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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

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…

Computer Vision and Pattern Recognition · Computer Science 2020-09-22 Mingxiang Chen , Qichang Chen , Lei Gao , Yilin Chen , Zhecheng Wang

Neural Cellular Automata (NCAs) offer a way to study the growth of two-dimensional artificial organisms from a single seed cell. From the outset, NCA-grown organisms have had issues with stability, their natural boundary often breaking down…

Neural and Evolutionary Computing · Computer Science 2025-12-11 James Stovold

In this work, we address the task of natural image generation guided by a conditioning input. We introduce a new architecture called conditional invertible neural network (cINN). The cINN combines the purely generative INN model with an…

Computer Vision and Pattern Recognition · Computer Science 2019-07-11 Lynton Ardizzone , Carsten Lüth , Jakob Kruse , Carsten Rother , Ullrich Köthe

Recent extensions of Cellular Automata (CA) have incorporated key ideas from modern deep learning, dramatically extending their capabilities and catalyzing a new family of Neural Cellular Automata (NCA) techniques. Inspired by…

Computer Vision and Pattern Recognition · Computer Science 2022-11-03 Mattie Tesfaldet , Derek Nowrouzezahrai , Christopher Pal

In nature, the process of cellular growth and differentiation has lead to an amazing diversity of organisms -- algae, starfish, giant sequoia, tardigrades, and orcas are all created by the same generative process. Inspired by the incredible…

Neural and Evolutionary Computing · Computer Science 2022-02-03 Rasmus Berg Palm , Miguel González-Duque , Shyam Sudhakaran , Sebastian Risi

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 and Lattice Gases · Physics 2020-01-20 William Gilpin

Neural Cellular Automata (NCA) models have shown remarkable capacity for pattern formation and complex global behaviors stemming from local coordination. However, in the original implementation of NCA, cells are incapable of adjusting their…

Neural and Evolutionary Computing · Computer Science 2023-05-18 Ettore Randazzo , Alexander Mordvintsev , Craig Fouts

Developmental Graph Cellular Automata (DGCA) are a novel model for morphogenesis, capable of growing directed graphs from single-node seeds. In this paper, we show that DGCAs can be trained to grow reservoirs. Reservoirs are grown with two…

Neural and Evolutionary Computing · Computer Science 2025-12-11 Matias Barandiaran , James Stovold

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…

Neural and Evolutionary Computing · Computer Science 2022-04-26 Elias Najarro , Shyam Sudhakaran , Claire Glanois , Sebastian Risi

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…

Machine Learning · Computer Science 2021-10-28 Daniele Grattarola , Lorenzo Livi , Cesare Alippi

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…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Andres Moreira

We present a conditional generative model to learn variation in cell and nuclear morphology and the location of subcellular structures from microscopy images. Our model generalizes to a wide range of subcellular localization and allows for…

Machine Learning · Statistics 2017-05-02 Gregory R. Johnson , Rory M. Donovan-Maiye , Mary M. Maleckar

Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…

Cellular Automata and Lattice Gases · Physics 2025-06-02 Markus Redeker

In this paper, we propose a novel approach to generate images (or other artworks) by using neural cellular automatas (NCAs). Rather than training NCAs based on single images one by one, we combined the idea with variational autoencoders…

Artificial Intelligence · Computer Science 2020-11-10 Mingxiang Chen , Zhecheng Wang

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

Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Cosma Rohilla Shalizi , Kristina Lisa Shalizi

Most of the Neural Cellular Automata (NCAs) defined in the literature have a common theme: they are based on regular grids with a Moore neighborhood (one-hop neighbour). They do not take into account long-range connections and more complex…

Artificial Intelligence · Computer Science 2026-04-03 Léo Pio-Lopez , Benedikt Hartl , Michael Levin

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…

Cellular Automata and Lattice Gases · Physics 2015-06-26 Navot Israeli , Nigel Goldenfeld

Generative modeling seeks to approximate the statistical properties of real data, enabling synthesis of new data that closely resembles the original distribution. Generative Adversarial Networks (GANs) and Denoising Diffusion Probabilistic…

Computer Vision and Pattern Recognition · Computer Science 2024-07-04 Marawan Elbatel , Konstantinos Kamnitsas , Xiaomeng Li