MarkovJunior is a probabilistic programming language where programs are combinations of rewrite rules and inference is performed via constraint propagation. MarkovJunior is named after mathematician Andrey Andreyevich Markov, who defined and studied what is now called Markov algorithms.
MarkovJunior is written in C# and XML and runs using the .NET framework.
For a more in-depth deconstruction of how the MarkovJunior algorithm works, please refer to the original repository by Maxim Gumin (mxgmm).
MarkovJunior interpreter is a console application that depends only on the standard library. Get .NET Core for Windows, Linux or macOS and run
dotnet run --configuration Release MarkovJunior.csproj
Alternatively, download and run the latest release for Windows.
Generated results are put into the output folder. Edit models.xml to change model parameters. Open .vox files with MagicaVoxel.
The first step in using MarkovJunior to recreate EBSDs is to choose a reference EBSD. The one I chose was a stainless steel EBSD from a paper by C.J. Todaro, it's pictured below.
The next step is to extract information, such as the volume fraction, # of centroids, and orientation fraction from the reference.
The folder labeled Stats Extraction (its a subfolder of "Research Project") contains 2 stats extraction files (they are both the same program, but one is a python file and the other is a jupyter notebook).
Either file can be used to get these values from the reference.
The 3rd step is to use the MarkovJunior algorithm to input the statistics to generate a tessalation.
The Voronoi.xml model, when ran, produces a tessalation from the growth of 2000+ centroids, each with one of 8 distinct colors. The colors that are represented by each letter can be found in palette.xml.
The 8 centroid colors used were Emerald, Gray, Blue ,Red, Yellow, Brown, Purple, and Orange.
In the Voronoi model, the 2 instances of the probability variables can be used to control the orientation fraction and volume fraction, respictively.
In the algorithm, models.xml can be used to generate both a 2D and 3D voronoi tessalation.
The last step is to use the 2D tessalation to generate an EBSD. This can be done using either of the Stats Extraction files. The final EBSD generated is pictured below, as well as the comparisons in stats between the reference and generated.
This research was funded by the Army Educational Outreach Program (AEOP) and the Hopkins Extreme Materials Institute (HEMI) at Johns Hopkins University.