Publisher's Synopsis
Cellular Automata (CA) are spatiotemporal discrete systems (Neumann, 1966) that can model dynamic complex systems. A variety of problem domains have been reported to date in successful CA applications. Originally developed by John von Neumann in 1948, following suggestions from Stanislaw Ulam, for the purpose of showing that self-replicating automata could be constructed. Von Neumann's construction followed a complicated set of reproduction rules but later work showed that self-reproducing automata could be constructed with only simple update rules. A cellular automata consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. More generally, cellular automata are of interest because they show that highly complex patterns can arise from the application of very simple update rules. While conceptually simple, they provide a robust modeling class for application in a variety of disciplines, e.?g. as well as fertile grounds for theoretical research. Additive cellular automata are the simplest class of cellular automata. Additive Cellular Automata: Theory and Applications will help you understand the basics of CA and prepare for further research. The book demonstrates the matrix algebraic tools that describe both group and non-group CA and intends an extensive variety of applications to resolve real life problems. This book develops the theory of additive cellular automata (ACA). The theoretical framework proposed, provides the complete characterization of the cyclic state space generated by an ACA. An ACA is additive in the sense that it employs affine transformation rather than a linear transformation implemented in a typical linear cellular automata (LCA). The theory of LCA provides the foundation of the proposed characterization of ACA.