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Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…

Neural and Evolutionary Computing · Computer Science 2023-11-29 Magnus Petersen

Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. In this work, we show that the neural network (NN)…

Neural and Evolutionary Computing · Computer Science 2021-03-03 Alejandro Hernandez Ruiz , Armand Vilalta , Francesc Moreno-Noguer

Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…

Pattern Formation and Solitons · Physics 2024-04-23 Alex D. Richardson , Tibor Antal , Richard A. Blythe , Linus J. Schumacher

Neural Cellular Automata (NCA) is a class of Cellular Automata where the update rule is parameterized by a neural network that can be trained using gradient descent. In this paper, we focus on NCA models used for texture synthesis, where…

Computer Vision and Pattern Recognition · Computer Science 2026-01-30 Ehsan Pajouheshgar , Yitao Xu , Sabine Süsstrunk

Neural Cellular Automata (NCAs) have been proven effective in simulating morphogenetic processes, the continuous construction of complex structures from very few starting cells. Recent developments in NCAs lie in the 2D domain, namely…

Machine Learning · Computer Science 2021-06-07 Shyam Sudhakaran , Djordje Grbic , Siyan Li , Adam Katona , Elias Najarro , Claire Glanois , Sebastian Risi

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

Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of…

Artificial Intelligence · Computer Science 2025-06-26 Salvatore Milite , Giulio Caravagna , Andrea Sottoriva

Neural Cellular Automata (NCA) have shown a remarkable ability to learn the required rules to "grow" images, classify morphologies, segment images, as well as to do general computation such as path-finding. We believe the inductive prior…

Artificial Intelligence · Computer Science 2021-05-18 Alexander Mordvintsev , Eyvind Niklasson , Ettore Randazzo

Neural cellular automata (NCA) provide a lightweight alternative to encoder-decoder segmentation networks. However, it can be difficult to decide when a prediction should be trusted. Here, we study uncertainty estimation for NCA-based…

Image and Video Processing · Electrical Eng. & Systems 2026-05-27 Ario Sadafi , Michael Deutges , Nassir Navab , Carsten Marr

Inspired by cellular growth and self-organization, Neural Cellular Automata (NCAs) have been capable of "growing" artificial cells into images, 3D structures, and even functional machines. NCAs are flexible and robust computational systems…

Neural and Evolutionary Computing · Computer Science 2022-05-16 Shyam Sudhakaran , Elias Najarro , Sebastian Risi

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

Biological systems exhibit remarkable morphogenetic plasticity, where a single genome can encode various specialized cellular structures triggered by local chemical signals. In the domain of Deep Learning, Differentiable Neural Cellular…

Neural and Evolutionary Computing · Computer Science 2025-12-10 Ali Sakour

Neural Cellular Automata (NCA) have proven to be effective in a variety of fields, with numerous biologically inspired applications. One of the fields, in which NCAs perform well is the generation of textures, modelling global patterns from…

Neural and Evolutionary Computing · Computer Science 2025-11-25 Mirela-Magdalena Catrina , Ioana Cristina Plajer , Alexandra Baicoianu

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

Neural Cellular Automata (NCAs) are bio-inspired dynamical systems in which identical cells iteratively apply a learned local update rule to self-organize into complex patterns, exhibiting regeneration, robustness, and spontaneous dynamics.…

Computer Vision and Pattern Recognition · Computer Science 2026-05-05 Ehsan Pajouheshgar , Yitao Xu , Ali Abbasi , Alexander Mordvintsev , Wenzel Jakob , Sabine Süsstrunk

Memristors are novel non volatile devices that manage to combine storing and processing capabilities in the same physical place.Their nanoscale dimensions and low power consumption enable the further design of various nanoelectronic…

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

A broad range of computational models have been proposed to predict microstructure development during solidification processing but they have seldom been compared to each other on a quantitative and systematic basis. In this paper, we…

Materials Science · Physics 2022-11-08 S. M. Elahi , R. Tavakoli , I. Romero , D. Tourret

Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…

Computer Vision and Pattern Recognition · Computer Science 2026-01-30 Yitao Xu , Ehsan Pajouheshgar , Sabine Süsstrunk

Rapid advancements in deep learning over the past decade have fueled an insatiable demand for efficient and scalable hardware. Photonics offers a promising solution by leveraging the unique properties of light. However, conventional neural…

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