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Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…

Quantum Physics · Physics 2009-11-10 Yaakov S. Weinstein , C. Stephen Hellberg

Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a…

Formal Languages and Automata Theory · Computer Science 2025-11-18 Dana Fisman , Noa Izsak

Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…

Disordered Systems and Neural Networks · Physics 2024-07-22 Freya Behrens , Barbora Hudcová , Lenka Zdeborová

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…

Dynamical Systems · Mathematics 2025-01-07 Sara Dridi

We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA…

Quantum Physics · Physics 2009-11-11 Norio Inui , Shuichi Inokuchi , Yoshihiro Mizoguchi , Norio Konno

Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…

Cellular Automata and Lattice Gases · Physics 2021-04-05 Hugo Cisneros , Josef Sivic , Tomas Mikolov

Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial…

Cellular Automata and Lattice Gases · Physics 2025-07-28 Sanyam Jain , Stefano Nichele

We study classical and quantum spin models derived from one-dimensional cellular automata (CA) with nonlinear update rules, focusing on rules 30, 54 and 201. We argue that the classical models, defined such that their ground states…

Statistical Mechanics · Physics 2026-04-07 Konstantinos Sfairopoulos , Luke Causer , Jamie F. Mair , Stephen Powell , Juan P. Garrahan

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,…

Machine Learning · Computer Science 2025-06-24 Jaime A. Berkovich , Noah S. David , Markus J. Buehler

This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…

Computational Complexity · Computer Science 2015-12-22 Yoshihiko Kayama

Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise…

Neural and Evolutionary Computing · Computer Science 2025-12-03 Kevin Xu , Risto Miikkulainen

Modeling the immune system so that its essential functionalities stand out without the need for every molecular or cellular interaction to be taken into account has been challenging for many decades. Two competing approaches have been the…

Cellular Automata and Lattice Gases · Physics 2017-11-13 Kátia K. Cassiano , Valmir C. Barbosa

We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…

Cellular Automata and Lattice Gases · Physics 2007-12-13 Jean-Baptiste Rouquier , Michel Morvan

We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state $\sigma_i(t) \in \{0,1\}$ of a cell $i$ does not only depend on the states in its local neighborhood at time $t-1$, but also on the memory of…

Statistical Mechanics · Physics 2007-05-23 Thimo Rohlf , Constantino Tsallis

A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We…

Chaotic Dynamics · Physics 2016-04-15 Vladimir García-Morales

Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…

Quantum Physics · Physics 2020-12-02 Terry Farrelly

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…

Artificial Intelligence · Computer Science 2025-09-16 Benedikt Hartl , Michael Levin , Léo Pio-Lopez

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…

Discrete Mathematics · Computer Science 2017-09-01 Carlos Martin

Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…

Formal Languages and Automata Theory · Computer Science 2012-08-15 Anaël Grandjean , Gaétan Richard , Véronique Terrier

Describing complex phenomena by means of cellular automata (CA) has shown to be a very effective approach in pure and applied sciences. In fact, the number of published papers concerning this topic has tremendously increased over the last…

Cellular Automata and Lattice Gases · Physics 2012-06-13 Luan Carlos de Sena Monteiro Ozelim , André Luís Brasil Cavalcante , Lucas Parreira de Faria Borges