Cellular Automata with Memory

Résumé : Memory is a universal function of organized matter. What is the mathematics of memory? How does the memory affect space-time§behaviour of spatially extended systems? Does the memory increase complexity? Cellular automaton models give us the answers. A cellular automaton is an array of locally connected finite state machines or cells. The cells update their states simultaneously in§discrete time by the same cell-state transition rule. Classical cellular automata are memoryless: a cell updates its state depending on§current states of its neigbours.§§The book revolutionizes the conventional view on cellular automaton evolution by allowing cells to update their states looking at past§states of their neighbours and analyzes the effect of memory on a wide range of spatialized discrete dynamical systems scenarios.§§The book demonstrates that cellular automata with memory are not only priceless tools for modelling of natural phenomena but unique§mathematical and aestethic objects.§§Dr. Ramon Alonso-Sanz is a Senior Lecturer in Statistics and Operational Research in the Polytechnic University of Madrid (UPM) Spain. He has a long experience in teaching Mathematics Statistics Operational Research and and lately Cellular Automata to students at UPM. He is member of the research Group of Complex Systems of UPM since its foundation in 2 5 and of the Int. Group of§Unconventional Computing since 2 6.§Dr. Alonso-Sanz has been involved is numerous Spanish funded research projects and he is currently involved in the UK EPSRC funded§Project: «Discrete Dynamical Systems with Memory: A New Tool for Modelling Complexity». He co-organized AUTOMATA the annual meeting of cellular automatists in 2 8.