The Mandelbrot potential mountain: rendering the set's Green function as 3D terrain
geoffreyirving · x · 2026-10-31
A striking math visualization titled 'The Mandelbrot potential mountain': the author renders the Green's function G outside the Mandelbrot set as terrain height (1 − G^0.35), turning equipotentials and external rays into a 3D fractal landscape.
- Equipotential bands shaded at G = 2^-k; external rays marked at angles 0, 1/3, 1/2, 2/3 and k/7
- Main cardioid, bulbs p=2 through 7, and primitive islands color-coded as the cascade splits the set
- Computed in f64, display-only, not certified
Hardcore mathematical aesthetics at its finest.
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