mandelbrot

mandelbrot, an Octave 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.

Usage:

mandelbrot ( m, n, count_max )

• m is the number of pixels in the X direction (try 101);
• n is the number of pixels in the Y direction (try 101);
• count_max is the number of iterations (start with 21);

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 an Octave version and a Python version.

Related Data and Programs:

mandelbrot_test

fern, an Octave code which uses MATLAB graphics to display the Barnsley fractal fern.

fibonacci_spiral, an Octave code which displays points on a Fibonacci spiral, suggesting the arrangement of seeds in a sunflower, for instance.

hilbert_curve, an Octave 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.m, the source code.