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The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
Since their inception at {\it Macy conferences} in later 1940s complex systems remain the most controversial topic of inter-disciplinary sciences. The term `complex system' is the most vague and liberally used scientific term. Using…
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…
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited…
We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial…
Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems…
Evolutionary complexity is here measured by the number of trials/evaluations needed for evolving a logical gate in a non-linear medium. Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour. We…
Biological systems are notorious for complex behavior within short timescales (e.g. metabolic activity) and longer time scales (e.g. evolutionary selection), along with their complex spatial organization. Because of their complexity and…
We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…