Automata Network Dynamical Systems for Construction of Fractal Objects

Vasily M. Severyanov
severyan@jinr.ru
Joint Institute for Nuclear Research
141980 Dubna, Russia

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. In addition, in the 2D case the algorithm enables for interactive construction of fractals and the iterated function systems describing them. It is worth to note that the automata networks can be considered as a special case of Cellular Automata, the main difference is our automata networks have non-regular structure of the system of the cell neighborhoods. An evolving algebra description of the automata network dynamical systems is also given.