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Automata Network Dynamical Systems for Construction of Fractal Objects


V. M. Severyanov


Laboratory of Computing Techniques and Automation,
Joint Institute for Nuclear Research,
141980 Dubna, Russia


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Abstract:

The fractal geometry plays an important role in the contemporary science. In some sense, objects with integer dimension are partial cases of the more general realm of entities having ragged shape and fractional dimension. Fractals of a broad class are described by Deterministic Iterated Function Systems. Simultaneously the iterated function systems give a base for Automata Networks capable to realize their latent dynamics. When such a dynamics is becoming alive (with the help of an appropriate automata network), it finishes in a steady state which is (in the general case) a fractal set. In the report, an algorithm is described for building an automata network for a given iterated function system. It is worth to note that the automata networks can be considered as a generalization of cellular automata, the main difference is our automata networks have non-regular structure of the system of the cell neighborhoods. An evolving algebra approach for description of the automata network dynamical systems is also mentioned.



 
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Next: Introduction
IMACS ACA'98 Electronic Proceedings