# Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organization

arXiv: https://arxiv.org/abs/2506.20486 · HTML: https://mlsanity.com/paper/2506.20486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 25 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Cellular automata as convolutional neural networks](https://mlsanity.com/paper/1809.02942/) (2018)
- [Learning Graph Cellular Automata](https://mlsanity.com/paper/2110.14237/) (2021)
- [Variational Neural Cellular Automata](https://mlsanity.com/paper/2201.12360/) (2022)
- [Attention-based Neural Cellular Automata](https://mlsanity.com/paper/2211.01233/) (2022)
- [Learning to Generate 3D Shapes with Generative Cellular Automata](https://mlsanity.com/paper/2103.04130/) (2021)
- [Learning spatio-temporal patterns with Neural Cellular Automata](https://mlsanity.com/paper/2310.14809/) (2023)
- [Neural Cellular Automata Manifold](https://mlsanity.com/paper/2006.12155/) (2020)
- [Latent Neural Cellular Automata for Resource-Efficient Image Restoration](https://mlsanity.com/paper/2403.15525/) (2024)
- [Outdoor Scene Extrapolation with Hierarchical Generative Cellular Automata](https://mlsanity.com/paper/2406.08292/) (2024)

## Abstract (arXiv)

Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of real-world biological and physical systems. We propose the Mixture of Neural Cellular Automata (MNCA), a novel framework incorporating the idea of mixture models into the NCA paradigm. By combining probabilistic rule assignments with intrinsic noise, MNCAs can model diverse local behaviors and reproduce the stochastic dynamics observed in biological processes. We evaluate the effectiveness of MNCAs in three key domains: (1) synthetic simulations of tissue growth and differentiation, (2) image morphogenesis robustness, and (3) microscopy image segmentation. Results show that MNCAs achieve superior robustness to perturbations, better recapitulate real biological growth patterns, and provide interpretable rule segmentation. These findings position MNCAs as a promising tool for modeling stochastic dynamical systems and studying self-growth processes.