This app generates pictures of the Julia sets.

The Julia set of a complex point c is defined to be the set of complex points z such that the following sequence does not diverge.

$$a_0 = z$$ $$a_n = a_{n-1}^2 + c$$

This app generates a picture coloring each point of the complex plane with a different color depending on how “quickly” the sequence diverges when it starts at that point.

Since the Mandelbrot set is deeply linked with the Julia set (c is a point of the Mandelbrot set if, and only if, the Julia set of that point is not empty) the app displays a picture of the Mandelbrot set to guide the choice of c.

Julia

Mandelbrot

c =

+ i

Resolution: 200

How to use

  • Enter a complex number at the fields and submit it to see the corresponding Julia set on the left canvas
  • You can hold the Z key and point with the mouse to the Mandelbrot set, so you can see the Julia set of that point on the left canvas
  • You can increase or decrease the resolution using the “+” and “-” buttons