Mathematics · Study 042
Julia Morph
A Julia set redrawn every frame as its parameter moves. Steer the constant c with your pointer and watch the fractal shatter and re-fuse.
What you're looking at
A Julia set uses the same rule as the Mandelbrot set, z squared plus c, but fixes c and asks which starting points z stay bounded. Every choice of c gives a different shape. Here c either circles the origin on its own or follows your pointer, and the whole picture is recomputed live at low resolution.
The idea behind it
Gaston Julia studied these sets in 1918, decades before anyone could draw them. The link to the Mandelbrot set is exact: when c lies inside the Mandelbrot set the Julia set is one connected piece, and when c lies outside it falls apart into dust.
Try this
Move the pointer to choose c. The centre of the canvas is zero. Try the edges of the cardioid.
