arXiv subjects

Genaro J. Martínez

Publications and source records attributed to Genaro J. Martínez.

6 recordsLinked to original sources

arXiv2021

Following the spacial dynamics of COVID-19 in Mexico and some notes

Actually, after one year it is recognized that the evolution of COVID-19 is different in each country or region around the world. In this paper, we do a revision to the date about COVID-19 evolution in Mexico, we explain where the main epicenter and states with most high impact. Mexico has a particular geographical position in the American continent because it is a natural bridge between the USA and Latin America, that represents a special point of propagation because between other facts this virus is transported by people of different nationalities migrating to the USA. The research in this paper helps to understand why Mexico is one of the countries with the most high mortality impact by this new virus and how the lockdown works in the population. Finally, we give a practical perspective as this evolution is a complex system.

physics.soc-ph↗

arXiv2018

Simple networks on complex cellular automata: From de Bruijn diagrams to jump-graphs

We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of attraction, and jump-graphs. These networks are used to understand properties of spatially-extended dynamical systems: emergence of non-trivial patterns, self-organisation, reversibility and chaos. Particular attention is paid to networks determined by travelling self-localisations, or gliders.

nlin.CG↗

arXiv2014

Logic gates and complex dynamics in a hexagonal cellular automaton: the Spiral rule

In previous works, hexagonal cellular automata (CA) have been studied as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky reaction. In this paper, we analyse a special kind of hexagonal CA, {\it Spiral rule}. Such automaton shows a non-trivial complex behaviour related to discrete models of reaction-diffusion chemical media, dominated by spiral guns which easily emerge from random initial conditions. The computing capabilities of this automaton are shown by means of logic gates. These are defined by collisions between mobile localizations. Also, an extended classification of complex self-localisation patterns is presented, including some self-organised patterns.

nlin.CG↗

arXiv2014

Complete Characterization of Structure of Rule 54

The dynamics of rule 54 one-dimensional two-state cellular automaton (CA) are a discrete analog of a space-time dynamics of excitations in nonlinear active medium with mutual inhibition. A cell switches its state 0 to state 1 if one of its two neighbors is in state 1 (propagation of a perturbation) and a cell remains in state 1 only if its two neighbors are in state 0. A lateral inhibition is because a 1-state neighbor causes a 1-state cell to switch to state 0. The rule produces a rich spectrum of space-time dynamics, including gliders and glider guns just from four primitive gliders. We construct a catalogue of gliders and describe them by tiles. We calculate a subset of regular expressions $Ψ_{R54}$ to encode gliders. The regular expressions are derived from de Bruijn diagrams, tile-based representation of gliders, and cycle diagrams sometimes. We construct an abstract machine that recognizes regular expressions of gliders in rule 54 and validate $Ψ_{R54}$. We also propose a way to code initial configurations of gliders to depict any type of collision between the gliders and explore self-organization of gliders, formation of larger tiles, and soliton-like interactions of gliders and computable devices.

nlin.CG↗

arXiv2013

Complexity Analysis in Cyclic Tag System Emulated by Rule 110

It is known that elementary cellular automaton rule 110 is capable of supporting universal computation by emulating cyclic tag system. Since the whole information necessary to perform computation is stored in the configuration, it is reasonable to investigate the complexity of configuration for the analysis of computing process. In this research we employed Lempel-Ziv complexity as a measure of complexity and calculated it during the evolution of emulating cyclic tag system by rule 110. As a result, we observed the stepwise decline of complexity during the evolution. That is caused by the transformation from table data to moving data and the elimination of table data by a rejector.

cs.OH↗

arXiv2013

Expressiveness of Elementary Cellular Automata

We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically inspired parameters for biodiversity are applied to the configurations of cellular automata. This article contains a survey of the Elementary Cellular Automata in terms of their expressiveness and an evaluation whether expressiveness is a meaningful term in the context of simulated biology.

nlin.CG↗