Related papers: Detecting emergent processes in cellular automata …
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…
Each cell of a two-dimensional lattice is painted one of k colors, arranged in a "color wheel." The colors advance (0 to k-1 mod k) either automatically or by contact with at least a threshold number of successor colors in a prescribed…
Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…
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…
We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…
We present a probabilistic 3D generative model, named Generative Cellular Automata, which is able to produce diverse and high quality shapes. We formulate the shape generation process as sampling from the transition kernel of a Markov…
We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…
Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural…
Two coarse-grained models which capture some universal characteristics of stripe forming systems are stud- ied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence…
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at…
Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and…
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…
Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…
A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes,…
Sand pile formation is often used to describe stratified chaos in dynamic systems due to self-emergent and scale invariant behaviour. Cellular automata (Bak-Tang-Wiesenfeld model) are often used to describe chaotic behaviour, as simulating…
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…
Can complex engineered and biological networks be coarse-grained into smaller and more understandable versions in which each node represents an entire pattern in the original network? To address this, we define coarse-graining units (CGU)…
The edge detection task is essential in image processing aiming to extract relevant information from an image. One recurring problem in this task is the weaknesses found in some detectors, such as the difficulty in detecting loose edges and…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of…