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The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
Cellular automata (CA) models are widely used to simulate complex systems with emergent behaviors, but identifying hidden parameters that govern their dynamics remains a significant challenge. This study explores the use of Convolutional…
The discovery of complex multicellular organism development took millions of years of evolution. The genome of such a multicellular organism guides the development of its body from a single cell, including its control system. Our goal is to…
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…
In contrast to deep reinforcement learning agents, biological neural networks are grown through a self-organized developmental process. Here we propose a new hypernetwork approach to grow artificial neural networks based on neural cellular…
We introduce Neural Particle Automata (NPA), a Lagrangian generalization of Neural Cellular Automata (NCA) from static lattices to dynamic particle systems. Unlike classical Eulerian NCA where cells are pinned to pixels or voxels, NPA model…
Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…
Step size in continuous cellular automata (CA) plays an important role in the stability and behavior of self-organizing patterns. Continous CA dynamics are defined by formula very similar to numerical estimation of physics-based ordinary…
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…
Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
Information-theoretic fitness functions are becoming increasingly popular to produce generally useful, task-independent behaviors. One such universal function, dubbed empowerment, measures the amount of control an agent exerts on its…
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…
Information can evolve as a physical consequence of non-equilibrium dynamics, even in the absence of genes, replication, or predefined fitness functions. We present Stability-Driven Assembly (SDA), a framework in which stochastic assembly…
Evolving one-dimensional cellular automata (CAs) with genetic algorithms has provided insight into how improved performance on a task requiring global coordination emerges when only local interactions are possible. Two approaches that can…
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…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
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…
In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to…