Transactions on Machine Learning Research (TMLR) · 2026

A New Kind of Network? Review and Reference Implementation of Neural Cellular Automata

Martin Spitznagel, Janis Keuper

Why this publication matters

Complex patterns can emerge when many simple units repeatedly follow local rules. This review explains how neural cellular automata learn such rules and provides a shared software framework for experimenting with them. The combination makes a less conventional model family easier to understand, reproduce, and extend.

Abstract

Stephen Wolfram proclaimed in his 2003 seminal work “A New Kind Of Science” that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used mathematical formalizations, e.g. differential equations, to improve the modeling of complex systems. Over two decades later, while Cellular Automata have still been waiting for a substantial breakthrough in scientific applications, recent research showed new and promising approaches which combine Wolfram’s ideas with learnable Artificial Neural Networks: So-called Neural Cellular Automata (NCA) are able to learn the complex update rules of CA from data samples, allowing them to model complex, self-organizing generative systems. The aim of this paper is to review the existing work on NCA and provide a unified modular framework and notation, as well as a reference implementation in the open-source library NCAtorch. Project Website: https://www.neural-cellular-automata.org/ Source Code: https://github.com/mspitzna/NCAtorch

Abstract source ↗

Figures

A cellular automaton evolving through local update rules over time. — **Figure 1.** Visualization of a simple, 1D CA with binary states. a) shows the recursive update of grid states over time by applying the update rules R on the 3 × 1 cell neighborhoods shown in b). View in source ↗

**Figure 2.** Sketch of a basic CNN implementation of a 2D NCA with a 3D state space. The initial grid is fed into a CNN architecture which updates the state additively and is called recursively for each time step. During training, the network is trained via usual gradient updates computed per timestep. View in source ↗

Cite this paper

Download .bib

@article{spitznagel2026anewkind83,
  title = {{A New Kind of Network? Review and Reference Implementation of Neural Cellular Automata}},
  author = {Martin Spitznagel and Janis Keuper},
  journal = {Transactions on Machine Learning Research},
  year = {2026},
  url = {https://openreview.net/pdf?id=NRwjj0ZLq0}
}

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