it is useful for undergraduate students as well as established academicians and researchers. Further, the didactic and tutorial-like style makes it ideal supplementary reading for courses on quantum information and computation, game theory, cellular automata and simulation.