Detection of filter-like cellular automata spectra

Abstract

The Fourier spectra of one-dimensional cellular automata give a quantitative and qualitative characterisation of the average final configurations obtained out of their rules, as they are applied to sets of random initial configurations. The elementary cellular automata rule space presents spectra that bring to mind those of digital filters, and the same happens to some of the cellular automata rules obtained through composition of particular elementary cellular automata. As such, one might be willing to discover other filter type rules that might exist in larger spaces. In order to explore the possibility of detecting these cellular automata in a larger space, two methods are applied: a Multilayer Perceptron and the k-Nearest Neighbours classification algorithm. Both algorithms presented considerably high accuracies, with the Multilayer Perceptron showing an overall lower false negative rate, thus indicating that the methods may be generalised to other rule spaces and to the detection of other features, providing an automatic method to detect features in cellular automata spectra.