Today I learned about a visualisation project that tries to map the transitions from rubik cube states.
They flattened one-hot encoded colors on each of the faces of the cube to construct a vector that represents the state of a cube. They generated these representations for randomly generated cubes, after which they ran a solver to connect the states which led to the visualisation that you see above.
It's interesting to see clusters appear that seem to make sense. I would've expected that a neighborhood graph would be a more reliable starting point to represent the cubes states but just the one-hot encodings with euclidean distance seem sufficient to point out clusters where the solvers like to hang out.