Procedural Generation of Grain Orientations using the Wave Function
  Collapse Algorithm
G. Magny-Fokam D. Madisetti J. El-Awady
Statistics of grain sizes and orientations in metals correlate to the
material's mechanical properties. Reproducing representative volume elements
for further analysis of deformation and failure in metals, like 316L stainless
steel, is particularly important due to their wide use in manufacturing goods
today. Two approaches, initially created for video games, were considered for
the procedural generation of representative grain microstructures. The first is
the Wave Function Collapse (WFC) algorithm, and the second is constraint
propagation and probabilistic inference through Markov Junior, a free and
open-source software. This study aimed to investigate these two algorithms'
effectiveness in using reference electron backscatter diffraction (EBSD) maps
and recreating a statistically similar one that could be used in further
research. It utilized two stainless steel EBSD maps as references to test both
algorithms. First, the WFC algorithm was too constricting and, thus, incapable
of producing images that resembled EBSDs. The second, MarkovJunior, was much
more effective in creating a Voronoi tessellation that could be used to create
an EBSD map in Python. When comparing the results between the reference and the
generated EBSD, we discovered that the orientation and volume fractions were
extremely similar. With the study, it was concluded that MarkovJunior is an
effective machine learning tool that can reproduce representative grain
microstructures.