Nature, as was apparent after B. Mandelbrot [1], has a predominantly fractal structure. There comes a time of fractal geometry. The fractal geometry plays an important role in the contemporary science. Its goal is to present a model for irregularity and fragmentation in Nature. Its realm can be traced from scales of galaxies up to subnuclear scales. Integer-dimensional objects are special cases of fractal-dimensional ones, the latter being most commonly encountered. This being the case, fractal structures become an important part of the common language of science [2], and we have to have some appropriate methods and tools to describe and manipulate them.
Fractals of a broad class are described by Deterministic Iterated Function Systems (IFSs) [2]. Beyond that point Deterministic IFSs enable us to describe recurrent asymmetric binary Neural Networks [3,4] and a special class of Cellular Automata [5]. The last case is developed here further to the case of Automata Networks.
If an IFS is given, we can construct a Neural Network [3,4,8] or a Cellular Automaton [5] (think it as an Automata Network!) capable to realize its latent dynamics and generate an approximation of its attractor. The collage theorem [2] gives us hope to reach (in principle) any desired accuracy.
In the report, an algorithm is described for building an automata network for a given iterated function system. An evolving algebra approach for description of the automata network dynamical systems is also mentioned.