Present day classical computers, developed during the last sixty years are logic machines, based on binary logic and arithmetic, acting on discrete valued (binary coded) data. Its unique property is algorithmic (stored) programmability, invented by John von Neumann. The mathematical concept is based on a universal machine on integers (Turing machine). Cellular automata, introduced also by J. von Neumann, are fully parallel array processors with all discrete space, time and state values. Their beautiful properties have been recently rediscovered showing the deeper qualitative properties, if we allow the states and time to be continuous values like in CNN, a broader class of dynamics will be generated. Even more, the fundamental conditions to generate complex features at the edge of chaos have been established: the need of local activity. Taking one step further, and using the CNN-UM architecture, a new world of algorithms is opening.
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T. Roska (2005) studied this question.
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