Automata network dynamical systems for construction of fractal objects

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 a ragged shape and fractional dimension. Fractals of a broad class are described by deterministic iterated function systems (IFSs). Simultaneously, the iterated function systems give a base for ‘automata networks’ capable to realize their latent dynamics. When such a dynamics become 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 this report, an algorithm is described for building an automata network for a given iterated function system. It is worth noting that the ‘automata networks’ can be considered generalizations of cellular automata, the main difference is that 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.