 Automata network dynamical systems for construction of fractal objectsVasily M. Severyanov Mathematics and Computers in Simulation (MATCOM), 2001, vol. 57, issue 3, 317-324 Abstract: 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. Keywords: Fractal geometry; Iterated function systems; Automata networks; Evolving algebras (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:57:y:2001:i:3:p:317-324 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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