# Physical Neural Cellular Automata for 2D Shape Classification

arXiv: https://arxiv.org/abs/2203.07548 · HTML: https://mlsanity.com/paper/2203.07548/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 14 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Cellular automata as convolutional neural networks](https://mlsanity.com/paper/1809.02942/) (2018)
- [Growing 3D Artefacts and Functional Machines with Neural Cellular Automata](https://mlsanity.com/paper/2103.08737/) (2021)
- [Collective Intelligence for Deep Learning: A Survey of Recent Developments](https://mlsanity.com/paper/2111.14377/) (2021)
- [Regenerating Soft Robots through Neural Cellular Automata](https://mlsanity.com/paper/2102.02579/) (2021)

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

- [Goal-Guided Neural Cellular Automata: Learning to Control Self-Organising Systems](https://mlsanity.com/paper/2205.06806/) (2022)
- [Differentiable Logic Cellular Automata: From Game of Life to Pattern Generation](https://mlsanity.com/paper/2506.04912/) (2025)
- [Growing Steerable Neural Cellular Automata](https://mlsanity.com/paper/2302.10197/) (2023)
- [NCA-Morph: Medical Image Registration with Neural Cellular Automata](https://mlsanity.com/paper/2410.22265/) (2024)
- [Neural Cellular Automata Learn General Features in their Hidden Channels](https://mlsanity.com/paper/2609.21870/) (2026)
- [Neural Cellular Automata for Decentralized Sensing using a Soft Inductive Sensor Array for Distributed Manipulator Systems](https://mlsanity.com/paper/2502.01242/) (2025)
- [Applications of Neural Cellular Automata: State of the Art, Challenges and Opportunities](https://mlsanity.com/paper/2609.24595/) (2026)

## Abstract (arXiv)

Materials with the ability to self-classify their own shape have the potential to advance a wide range of engineering applications and industries. Biological systems possess the ability not only to self-reconfigure but also to self-classify themselves to determine a general shape and function. Previous work into modular robotics systems has only enabled self-recognition and self-reconfiguration into a specific target shape, missing the inherent robustness present in nature to self-classify. In this paper we therefore take advantage of recent advances in deep learning and neural cellular automata, and present a simple modular 2D robotic system that can infer its own class of shape through the local communication of its components. Furthermore, we show that our system can be successfully transferred to hardware which thus opens opportunities for future self-classifying machines. Code available at https://github.com/kattwalker/projectcube. Video available at https://youtu.be/0TCOkE4keyc.