## Classificação automática do comportamento dinâmico automato celulares binários unidimensionais

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##### Tipo

Tese

##### Data

2019-10-02

##### Autores

Nogueira, Marcelo Arbori

##### Orientador

Oliveira, Pedro Paulo Balbi de

##### Título da Revista

##### ISSN da Revista

##### Título de Volume

##### Membros da banca

Ruivo, Eurico Luiz Prospero

Costa , Pedro Contino da Silva

Schimit, Pedro Henrique Triguis

Bahamon, Dario

Costa , Pedro Contino da Silva

Schimit, Pedro Henrique Triguis

Bahamon, Dario

##### Programa

Engenharia Elétrica

##### Resumo

The variability of temporal evolution generated by cellular automata comes from the large
number of possible rules, their initial con guration, the number of states, the number
of cells in the neighborhood and the dimension of the lattice. Even for the simplest
cases, the number of rules in the space can easily reach billions, and even if the lattice is
one-dimensional, the number of possible temporal evolutions grows exponentially as the
lattice size grows. Therefore, to classify the typical dynamics of the temporal evolutions
is a dauting endeavour, so that any automated process for the task is clearly useful.
We report here the development of two classi ers of the dynamics presented by the
temporal evolutions, according to Wolfram's 4-class classi cation scheme, based on the
elementary space, but also aiming to apply it to a larger space, whose classi cation is
unknown, namely, the one with 4 cells in the neighbourhood and 2 possible states.
At rst, a review was made of the classi cation method developed byWuensche (1998),
in which, at each time step of the cellular automaton, the entropy variation observed in the
temporal evolution was associated with the generating rule classes. The results obtained
served as a reference for the classi ers developed further on.
One of the two classi ers relied on a convolutional neural network, trained to predict
the rule class that generated a temporal evolution. Since the 4 classes do not have the
same amount of rules, which a ects the network training, the rules were chosen randomly,
while keeping the same proportion for each class.
The second classi er used texture analysis to extract, from the temporal evolutions,
information of the neighborhood con gurations of the cells, which allowed for the construction
of a frequency spectrum of these con gurations. A single spectrum, with the
average frequency of each possible con guration associated with the generating rule was
then included in a dataset, and used in the k-NN algorithm to obtain the prediction of
the class at issue.
The classi ers were evaluated in two ways: at rst, to de ne the classes of the elementary
space, according to their typical behaviors, which are the most common ones
displayed in a set of temporal evolutions. The predicted classes could be compared with
the known classi cation of elementary space and total accuracy was observed for both.
For the space with 4 cells in the neighbourhood, a visual classi cation of the entire space
was performed. In this case, none of the classi ers achieved high accuracy. Still, they were
able to extract information from that space, which is larger than the elementary space.
Finally, confusion matrices were used to evaluate the quality of the classi ers with data
from both spaces, with both classi ers having di culties in classifying the space with 4
cells in the vicinity.

##### Descrição

##### Palavras-chave

autômato celular , rede neural convolucional , classificação de comportamento dinâmico , classes de Wolfram , espectro de con guração de vizinhança , aprendizado profundo

##### Citação

NOGUEIRA, Marcelo Arbori. Classificação automática do comportamento dinâmico automato celulares binários unidimensionais. 2019. 89 f. Tese (doutorado em Engenharia Elétrica e Computação) - Universidade Presbiteriana Mackenzie, São Paulo, 2019.