MANDELBROT
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
      

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.

Licensing:

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

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:

The C version:

• mandelbrot_c.c, the source code.
• mandelbrot_c.sh, commands to run the program on the ARC cluster NewRiver.
• mandelbrot_c.pgm, the image file.
• mandelbrot_c.txt, the output file.

The CUDA version:

• mandelbrot_cuda.cu, the source code.
• mandelbrot_cuda.sh, commands to run the program on the ARC cluster NewRiver.
• mandelbrot_cuda.pgm, the image file.
• mandelbrot_cuda.txt, the output file.

The MATLAB version:

• mandelbrot_matlab.m, the source code.
• matlab_input.txt, a file containing the name of the source code, to be input to MATLAB.
• mandelbrot_matlab.sh, commands to run the program on the ARC cluster NewRiver.
• mandelbrot_matlab.pgm, the image file.
• mandelbrot_matlab.txt, the output file.

The OPENMP (C) version:

• mandelbrot_openmp.c, the source code.
• mandelbrot_openmp.sh, commands to run the program on the ARC cluster NewRiver.
• mandelbrot_openmp.pgm, the image file.
• mandelbrot_openmp_1.txt, the output file for 1 OpenMP thread.
• mandelbrot_openmp_2.txt, the output file for 2 OpenMP threads.
• mandelbrot_openmp_4.txt, the output file for 4 OpenMP threads.
• mandelbrot_openmp_8.txt, the output file for 8 OpenMP threads.

The PYCUDA version:

• mandelbrot_pycuda.py, a PYCUDA program for computing an image of the Mandelbrot set.
• pycuda_newriver.sh, commands to run the program on the ARC cluster NewRiver.
• pycuda_newriver.txt, the output file.
• mandelbrot_pycuda.pgm, a PGM image of the set.

The PYTHON version:

• mandelbrot_python.py, the source code.
• mandelbrot_python.sh, commands to run the program on the ARC cluster NewRiver.
• mandelbrot_python.pgm, the image file.
• mandelbrot_python.txt, the output file.

You can go up one level to the EXAMPLES directory.