$μ$NCA: Texture Generation with Ultra-Compact Neural Cellular Automata

We study the problem of example-based procedural texture synthesis using highly compact models. Given a sample image, we use differentiable programming to train a generative process, parameterised by a recurrent Neural Cellular Automata (NCA) rule. Contrary to the common belief that neural networks should be significantly over-parameterised, we demonstrate that our model architecture and training procedure allows for representing complex texture patterns using just a few hundred learned parameters, making their expressivity comparable to hand-engineered procedural texture generating programs. The smallest models from the proposed $\mu$NCA family scale down to 68 parameters. When using quantisation to one byte per parameter, proposed models can be shrunk to a size range between 588 and 68 bytes. Implementation of a texture generator that uses these parameters to produce images is possible with just a few lines of GLSL or C code.