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Fibonacci Spiral

Fibonacci Spiral

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Fibonacci Spiral

Tune

Squares whose sides are the Fibonacci sequence. A quarter-circle in each chamber is the golden spiral; an inset at 1/φ is the septum.

Leonardo of Pisa (Fibonacci), 1202

Liber Abaci (1202) gave Europe the sequence 1, 1, 2, 3, 5, … Each new square’s side is the sum of the two before it. A quarter-circle in each square is the golden spiral; an inset at 1/φ reads as a shell chamber. Motion unfurls the tiling: each square buds from the last, the spiral follows, the frame zooms out with φ, then the sequence recedes.

organicgrid
Squares
1, 1, 2. Each new square’s side is the sum of the two before it.

Fibonacci Spiral

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All patterns
{"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":"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":"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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