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

julia_set, a C code which generates a TGA or TARGA graphics file of a Julia set.


MANDELBROT_ASCII, a C code which generates an ASCII image of the Mandelbrot fractal set using just two lines of C.

MANDELBROT_OPENMP, a C code 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;


  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:

Last revised on 13 July 2019.