Harold V. McIntosh

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Graph theory plays several important roles in the theory of cellular au-tomata, one of which consists in describing the evolution of the automaton, and another of which consists in relating local properties to global properties. Evolution is described by local rules mapping cell neighborhoods into its subsequent state; because successive neighborhoods(More)
One-dimensional cellular automata are dynamical systems characterized by discreteness (in space and time), determinism and local interaction. We present a procedure in order to calculate ancestors for a given sequence of states, this procedure is based on a special kind of graph called subset diagram. We use this diagram to specify subset tables for(More)
Rule 54, a two state, three neighbor cellular automaton in WolframÕs 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.
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)
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)
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)
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)
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)
Reversible cellular automata are discrete dynamical systems based on local interactions which are able to produce an invertible global behavior. Reversible automata have been carefully analyzed by means of graph and matrix tools, in particular the extensions of the ancestors in these systems have a complete representation by Welch diagrams. This paper(More)