Whereas there is only one Mandelbrot set, there is one Julia set for every complex number . The Mandelbrot set is an index of sorts into the Julia sets. If , then the Julia set is connected. Alternatively, if , then is not connected, in which case is charmingly referred to as fractal dust.

The following program shows the Mandelbrot set on the front side of the square pane, and the corresponding Julia set on the back. Here, the complex number is fixed by the center of the current view of . As you zoom and pan on (and press Go), is updated for the new value of .¹M[/latex] under zoom and pan but remains fixed for the Julia sets.]

Mandelbrot and Julia sets together

This joint Mandelbrot-Julia program is as efficient as the previous programs that render only one of the two sets. The fragment shader computes only one of the sets in each frame, depending on which side of the square pane is visible.