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
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.
