Related papers: Unraveling simplicity in elementary cellular autom…
This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
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…
Delvenne, K\r{u}rka and Blondel have defined new notions of computational complexity for arbitrary symbolic systems, and shown examples of effective systems that are computationally universal in this sense. The notion is defined in terms of…
We explore a community-detection cellular automata algorithm inspired by human heuristics, based on information diffusion and a non-linear processing phase with a dynamics inspired by human heuristics. The main point of the methods is that…
Identification of different neuronal cell types is critical for understanding their contribution to brain functions. Yet, automated and reliable classification of neurons remains a challenge, primarily because of their biological…
What fascinates us about animal behavior is its richness and complexity, but understanding behavior and its neural basis requires a simpler description. Traditionally, simplification has been imposed by training animals to engage in a…
Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have…
We search for regularities in the sequences of numbers of preimages for elementary cellular automata. For 46 out of 88 "minimal" rules, we find recognizable patterns, usually in the form of second order recurrence equations with constant…
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
We propose a characteristic representation ofone-dimensional and 2-state, 3-neighbor cellular automaton rules, which describes an effective form of each rule after many time steps. Simulated results of the representation show that complex…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the…
Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or evolvable) update rules that capture the adaptive…
We consider a problem of decomposition of a ternary function into a composition of binary ones from the viewpoint of communication complexity and algorithmic information theory as well as some applications to cellular automata.
We prove that many dynamical properties of group cellular automata (i.e., cellular automata defined on any finite group and with global rule which is an endomorphism), including surjectivity, injectivity, sensitivity to initial conditions,…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
Cell complexes (CCs) are a higher-order network model deeply rooted in algebraic topology that has gained interest in signal processing and network science recently. However, while the processing of signals supported on CCs can be described…