# Growing Steerable Neural Cellular Automata

arXiv: https://arxiv.org/abs/2302.10197 · HTML: https://mlsanity.com/paper/2302.10197/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 19 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Lenia - Biology of Artificial Life](https://mlsanity.com/paper/1812.05433/) (2018)
- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [Learning Graph Cellular Automata](https://mlsanity.com/paper/2110.14237/) (2021)
- [Growing Isotropic Neural Cellular Automata](https://mlsanity.com/paper/2205.01681/) (2022)
- [Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent](https://mlsanity.com/paper/2106.15240/) (2021)
- [E(n)-equivariant Graph Neural Cellular Automata](https://mlsanity.com/paper/2301.10497/) (2023)
- [Physical Neural Cellular Automata for 2D Shape Classification](https://mlsanity.com/paper/2203.07548/) (2022)
- [Differentiable Programming of Reaction-Diffusion Patterns](https://mlsanity.com/paper/2107.06862/) (2021)

## Built on by (most cited first, 6 of 6)

- [Biomaker CA: a Biome Maker project using Cellular Automata](https://mlsanity.com/paper/2307.09320/) (2023)
- [Identity Increases Stability in Neural Cellular Automata](https://mlsanity.com/paper/2508.06389/) (2025)
- [Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems](https://mlsanity.com/paper/2601.14096/) (2026)
- [Missing Data Imputation using Neural Cellular Automata](https://mlsanity.com/paper/2509.00651/) (2025)
- [Neuroevolution Arena: Nested Ecological Evaluation of Update-and-Inheritance Regimes across Neural Architectures](https://mlsanity.com/paper/2608.10323/) (2026)
- [Applications of Neural Cellular Automata: State of the Art, Challenges and Opportunities](https://mlsanity.com/paper/2609.24595/) (2026)

## Abstract (arXiv)

Neural Cellular Automata (NCA) models have shown remarkable capacity for pattern formation and complex global behaviors stemming from local coordination. However, in the original implementation of NCA, cells are incapable of adjusting their own orientation, and it is the responsibility of the model designer to orient them externally. A recent isotropic variant of NCA (Growing Isotropic Neural Cellular Automata) makes the model orientation-independent - cells can no longer tell up from down, nor left from right - by removing its dependency on perceiving the gradient of spatial states in its neighborhood. In this work, we revisit NCA with a different approach: we make each cell responsible for its own orientation by allowing it to "turn" as determined by an adjustable internal state. The resulting Steerable NCA contains cells of varying orientation embedded in the same pattern. We observe how, while Isotropic NCA are orientation-agnostic, Steerable NCA have chirality: they have a predetermined left-right symmetry. We therefore show that we can train Steerable NCA in similar but simpler ways than their Isotropic variant by: (1) breaking symmetries using only two seeds, or (2) introducing a rotation-invariant training objective and relying on asynchronous cell updates to break the up-down symmetry of the system.