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The evolutionary balance between innate and learned behaviors is highly intricate, and different organisms have found different solutions to this problem. We hypothesize that the emergence and exact form of learning behaviors is naturally…
Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial…
The physics of behavior seeks simple descriptions of animal behavior. The field has advanced rapidly by using techniques in low dimensional dynamics distilled from computer vision. Yet, we still do not generally understand the rules which…
We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
We propose a general method for constructing a fuzzy cellular automaton from a given cellular automaton. Unlike previous approaches that use fuzzy distinctive normal form, whose update function is restricted to third-order polynomials, our…
Cellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications,…
Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of…
The prediction of the behavior of the disease, the level of affectation in a population and the ways to control it are the most important aspects studied by epidemiology using tools such as historical data and mathematical models. So, our…
The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…
Elementary Cellular Automata (ECAs) exhibit diverse behaviours often categorized by Wolfram's qualitative classification. To provide a quantitative basis for understanding these behaviours, we investigate the global dynamics of such…
Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional to $\log n$. The new automaton is the original one, but with…
We study the dynamics of (synchronous) one-dimensional cellular automata with cyclical boundary conditions that evolve according to the majority rule with radius $ r $. We introduce a notion that we term cell stability with which we express…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…
The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…
Biological systems exhibit remarkable morphogenetic plasticity, where a single genome can encode various specialized cellular structures triggered by local chemical signals. In the domain of Deep Learning, Differentiable Neural Cellular…
We present a new classification of elementary cellular automata. It is based on the structure of the network of states, connected with the transitions between them; the latter are determined by the automaton rule. Recently an algorithm has…
We study the emergence of information integration in cellular automata (CA) with respect to states in the long run. Information integration is in this case quantified by applying the information-theoretic measure known as total correlation…