# Neural Cellular Automata Manifold

arXiv: https://arxiv.org/abs/2006.12155 · HTML: https://mlsanity.com/paper/2006.12155/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [Med-NCA: Robust and Lightweight Segmentation with Neural Cellular Automata](https://mlsanity.com/paper/2302.03473/) (2023)
- [Neural cellular automata: applications to biology and beyond classical AI](https://mlsanity.com/paper/2509.11131/) (2025)
- [EngramNCA: a Neural Cellular Automaton Model of Memory Transfer](https://mlsanity.com/paper/2504.11855/) (2025)
- [Generalization over different cellular automata rules learned by a deep feed-forward neural network](https://mlsanity.com/paper/2103.14886/) (2021)
- [Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organization](https://mlsanity.com/paper/2506.20486/) (2025)
- [On Growth and Form, and Function: Reusable Regulatory Handles Control Phenotypic Variation](https://mlsanity.com/paper/2609.29755/) (2026)

## Abstract (arXiv)

Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. In this work, we show that the neural network (NN) architecture of the NCA can be encapsulated in a larger NN. This allows us to propose a new model that encodes a manifold of NCA, each of them capable of generating a distinct image. Therefore, we are effectively learning an embedding space of CA, which shows generalization capabilities. We accomplish this by introducing dynamic convolutions inside an Auto-Encoder architecture, for the first time used to join two different sources of information, the encoding and cells environment information. In biological terms, our approach would play the role of the transcription factors, modulating the mapping of genes into specific proteins that drive cellular differentiation, which occurs right before the morphogenesis. We thoroughly evaluate our approach in a dataset of synthetic emojis and also in real images of CIFAR10. Our model introduces a general-purpose network, which can be used in a broad range of problems beyond image generation.