Cellular automata provide an interesting avenue into the study of complex systems in general, as well as having an intrinsic interest of their own. Because of their mathematical simplicity and representational robustness they have been used to model economic, political, biological, ecological, chemical, and physical systems. Almost any system which can be treated in terms of a discrete representation space in which the dynamics is based on local interaction rules can be modelled by a cellular automata. The aim of this book is to give an introduction to the analysis of cellular automata (CA) in terms of an approach in which CA rules are viewed as elements of a nonlinear operator algebra, which can be expressed in component form much as ordinary vectors are in vector algebra. Although a variety of different topics are covered, this viewpoint provides the underlying theme. The actual mathematics used is not complicated, and the material should be accessible to anyone with a junior-level university background, and a certain degree of mathematical maturity.
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Cellular automata provide one of the most interesting avenuesinto the study of complex systems in general, as well as having anintrinsic interest of their own. Because of their mathematicalsimplicity and representational robustness they have been used tomodel economic, political, biological, ecological, chemical, andphysical systems. Almost any system which can be treated in terms of adiscrete representation space in which the dynamics is based on localinteraction rules can be modelled by a cellular automata. The aim ofthis book is to give an introduction to the analysis of cellularautomata (CA) in terms of an approach in which CA rules are viewed aselements of a nonlinear operator algebra, which can be expressed incomponent form much as ordinary vectors are in vectoralgebra. Although a variety of different topics are covered, thisviewpoint provides the underlying theme. The actual mathematics usedis not hard, and the material should be accessible to anyone with ajunior level university background, and a certain degree ofmathematical maturity.
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