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<html>
<head>
<title>
MANDELBROT - Generate an ASCII Portable Pixel Map (PPM) Image of the Mandelbrot Set
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MANDELBROT <br> Generate an ASCII Portable Pixel Map (PPM) Image of the Mandelbrot Set
</h1>
<hr>
<p>
<b>MANDELBROT</b>
is a C++ program which
generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot set.
</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>
<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</b> is available in
<a href = "../../c_src/mandelbrot/mandelbrot.html">a C version</a> and
<a href = "../../cpp_src/mandelbrot/mandelbrot.html">a C++ version</a> and
<a href = "../../f77_src/mandelbrot/mandelbrot.html">a FORTRAN77 version</a> and
<a href = "../../f_src/mandelbrot/mandelbrot.html">a FORTRAN90 version</a> and
<a href = "../../m_src/mandelbrot/mandelbrot.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../c_src/forest_fire_simulation/forest_fire_simulation.html">
FOREST_FIRE_SIMULATION</a>,
a C program which
simulates the occurrence of fires and regrowth in a forest,
displaying the results using X Windows, by Michael Creutz.
</p>
<p>
<a href = "../../c_src/hodge/hodge.html">
HODGE</a>,
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
</p>
<p>
<a href = "../../cpp_src/mandelbrot_openmp/mandelbrot_openmp.html">
MANDELBROT_OPENMP</a>,
a C++ program which
generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set,
using OpenMP for parallel execution.
</p>
<p>
<a href = "../../cpp_src/ppma_io/ppma_io.html">
PPMA_IO<a>,
a C++ library which
handles the ASCII Portable Pixel Map (PPM) format.
</p>
<p>
<a href = "../../f_src/ranmap/ranmap.html">
RANMAP</a>,
a FORTRAN90 program which
creates a PostScript file
of images of iterated affine mappings;
</p>
<p>
<a href = "../../c_src/xising/xising.html">
XISING</a>,
a C program which
simulates the variation in ferromagnetism in a material,
displaying the results using X Windows.
</p>
<p>
<a href = "../../c_src/xwaves/xwaves.html">
XWAVES</a>,
a C program which
simulates the behavior of solution of certain forms of the wave equation,
displaying the results using X Windows.
</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.cpp">mandelbrot.cpp</a>, the source code.
</li>
<li>
<a href = "mandelbrot.sh">mandelbrot.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "mandelbrot.ppm">mandelbrot.ppm</a>,
the ASCII PPM file created by the program.
</li>
<li>
<a href = "mandelbrot.png">mandelbrot.png</a>,
a PNG version of the image.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for MANDELBROT.
</li>
<li>
<b>PPMA_WRITE</b> writes an ASCII portable pixel map file.
</li>
<li>
<b>PPMA_WRITE_DATA</b> writes the data of a PPMA file.
</li>
<li>
<b>PPMA_WRITE_HEADER</b> writes the header of a PPMA file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 22 July 2010.
</i>
<!-- John Burkardt -->
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