Related papers: Algorithmic Information Dynamics of Cellular Autom…
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…
Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
Cellular Automaton (CA) and an Integral Value Transformation (IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of…
A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger…
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…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
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…
The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of…
In dynamical systems, local interactions between dynamical units generate correlations which are stored and transmitted throughout the system, generating the macroscopic behavior. However a framework to quantify and study this at the…
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 (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by…
What is the most crucial characteristic of a system with life activity? Currently, many theories have attempted to explain the most essential difference between living systems and general systems, such as the self-organization theory and…
In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing…
Cellular automata (CA) dynamics are ordered in terms of two global parameters, computable {\sl a priori} from the description of rules. While one of them (activity) has been used before, the second one is new; it estimates the average…
This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…
Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…
Collision detection plays a key role in the simulation of interacting rigid bodies. However, owing to its computational complexity current methods typically prioritize either maximizing processing speed or fidelity to real-world behaviors.…
We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations…