Computing the Mandelbrot Set

MANDELBROT, examples which illustrate the computation of the MANDELBROT set, which is defined as the set of points which remain bounded under a given iteration.

The Mandelbrot set is a set of points C in the complex plane with the property that the iteration

        z(n+1) = z(n)^2 + c
remains bounded.

All the points in the Mandelbrot set are known to lie within the circle of radius 2 and center at the origin.

To make a plot of the Mandelbrot set, one starts with a given point C and carries out the iteration for a fixed number of steps. If the iterates never exceed 2 in magnitude, the point C is taken to be a member of the Mandelbrot set.

This set of examples concentrates on computing points of the Mandebrot set within the rectangle [-1.0,-0.6]x[0.0,0.4], using a 1000x1000 grid of points, and with a maximum number of iterations taken to be 200.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


  1. Alexander Dewdney,
    A computer microscope zooms in for a close look at the most complicated object in mathematics,
    Scientific American,
    Volume 257, Number 8, August 1985, pages 16-24.
  2. Heinz-Otto Peitgen, Hartmut Juergens, Dietmar Saupe,
    Chaos and Fractals - New Frontiers in Science,
    Springer, 1992,
    ISBN: 0-387-20229-3,
    LC: Q172.5.C45.P45.

Source Code:

The C version:

The CUDA version:

The MATLAB version:

The OPENMP (C) version:

The PYCUDA version:

The PYTHON version:

You can go up one level to the EXAMPLES directory.

Last revised on 11 May 2017.