# A Path to Universal Neural Cellular Automata

arXiv: https://arxiv.org/abs/2505.13058 · HTML: https://mlsanity.com/paper/2505.13058/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 7 of 7)

- [A Survey of Neuromorphic Computing and Neural Networks in Hardware](https://mlsanity.com/paper/1705.06963/) (2017)
- [HyperNCA: Growing Developmental Networks with Neural Cellular Automata](https://mlsanity.com/paper/2204.11674/) (2022)
- [Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems](https://mlsanity.com/paper/1908.06663/) (2019)
- [Toward Artificial Open-Ended Evolution within Lenia using Quality-Diversity](https://mlsanity.com/paper/2406.04235/) (2024)
- [Discovering Sensorimotor Agency in Cellular Automata using Diversity Search](https://mlsanity.com/paper/2402.10236/) (2024)
- [CAX: Cellular Automata Accelerated in JAX](https://mlsanity.com/paper/2410.02651/) (2024)
- [EngramNCA: a Neural Cellular Automaton Model of Memory Transfer](https://mlsanity.com/paper/2504.11855/) (2025)

## Built on by (most cited first, 6 of 6)

- [Neural cellular automata: applications to biology and beyond classical AI](https://mlsanity.com/paper/2509.11131/) (2025)
- [Learning Developmental Scaffoldings to Guide Self-Organisation](https://mlsanity.com/paper/2605.14998/) (2026)
- [Neural Field Turing Machine: A Differentiable Spatial Computer](https://mlsanity.com/paper/2509.03370/) (2025)
- [Self-Organising Digital Circuits](https://mlsanity.com/paper/2608.02606/) (2026)
- [Communication Heterogeneity and Collective Consensus in Neural Cellular Automata](https://mlsanity.com/paper/2606.21202/) (2026)
- [MetaLearnNCA: Few-Shot Offline Meta-Learning via Interacting Neural Cellular Automata](https://mlsanity.com/paper/2610.08479/) (2026)

## Abstract (arXiv)

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 have extended cellular automata into continuous domains, raising the question of whether these systems retain the capacity for universal computation. In parallel, neural cellular automata have emerged as a powerful paradigm where rules are learned via gradient descent rather than manually designed. This work explores the potential of neural cellular automata to develop a continuous Universal Cellular Automaton through training by gradient descent. We introduce a cellular automaton model, objective functions and training strategies to guide neural cellular automata toward universal computation in a continuous setting. Our experiments demonstrate the successful training of fundamental computational primitives - such as matrix multiplication and transposition - culminating in the emulation of a neural network solving the MNIST digit classification task directly within the cellular automata state. These results represent a foundational step toward realizing analog general-purpose computers, with implications for understanding universal computation in continuous dynamics and advancing the automated discovery of complex cellular automata behaviors via machine learning.