  Very recently, the Neural Cellular Automata (NCA) has been proposed to
simulate the morphogenesis process with deep networks. NCA learns to grow an
image starting from a fixed single pixel. In this work, we show that the neural
network (NN) architecture of the NCA can be encapsulated in a larger NN. This
allows us to propose a new model that encodes a manifold of NCA, each of them
capable of generating a distinct image. Therefore, we are effectively learning
an embedding space of CA, which shows generalization capabilities. We
accomplish this by introducing dynamic convolutions inside an Auto-Encoder
architecture, for the first time used to join two different sources of
information, the encoding and cells environment information. In biological
terms, our approach would play the role of the transcription factors,
modulating the mapping of genes into specific proteins that drive cellular
differentiation, which occurs right before the morphogenesis. We thoroughly
evaluate our approach in a dataset of synthetic emojis and also in real images
of CIFAR10. Our model introduces a general-purpose network, which can be used
in a broad range of problems beyond image generation.
