  The problem of generating microstructures of complex materials in silico has
been approached from various directions including simulation, Markov, deep
learning and descriptor-based approaches. This work presents a hybrid method
that is inspired by all four categories and has interesting scalability
properties. A neural cellular automaton is trained to evolve microstructures
based on local information. Unlike most machine learning-based approaches, it
does not directly require a data set of reference micrographs, but is trained
from statistical microstructure descriptors that can stem from a single
reference. This means that the training cost scales only with the complexity of
the structure and associated descriptors. Since the size of the reconstructed
structures can be set during inference, even extremely large structures can be
efficiently generated. Similarly, the method is very efficient if many
structures are to be reconstructed from the same descriptor for statistical
evaluations. The method is formulated and discussed in detail by means of
various numerical experiments, demonstrating its utility and scalability.
