Related papers: Generalization over different cellular automata ru…
Recent experiments by Springer and Kenyon have shown that a deep neural network can be trained to predict the action of $t$ steps of Conway's Game of Life automaton given millions of examples of this action on random initial states.…
Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements…
This paper introduces Differentiable Logic Cellular Automata (DiffLogic CA), a novel combination of Neural Cellular Automata (NCA) and Differentiable Logic Gates Networks (DLGNs). The fundamental computation units of the model are…
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…
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.…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
We develop a theory characterizing the fundamental capability of deep neural networks to learn, from evolution traces, the logical rules governing the behavior of cellular automata (CA). This is accomplished by first establishing a novel…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…
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…
John H. Conway's Game of Life, as well as cellular automata in the larger family of Life-like CA, are discrete: the cells have a binary state space and the birth and survival transition rules are 9-bits apiece. Inspired by Life, several…
Large Language Models demonstrate remarkable mathematical capabilities but at the same time struggle with abstract reasoning and planning. In this study, we explore whether Transformers can learn to abstract and generalize the rules…
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 discrete and computational models thatcan be shown as general models of complexity. They are used in varied applications to derive the generalized behavior of the presented model. In this paper we have took one such…
Conway's Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior…
Conway's Game of Life is the best-known cellular automaton. It is a classic model of emergence and self-organization, it is Turing-complete, and it can simulate a universal constructor. The Game of Life belongs to the set of semi-totalistic…
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,…
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…
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…
The deep Convolutional Neural Network (CNN) is the state-of-the-art solution for large-scale visual recognition. Following basic principles such as increasing the depth and constructing highway connections, researchers have manually…