I’ve been wondering if there is a nice way to traverse the 3-sphere via adjacent tetrahedral cells. It would be fun to use the 600-cell to quantize orientations instead of using a tesseract cube map. But quantizing without orthogonality seems to require doing an expensive search.

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This points at performing Bresenham's line rasterizing algorithm for walking across equilateral triangles in the hyperbolic plane as if they were Euclidean squares.

en.wikipedia.org/wiki/Bresenh...

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I just realized that the whole point of the modular group is to see the 2D structure of the rational numbers in terms of the integers.

The first action increments the numerator, the second action exchanges the numerator and denominator.

en.m.wikipedia.org/wiki/Modular...

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