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Torus Knots

Torus Knots

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Torus Knots

Tune

A closed curve winds around a torus in two directions. Parallel strands make a sculptural ribbon; small breaks at crossings reveal which strands pass in front.

Torus-knot geometry · coprime winding numbers

The two winding numbers are coprime, so each strand forms one closed knot rather than a disconnected link. Nearby minor radii make a ribbon on the torus. Short projected spans are sorted by depth and drawn with a paper-coloured clearance before the ink, opening the crossings.

isometricorganic

Torus Knots

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{"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":"hopf-fibres","seed":"","params":{"fibres":32,"latitude":0.7,"spread":290,"yaw":26,"pitch":46,"fade":0.65}}

Hopf Fibres

{"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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