Related papers: Cellular Automata as a Model of Physical Systems
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…
This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…
In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich…
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then…
We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1/2 and operates on an arbitrary input size. The Automaton reads an…
Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…
This article presents a new characterization of controllability and regional controllability of Deterministic Cellular Automata (CA for short). It focuses on analyzing these problems within the framework of control theory, which have been…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
The Global Cellular Automata (GCA) Model is a generalization of the Cellular Automata (CA) Model. The GCA model consists of a collection of cells which change their states depending on the states of their neighbors, like in the classical CA…
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs…
This paper proposes several algorithms and their Cellular Automata Machine (CAM) for drawing the State Transition Diagram (STD) of an arbitrary Cellular Automata (CA) Rule (any neighborhood, uniform/ hybrid and null/ periodic boundary) and…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
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…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
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…
In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…