# Texture Generation with Neural Cellular Automata

arXiv: https://arxiv.org/abs/2105.07299 · HTML: https://mlsanity.com/paper/2105.07299/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 15 May 2021.

## Builds on (most cited first, 13 of 13)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Texture Networks: Feed-forward Synthesis of Textures and Stylized Images](https://mlsanity.com/paper/1603.03417/) (2016)
- [Non-Stationary Texture Synthesis by Adversarial Expansion](https://mlsanity.com/paper/1805.04487/) (2018)
- [Learning Texture Manifolds with the Periodic Spatial GAN](https://mlsanity.com/paper/1705.06566/) (2017)
- [Learning a Neural 3D Texture Space from 2D Exemplars](https://mlsanity.com/paper/1912.04158/) (2019)
- [Lenia - Biology of Artificial Life](https://mlsanity.com/paper/1812.05433/) (2018)
- [Lenia and Expanded Universe](https://mlsanity.com/paper/2005.03742/) (2020)
- [GramGAN: Deep 3D Texture Synthesis From 2D Exemplars](https://mlsanity.com/paper/2006.16112/) (2020)
- [Texture Mixer: A Network for Controllable Synthesis and Interpolation of Texture](https://mlsanity.com/paper/1901.03447/) (2019)

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

- [μNCA: Texture Generation with Ultra-Compact Neural Cellular Automata](https://mlsanity.com/paper/2111.13545/) (2021)
- [Frequency-Time Diffusion with Neural Cellular Automata](https://mlsanity.com/paper/2401.06291/) (2024)
- [Pathfinding Neural Cellular Automata](https://mlsanity.com/paper/2301.06820/) (2023)
- [Multi-Texture Synthesis through Signal Responsive Neural Cellular Automata](https://mlsanity.com/paper/2407.05991/) (2024)
- [Neural Differential Appearance Equations](https://mlsanity.com/paper/2410.07128/) (2024)
- [Exploring Complex Dynamical Systems via Nonconvex Optimization](https://mlsanity.com/paper/2301.00923/) (2023)
- [TextNCA: Neural Cellular Automata for Language Modeling via Hierarchical Local Attention](https://mlsanity.com/paper/2608.02050/) (2026)
- [Applications of Neural Cellular Automata: State of the Art, Challenges and Opportunities](https://mlsanity.com/paper/2609.24595/) (2026)
- [Learning Traffic Flow Dynamics with Stochastic Physics-Informed Neural Cellular Automata](https://mlsanity.com/paper/2610.09946/) (2026)

## Abstract (arXiv)

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 they introduce lends itself to the generation of textures. Textures in the natural world are often generated by variants of locally interacting reaction-diffusion systems. Human-made textures are likewise often generated in a local manner (textile weaving, for instance) or using rules with local dependencies (regular grids or geometric patterns). We demonstrate learning a texture generator from a single template image, with the generation method being embarrassingly parallel, exhibiting quick convergence and high fidelity of output, and requiring only some minimal assumptions around the underlying state manifold. Furthermore, we investigate properties of the learned models that are both useful and interesting, such as non-stationary dynamics and an inherent robustness to damage. Finally, we make qualitative claims that the behaviour exhibited by the NCA model is a learned, distributed, local algorithm to generate a texture, setting our method apart from existing work on texture generation. We discuss the advantages of such a paradigm.