Abstract
AbstractUsing Rule 126 elementary cellular automaton (ECA), we demonstrate that a chaotic discrete system — when enriched with memory — hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced from original information of the ahistorical system. First, we analyze classic ECA Rule 126 to identify basic characteristics with mean field theory, basins, and de Bruijn diagrams. To derive this complex dynamics, we use a kind of memory on Rule 126; from here interactions between gliders are studied for detecting stationary patterns, glider guns, and simulating specific simple computable functions produced by glider collisions. © 2010 Wiley Periodicals, Inc. Complexity, 2010
Highlights
In this paper we are making use of the memory tool to get a complex system from a chaotic function in discrete dynamical environments
Recent results show that other chaotic functions (Rule 86 and Rule 101) yield complex dynamics selecting a kind of memory, including a controller to obtain self-organization by structure reactions and simple computations implemented by soliton reactions [17]
Based on the idea developed in previous results for obtaining complex dynamics from chaotic functions selecting memory and working systematically, it was suspected that a complex dynamics may emerge in Rule 126 given its relation to regular languages; making use of gliders coded by regular expressions, as it was studied in Rule 110 [26] and Rule 54 [21]
Summary
In this paper we are making use of the memory tool to get a complex system from a chaotic function in discrete dynamical environments. Based on the idea developed in previous results for obtaining complex dynamics from chaotic functions selecting memory and working systematically, it was suspected that a complex dynamics may emerge in Rule 126 given its relation to regular languages; making use of gliders coded by regular expressions, as it was studied in Rule 110 [26] and Rule 54 [21] In this way Rule 126 provides a special case of how a chaotic behaviour can be decomposed selecting a kind of memory into a extraordinary activity of gliders, glider guns, still-life structures and a huge number of reactions. Such features can be compared to Brain Brian’s rule behaviour or Conway’s Life but in one dimension; none traditional ECA could have a glider dynamics comparable to the one revealed in this ECA with memory denoted as φR126maj (following notation described in [18, 17])
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
