Ramón Alonso-Sanz

Reversible cellular automata with memory: two-dimensional patterns from a single site seed

Standard cellular automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends on its neighborhood configuration only at the preceding time step. Historic memory of all past iterations can be incorporated into CA by featuring each cell by a weighted mean of all its past states. In this paper, a new kind of reversible CA, which incorporates memory, is introduced in a two-dimensional scenario.

Discrete systems with memory

Cellular Automata and Memory Average Type Memory Other Memories Asynchrony and Probabilistic Rules Cycles and Random Sequences Three State Automata Reversible Dynamics Block Cellular Automata Structurally Dynamic Systems Boolean Networks Coupled Layers Continuous State Variable Spatial Games.

Memory versus spatial disorder in the support of cooperation

In the conventional spatial formulation of the iterated prisoners dilemma only the results generated in the last round are taken into account in deciding the next choice. Historic memory can be implemented by featuring players with a summary of their previous winnings and moves. The effect of memory as a mechanism of supporting cooperation versus spatial disorder is assessed when the players are allowed for continuous degree of cooperation, not the mere binary cooperation/defection disjunctive.

THE EFFECT OF MEMORY IN THE SPATIAL CONTINUOUS-VALUED PRISONER'S DILEMMA

The standard spatial formulation of the Prisoners Dilemma is a historic (memoryless, i.e. only results generated in the last round are taken into account in deciding the next choice), and binary (players are confined to fully cooperating or defecting). The spatial historic model admitting intermediate degrees of cooperation (fuzzy model) is studied in this work. Comparisons are made between the binary and fuzzy models. The effect of errors and discounting is also assessed.

ONE-DIMENSIONAL CELLULAR AUTOMATA WITH MEMORY: PATTERNS FROM A SINGLE SITE SEED

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remain the same, each site remembers a weighted mean of all its past states. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). The time evolution of one-dimensional CA with memory starting with a single live cell is studied. It is found that for α ≤ 0.5, the evolution corresponds to the standard (nonweighted) one, while for α > 0.5, there is a gradual decrease in the width of the evolving pattern, apart from discontinuities which sometimes may occur for certain rules and α values.

Spatial order prevails over memory in boosting cooperation in the iterated prisoner's dilemma

This paper presents some results on a spatial version of the iterated prisoners dilemma in which every player imitates in any iteration the optimal strategy of its neighbors. Neighbors are defined with different degrees of random variation (initial rewiring) based on a square lattice, and optimal is defined with different degrees of memory, ranging from only the single preceding iteration up to all preceding iterations. It is concluded that memory notably stimulates cooperation in the iterated prisoners dilemma played in ordered lattices, but it is unable to boost cooperation as the wiring network becomes highly disordered.

Are motorways rational from slime mould's point of view?

We analyse the results of our experimental laboratory approximation of motorway networks with slime mould Physarum polycephalum. Motorway networks of 14 geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK and USA. For each geographical entity, we represented major urban areas by oat flakes and inoculated the slime mould in a capital. After slime mould spanned all urban areas with a network of its protoplasmic tubes, we extracted a generalised Physarum graph from the network and compared the graphs with an abstract motorway graph using most common measures. The measures employed are the number of independent cycles, cohesion, shortest paths lengths, diameter, the Harary index and the Randić index. We obtained a series of intriguing results, and found that the slime mould approximates best of all the motorway graphs of Belgium, Canada and China, and that for all entities studied the best match between Physarum and motorway graphs is detected by the Randić index (molecular branching index).

A quantum battle of the sexes cellular automaton

The dynamics of a spatial quantum formulation of the iterated battle of the sexes game is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The effect of spatial structure is assessed in the quantum versus quantum players contest as well as in the unfair quantum versus classical players contest. The case of partial entangling is also scrutinized.

On a three-parameter quantum battle of the sexes cellular automaton

The dynamics of a spatial quantum formulation of the iterated battle of the sexes game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The effect of spatial structure is assessed when allowing the players to adopt quantum strategies that are no restricted to any particular subset of the possible strategies.

COMPLEX DYNAMICS OF ELEMENTARY CELLULAR AUTOMATA EMERGING FROM CHAOTIC RULES

We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behavior. CA are well-known computational substrates for studying emergent collective behavior, 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 the behavior of any given function. Examples include mechanical computation, λ and Z-parameters, mean field theory, differential equations and number conserving features. We aim to classify CA based on their behavior 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 behavior 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 an analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory exploring glider dynamics and reactions.