Mandelbrot Image using OpenMP

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

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.

Creating an image of the Mandelbrot set requires determining the behavior of many points C under the Mandelbrot mapping. But each point can be studied independently of the others, which makes this calculation suitable for a parallel implementation.


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


MANDELBROT_OPENMP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

DIJKSTRA_OPENMP, a C++ program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a C++ program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE_OPENMP, a C++ program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a C++ program which prints out "Hello, world!" using the OpenMP parallel programming environment.

MANDELBROT, a C++ program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set;

MD_OPENMP, a C++ program which carries out a molecular dynamics simulation in parallel, using OpenMP.

MULTITASK_OPENMP, a C++ program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a C++ program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

OPENMP, C++ programs which illustrate the use of OpenMP.

OPENMP_RCC, C++ programs which illustrate how a C program, using OpenMP, can be compiled and run in batch mode on the FSU High Performance Computing (HPC) cluster operated by the Research Computing Center (RCC).

POISSON_OPENMP, a C++ program which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.

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

PRIME_OPENMP, a C++ program which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a C++ program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

RANDOM_OPENMP, a C++ program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY_OPENMP, a C++ program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SCHEDULE_OPENMP, a C++ program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a C++ program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

ZIGGURAT_OPENMP, a C++ program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.


  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 03 September 2012.