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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…
Neural Cellular Automata (NCAs) are a model of morphogenesis, capable of growing two-dimensional artificial organisms from a single seed cell. In this paper, we show that NCAs can be trained to respond to signals. Two types of signal are…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
Consider a graph $G=(V,E)$ and a random initial vertex-coloring, where each vertex is blue independently with probability $p_{b}$, and red with probability $p_r=1-p_b$. In each step, all vertices change their current color synchronously to…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also,…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
Cellular Automata (CA) theory is a discrete model that represents the state of each of its cells from a finite set of possible values which evolve in time according to a pre-defined set of transition rules. CA have been applied to a number…
Describing complex phenomena by means of cellular automata (CA) has shown to be a very effective approach in pure and applied sciences. In fact, the number of published papers concerning this topic has tremendously increased over the last…
Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…
A cellular automata (CA) configuration is constructed that exhibits emergent failover. The configuration is based on standard Game of Life rules. Gliders and glider-guns form the core messaging structure in the configuration. The blinker is…
Rule 22 elementary cellular automaton (ECA) has a 3--cell neighborhood, binary cell states, where a cell takes state `1' if there is exactly one neighbor, including the cell itself, in state `1'. In Boolean terms the cell-state transition…
We have discovered a novel transition rule for binary cellular automata (CA) that yields self-replicating structures across two spatial and temporal scales from sparsely populated random initial conditions. Lower-level, shapeshifting…
In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed…
Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. We investigate what sort of self-stabilising…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
In this paper we consider the identification problem of Cellular Automata (CAs). The problem is defined and solved in the context of partial observations with time gaps of unknown length, i.e. pre-recorded, partial configurations of the…
The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular…
This article surveys some theoretical aspects of Cellular Automata (CAs) research. In particular, we discuss on maximal length CA. An n-cell CA is a maximal length CA, if all the configurations except one form a single cycle. There is a…