a4 – Hyperbola Lacework

Families of rotated / scaled hyperbolas x²/a² − y²/b² = 1 layered to create lace-like interference. Control parameter ranges, rotation, warps, and color mapping.

Parameters

Structure Branches (families) Hyperbolas / family a min a max b min b max Samples per curve

Warp & Rotation Global rotation speed Family angle spread (deg) Axis warp factor Breathing scale Time speed

Animate?

Rendering Stroke width Opacity Color rotation Color spread Lightness wave

Show asymptotes

Controls

Formula

Base: x²/a² − y²/b² = 1. Parameter t samples one branch: x = a cosh u, y = b sinh u. After rotation θ_f(t) and global Θ(t): apply linear transform R(Θ) R_f. Warp modifies a,b via a' = a(1 + warp sin(kf + t)), b' = b(1 + warp cos(kf + t)).

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a4 – Hyperbola Lacework

Parameters