# Conditional Morphogenesis: Emergent Generation of Structural Digits via Neural Cellular Automata

arXiv: https://arxiv.org/abs/2512.08360 · HTML: https://mlsanity.com/paper/2512.08360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 8 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 2 of 2)

- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Variational Neural Cellular Automata](https://mlsanity.com/paper/2201.12360/) (2022)

## Abstract (arXiv)

Biological systems exhibit remarkable morphogenetic plasticity, where a single genome can encode various specialized cellular structures triggered by local chemical signals. In the domain of Deep Learning, Differentiable Neural Cellular Automata (NCA) have emerged as a paradigm to mimic this self-organization. However, existing NCA research has predominantly focused on continuous texture synthesis or single-target object recovery, leaving the challenge of class-conditional structural generation largely unexplored. In this work, we propose a novel Conditional Neural Cellular Automata (c-NCA) architecture capable of growing distinct topological structures - specifically MNIST digits - from a single generic seed, guided solely by a spatially broadcasted class vector. Unlike traditional generative models (e.g., GANs, VAEs) that rely on global reception fields, our model enforces strict locality and translation equivariance. We demonstrate that by injecting a one-hot condition into the cellular perception field, a single set of local rules can learn to break symmetry and self-assemble into ten distinct geometric attractors. Experimental results show that our c-NCA achieves stable convergence, correctly forming digit topologies from a single pixel, and exhibits robustness characteristic of biological systems. This work bridges the gap between texture-based NCAs and structural pattern formation, offering a lightweight, biologically plausible alternative for conditional generation.