Complexity of Two-Dimensional Patterns

In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of ``regular language'' or ``local rule'' that are equivalent in d=1 lead to distinct classes in d >= 2. We explore the closure properties and computational complexity of these classes, including undecidability and L-, NL- and NP-completeness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in d >= 2 has a periodic point of a given period, and that certain ``local lattice languages'' are not finite-time images or limit sets of any CA. We also show that the entropy of a d-dimensional CA's finite-time image cannot decrease faster than t^{-d} unless it maps every initial condition to a single homogeneous state.Comment: To appear in J. Stat. Phy

Optimal Pedestrian Path Planning in Evacuation Scenario

Simulation of evacuation plans is a relatively complex problem. It is necessary to simulate a number of separate processes which interact in the result. Namely, they are pedestrian-pedestrian interactions, pedestrian-static object (e.g. wall) interactions and pedestrian-environment (fire, smoke, etc.) interactions. In this case, the evacuation simulation is controled on the microscopic level. Microscopic level considers each individual separately and pedestrian is planning his/her path to the exit with regard to the above-mentioned interactions. In this article we focus on path planning during evacuation and describe algorithms applied in this area. At the end we propose a method of the space evaluation with linear time complexity and planned path compared with commercial software tools

Computational Modalities of Belousov-Zhabotinsky Encapsulated Vesicles

We present both simulated and partial empirical evidence for the computational utility of many connected vesicle analogs of an encapsulated non-linear chemical processing medium. By connecting small vesicles containing a solution of sub-excitable Belousov-Zhabotinsky (BZ) reaction, sustained and propagating wave fragments are modulated by both spatial geometry, network connectivity and their interaction with other waves. The processing ability is demonstrated through the creation of simple Boolean logic gates and then by the combination of those gates to create more complex circuits

Reaction–diffusion chemistry implementation of associative memory neural network

Unconventional computing paradigms are typically very difficult to program. By implementing efficient parallel control architectures such as artificial neural networks, we show that it is possible to program unconventional paradigms with relative ease. The work presented implements correlation matrix memories (a form of artificial neural network based on associative memory) in reaction–diffusion chemistry, and shows that implementations of such artificial neural networks can be trained and act in a similar way to conventional implementations

A morphological adaptation approach to path planning inspired by slime mould

Path planning is a classic problem in computer science and robotics which has recently been implemented in unconventional computing substrates such as chemical reaction–diffusion computers. These novel computing schemes utilise the parallel spatial propagation of information and often use a two-stage method involving diffusive propagation to discover all paths and a second stage to highlight or visualise the path between two particular points in the arena. The true slime mould Physarum polycephalum is known to construct efficient transport networks between nutrients in its environment. These networks are continuously remodelled as the organism adapts its body plan to changing spatial stimuli. It can be guided towards attractant stimuli (nutrients, warm regions) and it avoids locations containing hazardous stimuli (light irradiation, repellents, or regions occupied by predatory threats). Using a particle model of slime mould we demonstrate scoping experiments which explore how path planning may be performed by morphological adaptation. We initially demonstrate simple path planning by a shrinking blob of virtual plasmodium between two attractant sources within a polygonal arena. We examine the case where multiple paths are required and the subsequent selection of a single path from multiple options. Collision-free paths are implemented via repulsion from the borders of the arena. Finally, obstacle avoidance is implemented by repulsion from obstacles as they are uncovered by the shrinking blob. These examples show proof-of-concept results of path planning by morphological adaptation which complement existing research on path planning in novel computing substrates

Autômatos celulares: melhorias de controlo e imunidade na simulação de fenômenos propagativos

Los autómatas celulares bidimensionales constituyen una potente herramienta para la  simulación de sistemas discretos complejos, son útiles en el tratamiento de fenómenos propagativos como epidemias  o incendios. El presente trabajo propone una serie de mejoras teóricas, funcionales y aplicativas  al estudio publicado en 2009 por Hoya, Martin del Rey, y Rodríguez,  específicamente orientadas al control de los patrones de propagación en autómatas celulares con reticulados homogéneos de tamaño variable, lo que permite la simulación de  conjuntos celulares inmunes  que actúan como barreras en los entornos estudiados. Como agente propagante se utilizó el modelo epidemiológico Susceptible-Infectado-Recuperado [SIR] de recuperación  de la influenza tipo A. El trabajo se desarrolló usando MATLAB®, lo que resultó en simulaciones más  realistas  y versátiles, que parecen ajustarse de manera más fiel a las observaciones realizadas en patrones conocidos de influenza.Two-dimensional cellular automata are a powerful tool for the simulation of complex discrete systems. They are useful in the treatment of propagative phenomena such as epidemics or fires. This paper proposes a series of theoretical, functional, and applicable improvements to the study published in 2009 by Hoya, Martin del Rio, and Rodríguez; it is specifically aimed at controlling the spread patterns in cellular automata with homogeneous resizable lattices, allowing the simulation of immune cell assemblies that act as barriers in the environments studied. As retardant agent, the Susceptible-Infected-Recovered [SIR] epidemiological model of influenza type A was used. The work was developed using MATLAB®, resulting in a collection of more realistic and versatile simulations that seems to fi, in a more accurate way, the observations made on known patterns of influenza.Os autômatos celulares bidimensionais são uma poderosaferramenta para a simulação de sistemas discretos complexos,são úteis no tratamento de fenômenos propagativos taiscomo epidemias ou incêndios. Este artigo propõe uma série demelhorias teóricas, funcionais e aplicáveis ao estudo publicadoem 2009 por Hoya, Martin del Rey e Rodriguez, especificamentedestinadas a controlar os padrões de dispersão em autômatoscelulares com reticulados homogêneos de tamanho variável,permitindo a simulação de conjuntos de células imunes queagem como barreiras nos ambientes estudados. Como agentepropagante foi utilizado o modelo epidemiológico Suscetível-Infectado-Recuperado [SIR] de recuperação da influenza tipo A.O trabalho foi desenvolvido usando MATLAB®, resultando emsimulações mais realistas e versáteis, que parecem caber maisfielmente às observações realizadas em padrões conhecidos deinfluenza

A probabilistic chemical programmable computer

The exponential growth of the power of modern digital computers is based upon the miniaturisation of vast nanoscale arrays of electronic switches, but this will be eventually constrained by fabrication limits and power dissipation. Chemical processes have the potential to scale beyond these limits performing computations through chemical reactions, yet the lack of well-defined programmability limits their scalability and performance. We present a hybrid digitally programmable chemical array as a probabilistic computational machine that uses chemical oscillators partitioned in interconnected cells as a computational substrate. This hybrid architecture performs efficient computation by distributing between chemical and digital domains together with error correction. The efficiency is gained by combining digital with probabilistic chemical logic based on nearest neighbour interactions and hysteresis effects. We demonstrated the implementation of one- and two- dimensional Chemical Cellular Automata and solutions to combinatorial optimization problems.Comment: 20 page manuscript, 6 figures, 112 page supplementary volum