InterJournal Complex Systems, 546
Status: Accepted
Manuscript Number: [546]
Submission Date: 20506
Revised On: 20910
Iterons: the emergent coherent structures of IAMs
Author(s): Pawel Siwak

Subject(s): CX.04.01, CX.04.02, CX.04.03, CX.04.04

Category: Article

Abstract:

Iterons of automata are periodic coherent propagating structures (substrings of symbols) that emerge in cellular nets of automata. They are like fractal objects; they owe their existence to iterated automata maps (IAMs) performed over strings. In this paper we present a unified automaton approach to the processing mechanisms capable of supporting coherent entities in evolving strings. We consider two issues. The first one is that automaton operations and converted strings interact like a medium (or field) and its disturbances. The other is that we identify the spatial extend of any coherent structure by the sequences of operations of the underlying automaton. The iterons comprise of particles and filtrons. For the filtrons we consider one-way 1-d homogeneous net with an automaton M, and show the filtrons as special M-segments that involve certain sequences of operations of automaton M. These sequences are related to a class of paths on the automaton state diagram. For the particles we consider de Bruijn graph G of their cellular automaton (CA), and show the particles as G-segments related to special sequences of elementary rules of CA. We present some examples of various phenomena of interacting filtrons, like multifiltron collisions, fusion, fission, and spontaneous decay or quasi-filtrons, and also some automata capable of supporting these events.

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