CONSERVATION FEATURES IN BINARY COLLISIONS FOR RULE 110 CELLULAR AUTOMATON

Jose M. Sausedo-Solorio ()
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Jose M. Sausedo-Solorio: Centro de Investigación Avanzada en Ingeniería Industrial, Universidad Autónoma del Estado de Hidalgo, Cd. Universitaria, Pachuca, Hidalgo 42184, México

International Journal of Modern Physics C (IJMPC), 2010, vol. 21, issue 07, 931-942

Abstract: This paper investigates collisions of gliders generated by one-dimensional Rule 110 cellular automaton. A specific value associated with each glider and an algebraic equation that describes the collision between two gliders were found. Because the products of the collision between two gliders may result in no gliders or one, two or more gliders, this equation states that the total sum of the associated values corresponding to colliding gliders equals the sum of the values of the gliders which are products of the collision. Moreover, an analogy is proposed between the glider collisions and the collisions of physical particles with the equation corresponding to colliding gliders being similar to the equation of energy conservation in physics. In this scheme, even without carrying out the temporal evolution for a collision, it can be determined if a possible combination of resulting gliders accomplishes the equation corresponding to that collision.

Keywords: Nonlinear dynamical systems; particle collision; cellular automata; Rule 110; gliders; conservation equation; 45.20.df; 89.20.Ff; 89.75.Fb (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0129183110015579

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