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Hopf Fibres

Hopf Fibres

© 2026·Created by Leon Poole·Privacy

Hopf Fibres

Tune

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.

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.

isometricorganic

Hopf Fibres

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All patterns
{"generator":"GART","pattern":"harmonic-shells","seed":"","params":{"lobes":4,"relief":0.38,"rings":30,"yaw":24,"pitch":28,"fade":0.65}}

Harmonic Shells

{"generator":"GART","pattern":"torus-knots","seed":"","params":{"knot":"2:3","strands":9,"spread":0.025,"yaw":18,"pitch":36,"radius":0.48,"rotation":-18,"clearance":1.5}}

Torus Knots

{"generator":"GART","pattern":"topography","seed":"terrain-04","params":{"motion":0,"motionSpeed":1,"seed":"terrain-04","landform":"island","levels":25,"roughness":0.3,"scale":2.4,"stretch":1.12}}

Topography

{"generator":"GART","pattern":"harmonograph","seed":"","params":{"motion":0,"motionSpeed":1,"ratio":"2:3","detune":0.012,"damping":0.004,"turns":45,"phase":90,"coupling":0.2,"rotation":-12}}

Harmonograph

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