Reliable Cellular Automata with Self-Organization

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in ``software'', it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary size and content. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of ``self-organization''. The latter means that unless a large amount of input information must be given, the initial configuration can be chosen homogeneous.Comment: 166 pages, 17 figure

Cellular automata for real-time generation of infinite cave levels

This paper presents a reliable and efficient approach to procedurally generating level maps based on the self-organization capabilities of cellular automata (CA). A simple CA-based algorithm is evaluated on an infinite cave game, generating playable and well-designed tunnel-based maps. The algorithm has very low computational cost, permitting realtime content generation, and the proposed map representation provides sufficient flexibility with respect to level design.peer-reviewe

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

Simulating city growth by using the cellular automata algorithm

The objective of this thesis is to develop and implement a Cellular Automata (CA) algorithm to simulate urban growth process. It attempts to satisfy the need to predict the future shape of a city, the way land uses sprawl in the surroundings of that city and its population. Salonica city in Greece is selected as a case study to simulate its urban growth. Cellular automaton (CA) based models are increasingly used to investigate cities and urban systems. Sprawling cities may be considered as complex adaptive systems, and this warrants use of methodology that can accommodate the space-time dynamics of many interacting entities. Automata tools are well-suited for representation of such systems. By means of illustrating this point, the development of a model for simulating the sprawl of land uses such as commercial and residential and calculating the population who will reside in the city is discussed

Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales

Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise measures of complexity, emergence, self-organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales.Comment: 42 pages, 11 figures, 2 table

Restricted density classification in one dimension

The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It is not known whether a one-dimensional cellular automaton with binary alphabet can classify all Bernoulli random configurations almost surely according to their densities. We show that any cellular automaton that washes out finite islands in linear time classifies all Bernoulli random configurations with parameters close to 0 or 1 almost surely correctly. The proof is a direct application of a "percolation" argument which goes back to Gacs (1986).Comment: 13 pages, 5 figure