Harold V. McIntosh

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Rule 54, a two state, three neighbor cellular automaton in Wolfram s systems of nomenclature, is less complex that Rule 110, but nevertheless possess a rich and complex dynamics. We provide a systematic and exhaustive analysis of glider behavior and interactions, including a catalog of collisions. Many of them shows promise are computational elements. 2005(More)
The one-dimensional cellular automaton Rule 110 shows a very ample and diversified glider dynamics. The huge number of collision-based reactions presented in its evolution space are useful to implement some specific (conventional and unconventional) computable process, hence Rule 110 may be used to implement any desired simulation. Therefore there is(More)
Two algorithms for calculating reversible one-dimensional cellular automata of neighborhood size 2 are presented. It is explained how this kind of automata represents all the rest. Using two basic properties of these systems such as the uniform multiplicity of ancestors and Welch indices, these algorithms only require matrix products and the transitive(More)
Centro de Investigación Avanzada en Ingenierı́a Industrial, UAEH Carr. Pachuca-Tulancingo Km. 4.5, 42020 Pachuca, México E-mail: jseck@uaeh.reduaeh.mx Escuela Superior de Cómputo, IPN Juan de Dios Bátiz S/N, Lindavista, 07738, México, D. F, México E-mail: genarojm@correo.unam.mx Departamento de Aplicación de Microcomputadoras, BUAP Apartado Postal 461,(More)
Rule 110 is a complex elementary cellular automaton able of supporting universal computation and complicated collision-based reactions between gliders. We propose a representation for coding initial conditions by means of a finite subset of regular expressions. The sequences are extracted both from de Bruijn diagrams and tiles specifying a set of phases fi(More)
This paper implements the cyclic tag system (CTS) in Rule 110 developed by Cook in [1, 2] using regular expressions denominated phases fi 1 [3]. The main problem in CTS is coding the initial condition based in a system of gliders. In this way, we develop a method to control the periodic phases of the strings representing all gliders until now known in Rule(More)
Rule 54, in Wolfram’s notation, is one of elementary yet complexly behaving one-dimensional cellular automata. The automaton supports gliders, glider guns and other non-trivial long transients. We show how to characterize gliders in Rule 54 by diagram representations as de Bruijn and cycle diagrams; offering a way to present each glider in Rule 54 with(More)
A reversible cellular automaton is one whose evolution, and therefore the entire past history of any con guration, can be uniquely deciphered. There are degrees of reversibility, depending upon whether the con gurations considered are arbitrary, periodic, or quiescent at in nity; which are subsidiary to more general questions of injectivity and(More)