ASCII Portable Pixel Map (PPM) Image of the Mandelbrot Set

MANDELBROT is a C++ program which generates an ASCII Portable Pixel Map (PPM) 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
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.


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


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:

FOREST_FIRE_SIMULATION, a C program which simulates the occurrence of fires and regrowth in a forest, displaying the results using X Windows, by Michael Creutz.

HODGE, a C program which implements a 2D cellular automaton, that can be regarded as a model of the spread of an illness, and whose parameters can be tuned to exhibit stability, regular waves, or a variety of chaotic behavior. This is a simplified version of a program by Martin Gerhardt and Heike Schuster

MANDELBROT_OPENMP, a C++ program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.

PPMA_IO, a C++ library which handles the ASCII Portable Pixel Map (PPM) format.

RANMAP, a FORTRAN90 program which creates a PostScript file of images of iterated affine mappings;

XISING, a C program which simulates the variation in ferromagnetism in a material, displaying the results using X Windows.

XWAVES, a C program which simulates the behavior of solution of certain forms of the wave equation, displaying the results using X Windows.


  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:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 22 July 2010.