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

TL;DR

This paper introduces a novel conditional neural cellular automata model that can generate specific digit structures from a single seed, guided by class labels, demonstrating stable, localized, and biologically inspired pattern formation.

Contribution

The work presents a new c-NCA architecture capable of class-conditional structural digit generation, bridging the gap between texture synthesis and biological morphogenesis in neural cellular automata.

Findings

Successfully generates distinct MNIST digits from a single pixel seed.

Achieves stable convergence and robustness in structural pattern formation.

Enforces locality and translation equivariance in the generative process.

Abstract

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.