Block transformation of hybrid cellular automata

By introducing the sequence-block transformation and vector-block transformation, a discussion of symbolic dynamics of hybrid cellular automation (HCA) and hybrid cellular automation with memory (HCAM) is presented in this paper. As the local evolution rules of HCA and HCAM are not uniform, the new uniform cellular automata (CAs) with multiple states can be constructed by specific block transformations. It is proved that the new CA rules are topologically conjugate with the originals. Furthermore, the complex dynamics of the HCA and HCAM rules can be investigated via the new CA rules

Cellular automaton supercolliders

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems

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

On logical gates in precipitating medium: cellular automaton model

We study a two-dimensional semi-totalistic binary cell-state cellular automaton, which imitates a reversible precipitation in an abstract chemical medium. The systems exhibits a non-trivial growth and nucleation. We demonstrate how basic computational operation can be realized in the system when the propagation of the growing patterns is self-restricted by stationary localizations. We show that precipitating patterns of different morphology compete between each other and thus implement serial and non-serial logical gates

Spectral properties of reversible one-dimensional cellular automata

Reversible cellular automata are invertible dynamical systems characterized by discreteness, determinism and local interaction. This article studies the local behavior of reversible one-dimensional cellular automata by means of the spectral properties of their connectivity matrices. We use the transformation of every one-dimensional cellular automaton to another of neighborhood size 2 to generalize the results exposed in this paper. In particular we prove that the connectivity matrices have a single positive eigenvalue equal to 1; based on this result we also prove the idempotent behavior of these matrices. The significance of this property lies in the implementation of a matrix technique for detecting whether a one-dimensional cellular automaton is reversible or not. In particular, we present a procedure using the eigenvectors of these matrices to find the inverse rule of a given reversible one-dimensional cellular automaton. Finally illustrative examples are provided

Presencia de productos orgánicos en Twitter desde la perspectiva del análisis de redes sociales

El objetivo de esta investigación fue analizar cómo está estructurada la red de actores que hablan de productos orgánicos en Twitter y, a través de la identificación de actores clave, conocer la influencia que ejercen dentro de las redes; al hacerlo, desarrollamos ideas significativas que permitan a los usuarios de medios sociales mejorar su interacción y posición dentro de la red. Se buscaron y descargaron los datos de los términos #organico(a) y #organicos(as) por un periodo de seis meses. Para su procesamiento y estudio, se utilizó el enfoque teórico y metodológico del análisis de redes sociales (ARS). La red general se formó por 14,329 tweets únicos, publicados por 6,667 usuarios, configurando una red de 6,521 vínculos directos. Para entender con mayor detalle las interacciones, se segmentó la red con base en dos tipos de relaciones: (1) retweets y (2) menciones o respuestas, ambas redes mostraron estructuras diferentes. Se encontró que el conjunto de relaciones que estructuran la red social está asociado a productos, países y temas, así como a diversos actores clave. Además, la expresión de los orgánicos en Twitter sigue de cerca la visión general de considerarse benéficos para la salud y el medio ambiente.The objective of this research was to analyse how the network of actors talking about organic products on Twitter is structured and, through the identification of key players, to assess the influence they exert within the networks. Doing this, we develop meaningful ideas that allow social media users to improve their interaction and position on networks. The data of the terms #organico(a) and #organicos(as) were searched and downloaded for a six-month period. For its processing and study, the theoretical and methodological approach of social networks analysis (SNA) was used. The general network was formed by 14,329 unique tweets, published by 6,667 users, shaping a network with 6,521 direct links. To understand the interactions in greater detail, the network was segmented based on two types of relationships: (1) retweets and (2) mentions or replies to, both networks showed different structures. It was found that the set of relationships that structure the social network is associated with products, countries, and topics, as well as several key players. Furthermore, the expression of organic on Twitter closely follows the general vision of being considered beneficial for health as well as the environment.O objetivo desta pesquisa foi analisar como se estrutura a rede de atores que falam sobre produtos orgânicos no Twitter e, por meio da identificação dos atores-chave, conhecer a influência que eles exercem nas redes; Ao fazer isso, desenvolvemos ideias significativas que permitem aos usuários de mídia social melhorar sua interação e posição na rede. Os dados dos termos #organico (a) e #organicos (as) foram pesquisados ​​e baixados por um período de seis meses. Para seu processamento e estudo, utilizou-se a abordagem teórico-metodológica da análise de redes sociais (ARS). A rede geral foi composta por 14.329 tweets únicos, publicados por 6.667 usuários, perfazendo uma rede de 6.521 links diretos. Para compreender mais detalhadamente as interações, a rede foi segmentada com base em dois tipos de relacionamento: (1) retuítes e (2) menções ou respostas, ambas as redes apresentavam estruturas diferentes. Constatou-se que o conjunto de relações que estruturam a rede social está associado a produtos, países e temas, bem como a diversos atores-chave. Além disso, a expressão do orgânico no Twitter segue de perto a visão geral de ser considerado benéfico à saúde e ao meio ambiente