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The appearance of these triangles suggests the analysis of the plane generated by the evolution of Rule as a two dimensional shift of finite type.

Some researches lines about Rule Matthew Cook wrote an eight page introduction [Cook 99] listing gliders okada junichi dating services A through H and a glider gun.

Thus the transition function transforms the neighbourhoods,and into state 1 and the neighbourhoodsand into state 0. The most important result both in the study of Rule and in cellular automata theory in the last twenty years, is well represented by the demonstration made by Cook that Rule is universal.

Depending on the values in cells of the neighbourhood, a new value is defined for the central cell in the next generation.

Rule is one of 4 equivalent rules: The transition function simultaneously evaluates a central cell with regard to its left and right neighbours. In that document Cook makes a comparison between Rule and Life, finding some similarities and suggesting that Rule may be called LeftLife.

Elemental Cellular Automaton Rule The existence of several periodic structures known as gliders in the evolution space of the one-dimensional cellular automaton Rulehas important lines of investigation in cellular automata theory such as: Thus number talks about the decimal notation of the evolution rule which is the binary sequence Whatever the merits of this classification, Rule was awarded its own appendix Table 15 in reference [Wolfram 94].

## File usage

The demonstration is realized simulating a novel cyclic tag system CTS [Cook 04] and [Wolfram 02]; with well-defined blocks of gliders by means of collisions. In the model of Conway, universality is demonstrated simulating a register machine through logic gates, constructing the system with gliders and glider guns.

All snapshots start with equivalent random initial conditions. The automaton is defined by a finite one-dimensional array where each one of its elements takes the value 0 or 1 from the state set, this array represents the initial configuration of the system.

The subset of regular expressions is explained and given in detail see regular language in Rule section. A neighbourhood is formed by three cells, a central element,a neighbour to the right and another into the left. Then we can say that Cook has the last reduction with the simplest cellular automaton able to produce universal computation.

The transition function evaluates synchronously each neighbourhood to calculate the new configuration. Rule is a one-dimensional cellular automaton with two states and a linear three cells neighbourhood.

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It has even been suggested that Rule belongs to the exceptional class IV of automata whose chaotic aspects are mixed with regular behaviours; but in this case the background where the chaotic behaviour occurs is textured rather than quiescent, a tacit assumption in the original classification.

The relevance of the demonstration realized by Cook is to reduce the neighbourhood, state set and dimensionality to the possible minimum. Gliders in the CTS are useful to represent process collision-based computing.

It contains specimens of evolution including a list of thirteen gliders compiled by Doug Lind and also presents the conjecture that the rule could be universal.

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The list of Cook shows new gliders which do not appear in the list of Lind, gliders with rare extensions and a pair of gliders of complicated construction. In this time, some researches have finished important and related works around of the universality in Rule This study would seem to be reflected in an approach to equilibrium statistics, via a power law rather than exponentially.

Equivalent rules with Rule At the present time Paul Rendell has implemented a complicated universal Turing machine in Life.