Genaro Juárez Martínez

Approximating Mexican highways with slime mould

Plasmodium of Physarum polycephalum is a single cell visible by unaided eye. During its foraging behavior the cell spans spatially distributed sources of nutrients with a protoplasmic network. The geometrical structure of the protoplasmic networks allows the plasmodium to optimize transport of nutrients between remote parts of its body. Assuming major Mexican cities are sources of nutrients that need to be distributed across Mexico, how much does the structure of the Physarum protoplasmic network correspond to the structure of Mexican Federal highway network? To address the issue we undertook a series of laboratory experiments with living P. polycephalum. We represent geographical locations of major cities (19 locations) by oat flakes, place a piece of plasmodium in the area corresponding to Mexico city, record the plasmodium’s foraging behavior and extract topology of the resulting nutrient transport networks. Results of our experiments show that the protoplasmic network formed by Physarum is isomorphic, subject to limitations imposed, to a network of principal highways. Ideas and results in the paper may contribute towards future developments in bio-inspired road planning.

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 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.

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).

Bio-Imitation of Mexican Migration Routes to the USA with Slime Mould on 3D Terrains

Plasmodium of Physarum polycephalum (P. polycephalum) is a large single cell visible by an unaided eye. It shows sophisticated behavioural traits in foraging for nutrients and developing an optimal transport network of protoplasmic tubes spanning sources of nutrients. When placed in an environment with distributed sources of nutrients the cell ‘computes’ an optimal graph spanning the nutrients by growing a network of protoplasmic tubes. P. polycephalum imitates development of man-made transport networks of a country when configuration of nutrients represents major urban areas. We employed this feature of the slime mould to imitate mexican migration to USA. The Mexican migration to USA is the World’s largest migration system. We bio-physically imitated the migration using slime mould P. polycephalum. In laboratory experiments with 3D Nylon terrains of USA we imitated development of migratory routes from Mexico-USA border to ten urban areas with high concentration of Mexican migrants. From results of laboratory experiments we extracted topologies of migratory routes, and highlighted a role of elevations in shaping the human movement networks.

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.

On generative morphological diversity of elementary cellular automata

Purpose – Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space‐time configurations. No one has tried to analyze a generative power of cellular‐automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large‐scale spatially extended systems.Design/methodology/approach – Let all but one cell be in alike state in initial configuration of a one‐dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three‐by‐three cell blocks occurred in the automatons space‐time configuration.Findings – The paper builds a hierarchy of generative diversity of one‐dimensional cellular automata with binary cell‐states and ternary neighborhoods, discusses necessary conditions for a cell‐state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions.Research limita...

Invertible behavior in elementary cellular automata with memory

Elementary cellular automata (ECAs) have been studied for their ability to generate complex global behavior, despite their simplicity. One variation of ECAs is obtained by adding memory to each cell in a neighborhood. This process generates a provisional configuration in which the application of an evolution rule establishes the dynamics of the system. This version is known as an ECA with memory (ECAM). Most previous work on ECAMs analyzed the complex behavior taking chaotic ECAs. However, the present paper investigates reversible ECAMs as obtained from reversible and permutative ECAs. These ECAs have at least one ancestor for every configuration; thus, the correct permutation of states may specify the memory function to obtain reversible ECAMs. For permutative ECAs, which are often irreversible, we demonstrate that the use of a quiescent state and the correct manipulation of de Bruijn blocks produce reversible ECAMs.

Localization Dynamics in a Binary Two-Dimensional Cellular Automaton: The Diffusion Rule

We study a two-dimensional cellular automaton (CA), called Diffusion Rule, which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations (gliders, oscillators, glider guns, puffer trains), analyze spatio-temporal dynamics of collisions between gliders, and discuss possible applications in unconventional computing.

EXPRESSIVENESS OF ELEMENTARY CELLULAR AUTOMATA

We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically inspired parameters for biodiversity are applied to the configurations of cellular automata. This paper contains a survey of the Elementary Cellular Automata in terms of their expressiveness and an evaluation whether expressiveness is a meaningful term in the context of simulated biology.

On the Representation of Gliders in Rule 54 by De Bruijn and Cycle Diagrams

Rule 54, in Wolframs notation, is one of elementary yet complexly behaving one-dimensional cellular automata. The automaton supports gliders, glider guns and other non-trivial long transients. We show how to characterize gliders in Rule 54 by diagram representations as de Bruijn and cycle diagrams; offering a way to present each glider in Rule 54 with particular characteristics. This allows a compact encoding of initial conditions which can be used in implementing non-trivial collision-based computing in one-dimensional cellular automata.