Neural Cellular Automata (NCA We use NCA to refer to both Neural Cellular Automata and Neural Cellular Automaton.) are capable of learning a diverse set of behaviours: from generating stable, regenerating, static images , to segmenting images , to learning to “self-classify” shapes . The inductive bias imposed by using cellular automata is powerful. A system of individual agents running the same learned local rule can solve surprisingly complex tasks. Moreover, individual agents, or cells, can learn to coordinate their behavior even when separated by large distances. By construction, they solve these tasks in a massively parallel and inherently degenerate Degenerate in this case refers to the biological concept of degeneracy. way. Each cell must be able to take on the role of any other cell - as a result they tend to generalize well to unseen situations.

In this work, we apply NCA to the task of texture synthesis. This task involves reproducing the general appearance of a texture template, as opposed to making pixel-perfect copies. We are going to focus on texture losses that allow for a degree of ambiguity. After training NCA models to reproduce textures, we subsequently investigate their learned behaviors and observe a few surprising effects. Starting from these investigations, we make the case that the cells learn distributed, local, algorithms.

To do this, we apply an old trick: we employ neural cellular automata as a differentiable image parameterization .