# Neural cellular automata: applications to biology and beyond classical AI

arXiv: https://arxiv.org/abs/2509.11131 · HTML: https://mlsanity.com/paper/2509.11131/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 132 references that are in the map.
- First posted on arXiv 14 Sep 2025.

## Builds on (most cited first, 30 of 45)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [A Review of Cooperative Multi-Agent Deep Reinforcement Learning](https://mlsanity.com/paper/1908.03963/) (2019)
- [ARC Prize 2024: Technical Report](https://mlsanity.com/paper/2412.04604/) (2024)
- [A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data](https://mlsanity.com/paper/2402.16991/) (2024)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [Learning to Control Self-Assembling Morphologies: A Study of Generalization via Modularity](https://mlsanity.com/paper/1902.05546/) (2019)
- [Cellular automata as convolutional neural networks](https://mlsanity.com/paper/1809.02942/) (2018)
- [The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instability](https://mlsanity.com/paper/2310.17467/) (2023)
- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [Variational Neural Cellular Automata](https://mlsanity.com/paper/2201.12360/) (2022)
- [Attention-based Neural Cellular Automata](https://mlsanity.com/paper/2211.01233/) (2022)
- [Technological Approach to Mind Everywhere (TAME): an experimentally-grounded framework for understanding diverse bodies and minds](https://mlsanity.com/paper/2201.10346/) (2021)
- [Med-NCA: Robust and Lightweight Segmentation with Neural Cellular Automata](https://mlsanity.com/paper/2302.03473/) (2023)
- [HyperNCA: Growing Developmental Networks with Neural Cellular Automata](https://mlsanity.com/paper/2204.11674/) (2022)
- [Diffusion Models are Evolutionary Algorithms](https://mlsanity.com/paper/2410.02543/) (2024)
- [Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent](https://mlsanity.com/paper/2106.15240/) (2021)
- [Regenerating Soft Robots through Neural Cellular Automata](https://mlsanity.com/paper/2102.02579/) (2021)
- [μNCA: Texture Generation with Ultra-Compact Neural Cellular Automata](https://mlsanity.com/paper/2111.13545/) (2021)
- [There's Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-scale Machines](https://mlsanity.com/paper/2212.10675/) (2022)
- [ARC-NCA: Towards Developmental Solutions to the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2505.08778/) (2025)
- [Neural Cellular Automata for ARC-AGI](https://mlsanity.com/paper/2506.15746/) (2025)
- [Differentiable Logic Cellular Automata: From Game of Life to Pattern Generation](https://mlsanity.com/paper/2506.04912/) (2025)
- [Evolving Modular Soft Robots without Explicit Inter-Module Communication using Local Self-Attention](https://mlsanity.com/paper/2204.06481/) (2022)
- [CAX: Cellular Automata Accelerated in JAX](https://mlsanity.com/paper/2410.02651/) (2024)

## Built on by (most cited first, 9 of 9)

- [On the Spatiotemporal Dynamics of Generalization in Neural Networks](https://mlsanity.com/paper/2602.01651/) (2026)
- [Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems](https://mlsanity.com/paper/2601.14096/) (2026)
- [BraiNCA: brain-inspired neural cellular automata and applications to morphogenesis and motor control](https://mlsanity.com/paper/2604.01932/) (2026)
- [Communication Heterogeneity and Collective Consensus in Neural Cellular Automata](https://mlsanity.com/paper/2606.21202/) (2026)
- [Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automaton](https://mlsanity.com/paper/2607.27320/) (2026)
- [The Artificial Experimentalist: Discovery and Control of Self-Organizing Phenomena with Autotelic Reinforcement Learning](https://mlsanity.com/paper/2608.26116/) (2026)
- [Learning PDE Time-Stepping with Neural Cellular Automata](https://mlsanity.com/paper/2608.30328/) (2026)
- [Applications of Neural Cellular Automata: State of the Art, Challenges and Opportunities](https://mlsanity.com/paper/2609.24595/) (2026)
- [On Growth and Form, and Function: Reusable Regulatory Handles Control Phenotypic Variation](https://mlsanity.com/paper/2609.29755/) (2026)

## Abstract (arXiv)

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 self-regulatory dynamics of living matter. By embedding Artificial Neural Networks (ANNs) as local decision-making centers and interaction rules between localized agents, NCA can simulate processes across molecular, cellular, tissue, and system-level scales, offering a multiscale competency architecture perspective on evolution, development, regeneration, aging, morphogenesis, and robotic control. These models not only reproduce biologically inspired target patterns but also generalize to novel conditions, demonstrating robustness to perturbations and the capacity for open-ended adaptation and reasoning. Given their immense success in recent developments, we here review current literature of NCAs that are relevant primarily for biological or bioengineering applications. Moreover, we emphasize that beyond biology, NCAs display robust and generalizing goal-directed dynamics without centralized control, e.g., in controlling or regenerating composite robotic morphologies or even on cutting-edge reasoning tasks such as ARC-AGI-1. In addition, the same principles of iterative state-refinement is reminiscent to modern generative Artificial Intelligence (AI), such as probabilistic diffusion models. Their governing self-regulatory behavior is constraint to fully localized interactions, yet their collective behavior scales into coordinated system-level outcomes. We thus argue that NCAs constitute a unifying computationally lean paradigm that not only bridges fundamental insights from multiscale biology with modern generative AI, but have the potential to design truly bio-inspired collective intelligence capable of hierarchical reasoning and control.