Heinz Hopf1894–1971
Hopf fibration
German mathematician whose Hopf fibration links every point on a sphere to a circle, creating one of topology’s most striking structures.
Hopf Fibres
Circles from a four-dimensional sphere project into a linked bundle. Every pair is linked once; a chosen band of fibres becomes a flowing, hollow sculpture.
About this pattern
Heinz Hopf, 1931 · stereographic projection
Each curve is one fibre of the Hopf map. We parameterise its circle on S³ and stereographically project into three dimensions, then draw a two-dimensional view. Latitude chooses the bundle, spread reveals a portion of it, and the rear arcs fade into the page.
Behind the mathematics