Golden-Angle Spiral: Three Equivalent Views

N = 36 qubit states sampled on the Bloch sphere.
Polar angle: equal-area mapping z = cos θ  ·  Azimuthal increment: Δφ = (3−√5)π ≈ 2.39996 rad
Full turns: 14  ·  Wrapped phases: 36  ·  Shannon entropy: 5.322 bits (near-optimal)

Wrapped Phase φ mod 2π — all 14 turns collapse onto one circle

36 states · 14 full turns collapsed

Unwrapped Chain Each turn gets its own circle — continuity preserved

Turn index increases left → right, top → bottom

Bloch Sphere Spiral Equal-area latitudes · golden-angle azimuth · 3D projection
|+⟩ |−⟩ x y

Polar angle from equal-area z = cos θ  ·  Azimuth n·Δφ

N = 36
Δφ = (3−√5)π ≈ 2.39996 rad
Full turns = 14
Entropy = 5.322 / 5.322 bits
Min/max bin (40 bins) = 3 / 10
State n
Phase on circle