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<html>
<head>
<title>
MANDELBROT_OPENMP - Mandelbrot Image using OpenMP
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MANDELBROT_OPENMP <br> Mandelbrot Image using OpenMP
</h1>
<hr>
<p>
<b>MANDELBROT_OPENMP</b>
is a FORTRAN90 program which
generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot set,
using OpenMP for parallel execution.
</p>
<p>
The Mandelbrot set is a set of points C in the complex plane with
the property that the iteration
<pre>
z(n+1) = z(n)^2 + c
</pre>
remains bounded.
</p>
<p>
All the points in the Mandelbrot set are known to lie within the circle
of radius 2 and center at the origin.
</p>
<p>
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.
</p>
<p>
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.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>MANDELBROT_OPENMP</b> is available in
<a href = "../../c_src/mandelbrot_openmp/mandelbrot_openmp.html">a C version</a> and
<a href = "../../cpp_src/mandelbrot_openmp/mandelbrot_openmp.html">a C++ version</a> and
<a href = "../../f77_src/mandelbrot_openmp/mandelbrot_openmp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/mandelbrot_openmp/mandelbrot_openmp.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/dijkstra_openmp/dijkstra_openmp.html">
DIJKSTRA_OPENMP</a>,
a FORTRAN90 program which
uses OpenMP to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../f_src/fft_openmp/fft_openmp.html">
FFT_OPENMP</a>,
a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform
in parallel, using OpenMP.
</p>
<p>
<a href = "../../f_src/heated_plate_openmp/heated_plate_openmp.html">
HEATED_PLATE_OPENMP</a>,
a FORTRAN90 program which
solves the steady (time independent) heat equation in a 2D
rectangular region, using OpenMP to run in parallel.
</p>
<p>
<a href = "../../f_src/hello_openmp/hello_openmp.html">
HELLO_OPENMP</a>,
a FORTRAN90 program which
prints out "Hello, world!" using the OpenMP parallel programming environment.
</p>
<p>
<a href = "../../f_src/mandelbrot/mandelbrot.html">
MANDELBROT</a>,
a FORTRAN90 program which
generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set;
</p>
<p>
<a href = "../../f_src/md_openmp/md_openmp.html">
MD_OPENMP</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation in parallel,
using OpenMP.
<p>
<p>
<a href = "../../f_src/multitask_openmp/multitask_openmp.html">
MULTITASK_OPENMP</a>,
a FORTRAN90 program which
demonstrates how to "multitask", that is, to execute several unrelated
and distinct tasks simultaneously, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/mxv_openmp/mxv_openmp.html">
MXM_OPENMP</a>,
a FORTRAN90 program which
computes a dense matrix product C=A*B,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../f_src/mxv_openmp/mxv_openmp.html">
MXV_OPENMP</a>,
a FORTRAN90 program which
compares the performance of plain vanilla Fortran and the FORTRAN90
intrinsic routine MATMUL, for the matrix multiplication problem
y=A*x, with and without parallelization by OpenMP.
<p>
<p>
<a href = "../../f_src/openmp/openmp.html">
OPENMP</a>,
FORTRAN90 programs which
illustrate the use of OpenMP.
<p>
<p>
<a href = "../../f_src/poisson_openmp/poisson_openmp.html">
POISSON_OPENMP</a>,
a FORTRAN90 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.
</p>
<p>
<a href = "../../f_src/ppma_io/ppma_io.html">
PPMA_IO<a>,
a FORTRAN90 library which
handles the ASCII Portable Pixel Map (PPM) format.
</p>
<p>
<a href = "../../f_src/prime_openmp/prime_openmp.html">
PRIME_OPENMP</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/quad_openmp/quad_openmp.html">
QUAD_OPENMP</a>,
a FORTRAN90 program which
approximates an integral using a quadrature rule, and carries out the
computation in parallel using OpenMP.
</p>
<p>
<a href = "../../f_src/random_openmp/random_openmp.html">
RANDOM_OPENMP</a>,
a FORTRAN90 program which
illustrates how a parallel program using OpenMP can generate multiple
distinct streams of random numbers.
</p>
<p>
<a href = "../../f_src/satisfy_openmp/satisfy_openmp.html">
SATISFY_OPENMP</a>,
a FORTRAN90 program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../f_src/schedule_openmp/schedule_openmp.html">
SCHEDULE_OPENMP</a>,
a FORTRAN90 program which
demonstrates the default, static, and dynamic methods of "scheduling"
loop iterations in OpenMP to avoid work imbalance.
<p>
<p>
<a href = "../../f_src/sgefa_openmp/sgefa_openmp.html">
SGEFA_OPENMP</a>,
a FORTRAN90 program which
reimplements the SGEFA/SGESL linear algebra routines from
LINPACK for use with OpenMP.
</p>
<p>
<a href = "../../f_src/ziggurat_openmp/ziggurat_openmp.html">
ZIGGURAT_OPENMP</a>,
a FORTRAN90 program which
demonstrates how the ZIGGURAT library can be used to generate random numbers
in an OpenMP parallel program.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Alexander Dewdney,<br>
A computer microscope zooms in for a close look at the most complicated
object in mathematics,<br>
Scientific American,<br>
Volume 257, Number 8, August 1985, pages 16-24.
</li>
<li>
Heinz-Otto Peitgen, Hartmut Juergens, Dietmar Saupe,<br>
Chaos and Fractals - New Frontiers in Science,<br>
Springer, 1992,<br>
ISBN: 0-387-20229-3,<br>
LC: Q172.5.C45.P45.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "mandelbrot_openmp.f90">mandelbrot_openmp.f90</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
The image created by the program is an ASCII PPM file.
<ul>
<li>
<a href = "mandelbrot.ppm">mandelbrot.ppm</a>,
the image created by the program.
</li>
<li>
<a href = "mandelbrot.png">mandelbrot.png</a>,
a PNG version
</li>
</ul>
</p>
<p>
MANDELBROT_LOCAL_GFORTRAN runs the program "locally" using the GFORTRAN compiler.
<ul>
<li>
<a href = "mandelbrot_local_gfortran.sh">mandelbrot_local_gfortran.sh</a>,
BASH commands to compile and run the sample program using GFORTRAN + OpenMP.
</li>
<li>
<a href = "mandelbrot_local_gfortran_output.txt">mandelbrot_local_gfortran_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for MANDELBROT_OPENMP.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 25 June 2012.
</i>
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