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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)

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)

We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations (gliders, oscillators, glider guns, puffer trains, etc), analyze spatio-temporal dynamics of collisions between… (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)

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)

Patterns, originating from different sources of perturbations , propagating in a precipitating chemical medium do usually compete for the space. They subdivide the medium onto the regions unique for an initial configuration of disturbances. This subdivision can be expressed in terms of computation. We adopt an analogy between precipitating chemical media… (More)

We investigate the construction of all the periodic structures or " gliders " up to now known in the evolution space of the one-dimensional cellular automaton Rule 110. The production of these periodic structures is developed and presented by means of glider collisions. We provide a methodology based on the phases of each glider to establish the necessary… (More)

Two symbol manipulation languages are presented. REC (an acronym for Regular Expression Compiler) is a very compact language possessing a simple control structure. C<sc>ONVERT</sc> is a pattern matching and substitution language well suited to problems whose solution may conveniently be expressed in terms of transformation rules. REC is useful when… (More)