Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore

• Autor(a) principal: Rocha, Felipe Gonçalves da
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do Mackenzie
• Texto Completo: https://dspace.mackenzie.br/handle/10899/28608
• topic: autômatos celulares bidimensionais; conservabilidade vizinhança de Moore; vizinhança de Moore; equivalência dinâmica; composição de regras; decomposição de regras por divisão e perturbação; CNPQ::ENGENHARIAS

Number conserving cellular automata can represent or model equally conservative realworld dynamics. In the literature, this property has been extensively addressed for the one-imensional case and for the two-dimensional von Neumann neighbourhood. The present work aimed at a computational exploration in the space of two-dimensional rules with Moore neighbourhood of unit radius. As such, the main related concepts were revisited, such as number conservation in the elementary space and in the two-dimensional case with von Neumann neighbourhood; the general conditions for number conservation in hyper-rectangular neighbourhoods; the composition of conservative rules; and the decomposition algorithm of division and disturbance rules. From this, it was possible to derive a regular expression for the identity and displacement rules; propose a method to list the traffic rules of the space at issue; and introduce a heuristic to obtain rules in the desired space, based on the composition of one-dimensional conservative rules. Additionally, when applying the split-and-perturb decomposition algorithm, the conservative rules in Moore neighbourhood obtained were revealed to be the same as those in von Neumann’s 4-dimensional neighbourhood. The conservative rules obtained were analysed from a phenomenological point of view, which led to their grouping into classes, and revealed a rich variety of patterns of temporal evolution.