Animation Pack
3 seamlessly looping conformal map animations — Möbius grids spinning through 360° and Joukowski airfoils breathing color.
Price
$10.00
Secure payment via PayPal · Instant download · Personal license
About the craft
Every piece in this bundle is rendered from real mathematical equations — no AI, no procedural noise filters, no stock libraries. Generated frame by frame from the underlying systems by a small studio of mathematicians and engineers.
Included
The mathematics
The complex plane is the natural home of conformal transformations — maps that preserve angles locally while warping distances. Möbius transformations of the form f(z) = (az + b) / (cz + d) move circles to circles and lines to lines, and they generate every angle-preserving symmetry of the Riemann sphere. The Joukowski transform w = z + 1/z maps a circle to an airfoil cross-section — the same one used in early aerodynamics to compute lift. Apply these maps to a regular grid and the result is unmistakably geometric and unmistakably mathematical: the lines bend exactly as the complex algebra demands. Each image and animation in this collection is computed from the underlying complex function — no Bézier curves, no artistic license.
f(z) = (az+b)/(cz+d), w = z + 1/z
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