Classificação automática do comportamento dinâmico automato celulares binários unidimensionais - Nogueira, Marcelo Arbori (2019)
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.