Takes a curve (on a plane), creates unordered pairs of all
points in the curve, and new point location is the midpoint,
elevation is the distance. I first encountered with this construction in a
3blue1brown video
This gif
is around for a while: stereographic projection of a spiral on a sphere. I had an idea to step up a dimension,
4d hypersphere projected onto 3d space. Obviously I don't see in 4d, and could made mistakes,
but this program is the result.