Having discussed Mondrian's apparent use of geometry (and my own surmise as to where he might have gone next) I was challenged to generate some images that show how simple geometric constructions can appear far-from-simple when drawn in a non-Euclidean geometry.
The image above is simply a grid of cross-overs drawn inside a "hemisphere". Here is what they would look like if drawn on the rectangular grid (i.e graph paper) with which we are all familiar.
The curved version is obtained from the linear version simply by twisting the pattern round until the loose ends join up.
The original image is simpler than it looks, is it not?