The shortest-possible trefoil knot on the simple cubic lattice.
Source code and further explanation: https://community.wolfram.com/groups/-/m/t/1634541
@shonk Nice, but it's too bad the positions that it stops long enough to let you see it clearly are all positions where the projection maps more than one lattice point to the same point of the plane, so that the height of the knot curve above the projection plane is ambiguous.
@11011110 Well, that was kind of intentional (and also, being able to see the intermediate frames more clearly wouldn't have helped, because I cheated and just showed projections to the plane with no crossing information).
But, just for you, here are (slightly low res) 3D views of the midpoint between each pause in the animation:
@shonk Thanks. I don't have enough zomes on hand right now to tell for sure, but it seems there's a much more symmetric and equally-minimal-length embedding, with segments of lengths \((3,2,1,2)^3\) and sixfold (3-dihedral) symmetry. But maybe you were looking for a smaller bounding box rather than more symmetry?
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