mandelbrot

mandelbrot, a Python code which generates an image of the Mandelbrot set.

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
      

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.

Licensing:

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

Languages:

mandelbrot is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

hilbert_curve, a Python code which computes the sequence of discrete Hilbert curves whose limit is a space-filling curve.

Reference:

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:

• mandelbrot.py, the source code.
• mandelbrot.sh, commands to run the program.
• mandelbrot.txt, the output file.

• mandelbrot.png, the image file.