The following applet finds Julia sets for the function z²+c using inverse iteration.

You supply the value of c, a complex number with a real and imaginary part.

What's going on?

• Each time the function z²+c is applied to a point on the complex plane, the point "moves" to a different location. If the function is then applied to this new point, the point may move again, and so on. For some points on the complex plane, repeatedly applying the function sends the point off to infinity. For others, the point stays inside a boundary on the plane. This program determines the boundary of the points in the complex plane that move toward infinity and those that stay bounded for a given value of c.
• A special case of this function occurs when c is also the starting point of this function's iterations on the complex plane. Points that stay bounded under this map are those in the Mandelbrot set. Here is an interactive Mandelbrot set applet, written by Professor Peter Alfeld of the University of Utah Mathematics Department.