a6 – Quadratic Potential Particle Flow

Particles advect along the rotated, gently nonlinear gradient field of quadratic potential V(x,y)=a x² + b x y + c y² distorted by time modulation, producing smooth filament flows.

Parameters

Quadratic Form a (xx) b (xy) c (yy) Rotation (deg) Nonlinearity Warp

Particles Count Trail length Step size Diffusion (jitter) Spawn margin

Animation Time speed Field drift Hue drift

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Rendering Stroke width Opacity Hue base Hue spread Light wave

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Formula

    V(x,y)=a x² + b x y + c y². Gradient ∇V=(2a x + b y, b x + 2c y). After rotation R(θ) and mild warping W we advect: p_{n+1}=p_n + dt * N( R(∇V) + warp * (x² - y², 2xy) + nonlin * |∇V|² * ∇V ) + diffusion.

   

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Parameters