Fractals11 of 113
Mandelbrot set
Benoît Mandelbrot, 1980
The points c for which z ↦ z² + c, started at zero, never runs off to infinity. The set is the solid shape. The lines around it are contours of escape: each one joins points that take the same number of steps to leave, and they crowd together at the edge. The zooms dive toward the seahorse valley and toward a small copy of the whole set on the real axis.
zₙ₊₁ = zₙ² + c, z₀ = 0
On mathcurve.com as Ensemble de Mandelbrot
Variant
Elsewhere
1Work the library cites and does not hold: in copyright, never released as a file, or not a file at all. The cited shelf
- 2004
A pop song about the set, from the album Where Tradition Meets Tomorrow. It names the Sierpinski gasket on the way.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer had doubts, 2026-10-09: The library record gives the title "Mandelbrot Set" for a 2004 song, but the holder's page, which says "In 2005 I left my day job writing software to pursue music full time.", never mentions this song, its album, or a Sierpinski gasket. The link rests on the matching title alone, and the note's album and gasket details are not borne out by any evidence shown.