Related papers: The GraftalLace Cellular Automaton
Cellular automata (CA) provide a minimal formalism for investigating how simple local interactions generate rich spatiotemporal behavior in domains as diverse as traffic flow, ecology, tissue morphogenesis and crystal growth. However,…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
Measuring similarity in urban spatial networks is key to understanding cities as complex systems. Yet most existing methods are not tailored for spatial networks and struggle to differentiate them effectively. We propose GCA-Sim, a…
An additive cellular automaton is a linear map on the set of infinite multidimensional arrays of elements in a finite cyclic group $\mathbb{Z}/m\mathbb{Z}$. In this paper, we consider simplices appearing in the orbits generated from…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
We have investigated the behavior of bistable cells made up of four quantum dots and occupied by two electrons, in the presence of realistic confinement potentials produced by depletion gates on top of a GaAs/AlGaAs heterostructure. Such a…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…
This paper presents a novel framework using neural cellular automata (NCA) to regenerate and predict geographic information. The model extends the idea of using NCA to generate/regenerate a specific image by training the model with various…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
This study significantly advances multi-texture synthesis using Neural Cellular Automata (NCAs) by introducing a novel training methodology that enables robust self-regeneration of textures in damaged regions. This inherent healing…
Quantum Cellular Automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
We present a new Life-like cellular automaton (CA) capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and $\lambda$ parameter similar to the game-of-Life, but is not based on birth/survival and is…
In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$.…
Quantum cellular automata (QCA) constitute space and time homogeneous discrete models for quantum field theories (QFTs). Although QFTs are defined without reference to particles, computations are done in terms of Feynman diagrams, which are…
An "odd-rule" cellular automaton (CA) is defined by specifying a neighborhood for each cell, with the rule that a cell turns ON if it is in the neighborhood of an odd number of ON cells at the previous generation, and otherwise turns OFF.…
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 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…
The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…