The identification of cellular automata

Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid CA is introduced

Lenia and Expanded Universe

We report experimental extensions of Lenia, a continuous cellular automata family capable of producing lifelike self-organizing autonomous patterns. The rule of Lenia was generalized into higher dimensions, multiple kernels, and multiple channels. The final architecture approaches what can be seen as a recurrent convolutional neural network. Using semi-automatic search e.g. genetic algorithm, we discovered new phenomena like polyhedral symmetries, individuality, self-replication, emission, growth by ingestion, and saw the emergence of "virtual eukaryotes" that possess internal division of labor and type differentiation. We discuss the results in the contexts of biology, artificial life, and artificial intelligence.Comment: 8 pages, 5 figures, 1 table; submitted to ALIFE 2020 conferenc

Growth and Decay in Life-Like Cellular Automata

We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding box placed around them? And do there exist patterns that die out completely? If both of these conditions are true, then a cellular automaton rule is likely to support spaceships, small patterns that move and that form the building blocks of many of the more complex patterns that are known for Life. If one or both of these conditions is not true, then there may still be phenomena of interest supported by the given cellular automaton rule, but we will have to look harder for them. Although our classification is very crude, we argue that it is more objective than Wolfram's (due to the greater ease of determining a rigorous answer to these questions), more predictive (as we can classify large groups of rules without observing them individually), and more accurate in focusing attention on rules likely to support patterns with complex behavior. We support these assertions by surveying a number of known cellular automaton rules.Comment: 30 pages, 23 figure

Resource Sharing and Coevolution in Evolving Cellular Automata

Evolving one-dimensional cellular automata (CAs) with genetic algorithms has provided insight into how improved performance on a task requiring global coordination emerges when only local interactions are possible. Two approaches that can affect the search efficiency of the genetic algorithm are coevolution, in which a population of problems---in our case, initial configurations of the CA lattice---evolves along with the population of CAs; and resource sharing, in which a greater proportion of a limited fitness resource is assigned to those CAs which correctly solve problems that fewer other CAs in the population can solve. Here we present evidence that, in contrast to what has been suggested elsewhere, the improvements observed when both techniques are used together depend largely on resource sharing alone.Comment: 8 pages, 1 figure; http://www.santafe.edu/~evca/rsc.ps.g