Phenomenology of reaction-diffusion binary-state cellular automata

We study a binary-cell-state eight-cell neighborhood two-dimensional cellular automaton model of a quasi-chemical system with a substrate and a reagent. Reactions are represented by semitotalistic transitions rules: every cell switches from state 0 to state 1 depending on if the sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if the sum of neighbors in state 1 belong to another specified interval. We investigate space-time dynamics of 1296 automata, establish morphology-bases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still-life compact patterns). We explore reaction-diffusion like patterns produced as a result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22. © World Scientific Publishing Company

Complex dynamics of elementary cellular automata emerging from chaotic rules

We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order and chaotic systems. A number of attempts have been made to classify CA functions on their space-time dynamics and to predict behaviour of any given function. Examples include mechanical computation, \lambda{} and Z-parameters, mean field theory, differential equations and number conserving features. We aim to classify CA based on their behaviour when they act in a historical mode, i.e. as CA with memory. We demonstrate that cell-state transition rules enriched with memory quickly transform a chaotic system converging to a complex global behaviour from almost any initial condition. Thus just in few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory exploring glider dynamics and reactions

Emergence of diverse epidermal patterns by integrating Turing pattern model and majority voting model

The Turing pattern model is one type of reaction-diffusion (RD) model. The first identification of pattern formation by the Turing pattern model in an actual animal was made in the 1990s with the observation of patterns in the sea anemone. But can we assume that all epidermal patterns in animals can be explained by the Turing pattern model? Even for fish, there are some fish that are clearly not Turing patterns, differing significantly from the patterns that can be generated by RD models. For example, the body pattern of the ornamental carp Nishiki goi produced in Japan varies randomly from individual to individual, and it is difficult to predict the pattern of the offspring from that of the parent fish. A model in which these fish patterns are formed randomly is the majority voting model. From this, it can be inferred that the epidermal pattern of fish can be explained by either the Turing pattern model or the majority voting model. But how do fish use these two different models? It is hard to imagine that completely different epidermal formation mechanisms are used among species of the same family. For this reason, there may be a more basic model that can produce patterns for either model. In this study, the Turing pattern model and the majority voting model were represented by cellular automata, and then a new model integrating these two models was proposed. By adjusting the parameters, this integrated model was able to create patterns that are equivalent to both the Turing pattern model and the majority voting model. By setting the intermediate parameters values of these two models, it was possible to create a variety of patterns that were more diverse than those created by each single model. Although this model is simpler than previously proposed models, it was able to confirm that it can create a variety of patterns

Majority Adder Implementation by Competing Patterns in Life-Like Rule B2/S2345

In this paper we present a two-dimensional chaotic cellular automaton, the Life rule B2/S2345, able to simulate the action of an adder with majority gates, stimulated by gliders collisions transformed as competing patterns. Values of Boolean variables are encoded into two types of patterns --- symmetric (FALSE) and asymmetric (TRUE) patterns -- which compete for the `empty' space when propagate in the channels. We construct basic logical gates and elementary arithmetical circuits by simulating logical signals with gliders reaction propagating geometrically restricted by stationary non-destructible still life. Therefore an implementation of universal logical gates and a majority binary adder is constructe

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