Related papers: Frobenius Revivals in Laplacian Cellular Automata:…
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values…
We study discrete Laplacians on two-dimensional lattices under modular iterations, focusing on the emergence of nontrivial large-scale patterns. While purely binary or constant modular sequences quickly collapse into strict periodicity, the…
Bayesian optimisation in the latent space of a Variational AutoEncoder (VAE) is a powerful framework for optimisation tasks over complex structured domains, such as the space of scientifically interesting molecules. However, existing…
Persistent activity is postulated to drive neural network plasticity and learning. To investigate its underlying cellular mechanisms, we developed a biophysically tractable model that explains the emergence, sustenance, and eventual…
While one-dimensional cellular automata have been well studied, there are relatively few results about multidimensional cellular automata; the investigation of cellular automata defined on Cayley trees constitutes an intermediate class.…
We present a method to eliminate redundancy in the transition tables of Boolean automata: schema redescription with two symbols. One symbol is used to capture redundancy of individual input variables, and another to capture permutability in…
It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular…
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…
Boolean networks have been widely used in many areas of science and engineering to represent various dynamical behaviour. In systems biology, they became useful tools to study the dynamical characteristics of large-scale biomolecular…
Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility…
Substantial efforts have been applied to engineer CA with desired emergent properties, such as supporting gliders. Recent work in continuous CA has generated a wide variety of compelling bioreminiscent patterns, and the expansion of CA…
Spontaneous self-replication in cellular automata has long been considered rare, with most known examples requiring careful design or artificial initialization. In this paper, we present formal, causal evidence that such replication can…
Recently, it was shown that a rich class of second-order (maximally) superintegrable systems has an underpinning Hesse-Frobenius structure, i.e.\ a Frobenius structure that is compatible with a Hessian structure such that the Hessian…
Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling is an important tool to fill this gap. Typical studies often employ detailed…
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…
What substrate features allow life? We exhaustively classify all 262,144 outer-totalistic binary cellular automata rules with Moore neighbourhood for self-replication and produce phase diagrams in the $(\lambda, F)$ plane, where $\lambda$…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
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.…
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…