a2 – Concentric Quadratic Forms (Rotated Ellipses)

Ellipses from quadratic forms x^T A x = c. Eigenvalues control axis lengths; rotation animates. Modulate eccentricity & color along radius.

Parameters

Structure Ellipses Samples per ellipse Radius scaling Base a-axis λ1 Base b-axis λ2 Eccentricity modulation

Animation Rotation speed Breathing scale Noise wobble Animation speed

Rendering Stroke width Opacity Color rotation Color spread Lightness wave

Controls

Formula

Ellipse i: x^T A_i x = c_i
A_i = R(θ_i) diag(1/λ1_i^2, 1/λ2_i^2) R(θ_i)^T
λk_i(t) = λk_base * (1 + eccMod*f_i + breathe*sin(t+φ_i))
θ_i(t) = θ0 + i*dθ + rotSpeed*t

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Parameters