Exploração computacional dos espectros de Fourier de autômatos celulares elementares assíncronos

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Etchebehere, Gustavo Santarsiere
Oliveira, Pedro Paulo Balbi de
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Ruivo, Eurico Prospero
Macau, Elbert Einstein Nehrer
Engenharia Elétrica
The spectral analysis and asynchronous cellular automata subjects are relevant among the cellular automata scientific community. Asynchronous cellular automata are variants of cellular automata at which the cells have their state shifted at distinct time paces, instead of being all updated at the same global pace, as in the conventional model. The asynchronous updates, deterministic or probabilistic, have been receiving a progressive rise of attention by the pertinent scientific community, due to the bigger flexibility the cellular automata acquire concerning computability as well as for the better suitability to model natural systems. Spectral analysis is a set of techniques to transpose data from the space domain to the frequency domain. Among its many applications, this technique is applied to the study the limit behavior of the cellular automata rules, which consist in calculating the Fourier spectrum of these cellular automata, for a given lattice size, number of iterations, and set of lattices as a sampling. At the present dissertation are done studies concerning the impact that distinct deterministic updating sequences have over the shape of the elementary space rules’ Fourier spectra. There have been defined three distinct asynchrony patterns families, each one displaying itself at ten distinct asynchrony patterns, for all the rules of the elementary space of cellular automata. There are described and classified the shape shifts of the spectra obtained by the lattice asynchronous updating, as well as other phenomena described with the experiment. The newly obtained spectra were groped in spectral similarity classes for study as well. The focus of the dissertation is to document, by means of computational explorations, how the presence of asynchrony effects the formation of the asynchronous automata Fourier spectra, and identify reasons for these phenomena.
espectro de Fourier , transformada discreta de Fourier , autômatos celulares elementares , autômatos celulares assíncronos , sistemas dinâmicos discretos , comportamento dinâmico
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ETCHEBEHERE, Gustavo Santarsiere. Exploração computacional dos espectros de Fourier de autômatos celulares elementares assíncronos. 2019. 81 f. Dissertação ( Engenharia Elétrica ) - Universidade Presbiteriana Mackenzie, São Paulo, 2019.