Narrow Results

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e., how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules are required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.

This paper investigates collisions of gliders generated by one-dimensional Rule 110 cellular automaton. A specific value associated with each glider and an algebraic equation that describes the collision between two gliders were found. Because the products of the collision between two gliders may result in no gliders or one, two or more gliders, this equation states that the total sum of the associated values corresponding to colliding gliders equals the sum of the values of the gliders which are products of the collision. Moreover, an analogy is proposed between the glider collisions and the collisions of physical particles with the equation corresponding to colliding gliders being similar to the equation of energy conservation in physics. In this scheme, even without carrying out the temporal evolution for a collision, it can be determined if a possible combination of resulting gliders accomplishes the equation corresponding to that collision.

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 semi-totalistic 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.

In a two-dimensional cellular automaton model of retained excitation every excited cell stays excited if the number of excited neighbors belong to some interval, the cell takes refractory state otherwise. Every resting cell is excited if the number of excited cells in its neighborhood belong to some other interval; cell-state transition from refractory to resting state is unconditional. We classify 1296 rules of retained excitation based on how dynamics of excitable lattices develop after initial stimulation. Several modes of space-time activity dynamics are discovered: not growing but persistent domains of activity, domains with rectangular, octagonal and almost circular growth, amoeba-like growing patterns, mobile and still localizations.

Since their inception at Macy conferences in later 1940s, complex systems have remained the most controversial topic of interdisciplinary sciences. The term "complex system" is the most vague and liberally used scientific term. Using elementary cellular automata (ECA), and exploiting the CA classification, we demonstrate elusiveness of "complexity" by shifting space-time dynamics of the automata from simple to complex by enriching cells with memory. This way, we can transform any ECA class to another ECA class — without changing skeleton of cell-state transition function — and vice versa by just selecting a right kind of memory. A systematic analysis displays that memory helps "discover" hidden information and behavior on trivial — uniform, periodic, and nontrivial — chaotic, complex — dynamical systems.