# Emergent Dynamics in Neural Cellular Automata

arXiv: https://arxiv.org/abs/2404.06406 · HTML: https://mlsanity.com/paper/2404.06406/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 9 Apr 2024.

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

- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [DyNCA: Real-time Dynamic Texture Synthesis Using Neural Cellular Automata](https://mlsanity.com/paper/2211.11417/) (2022)
- [Two-Stream Convolutional Networks for Dynamic Texture Synthesis](https://mlsanity.com/paper/1706.06982/) (2017)
- [Mesh Neural Cellular Automata](https://mlsanity.com/paper/2311.02820/) (2023)
- [Goal-Guided Neural Cellular Automata: Learning to Control Self-Organising Systems](https://mlsanity.com/paper/2205.06806/) (2022)
- [Collective control of modular soft robots via embodied Spiking Neural Cellular Automata](https://mlsanity.com/paper/2204.02099/) (2022)

## Built on by (most cited first, 1 of 1)

- [Neural Cellular Automata: From Cells to Pixels](https://mlsanity.com/paper/2506.22899/) (2025)

## Abstract (arXiv)

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 required for an NCA to display dynamic patterns remain unexplored. Here, we investigate the relationship between the NCA architecture and the emergent dynamics of the trained models. Specifically, we vary the number of channels in the cell state and the number of hidden neurons in the MultiLayer Perceptron (MLP), and draw a relationship between the combination of these two variables and the motion strength between successive frames. Our analysis reveals that the disparity and proportionality between these two variables have a strong correlation with the emergent dynamics in the NCA output. We thus propose a design principle for creating dynamic NCA.