(11, 2012)

Hypersphere is an exploration into the behavior of curves on the surface of a four-dimensional hypersphere. Created using custom-written software, the video presents a sampling of the infinite variety shapes that can be produced by simple curves. To facilitate visualizing these four-dimensional shapes, we examine their three-dimensional shadows and use coloration to denote the fourth. To obtain more variety, curves may be viewed from different angles in 4D space; this is analogous to rotating an object and watching its shadow change as different sides are exposed.