Evolution of Julia sets as parameter dives into crevice with argument 1/3 @davidamadore

Uploaded March 2020 | Updated September 2026, 2 weeks ago

Evolution of Julia sets as their parameter point follows the parameter ray with external argument 1/3, diving into the crevice between the main cardioid and its period 2 bud. The position of the parameter point is shown in red in the Mandelbrot inset at the bottom left. Its external argument is constantly 1/3 and it approaches the bud's root (−¾) exponentially slowly.

Evolution of Julia sets as parameter dives into crevice with argument 1/3

Cubic surface: deformation of three planes to the Cayley cubic surface

Cubic surface: deformation of three A2 singularities (with real planes) to three A1 singularities

Between the horizons of a Kerr black hole (the lazy geodesic)

Visiting a Kerr black hole (old version / combined view)

Waves on a flat torus (triangular lattice)

Orbiting a Kerr black hole (the last stable direct orbit)

Voronoi cells of the A8 lattice: 3D cross section with Coexter plane

Deforming a rotation by 2 full turns to a trivial one (sequential version)

$Mandelbrot set zoom video with varied shapes A zoom in a tiny region of the Mandelbrot set attempting to show a great variety of possible shapes (fractal lace, lightning shapes, twirly spirals and of course tiny Mandelbrots). Music is an excerpt of Schumanns Scenes from Childhood, courtesy of www.musopen.com. Video and sound are in the public domain. High quality version and more information can be found at http://www.madore.org/~david/math/mandelbrot.html$