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mandelbrot.html
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<html>
<head>
<title>
MANDELBROT - Generate an Image of the Mandelbrot Set
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MANDELBROT <br> Generate an Image of the Mandelbrot Set
</h1>
<hr>
<p>
<b>MANDELBROT</b>
is a MATLAB program which
generates an 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">
Usage:
</h3>
<p>
<blockquote>
<b>mandelbrot</b> ( <i>m</i>, <i>n</i>, <i>count_max</i> )
</blockquote>
where
<ul>
<li>
<i>m</i> is the number of pixels in the X direction (try 101);
</li>
<li>
<i>n</i> is the number of pixels in the Y direction (try 101);
</li>
<li>
<i>count_max</i> is the number of iterations (start with 21);
</ul>
</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 = "../../m_src/fern/fern.html">
FERN</a>,
a MATLAB program which
uses MATLAB graphics to display the Barnsley fractal fern.
</p>
<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 = "../../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.m">mandelbrot.m</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
The following files were generating using the values of M, N and COUNT_MAX
that are embedded in the filenames.
<ul>
<li>
<a href = "mandelbrot_101_101_21.png">mandelbrot_101_101_21.png</a>,
</li>
<li>
<a href = "mandelbrot_101_101_41.png">mandelbrot_101_101_41.png</a>,
</li>
<li>
<a href = "mandelbrot_101_101_81.png">mandelbrot_101_101_81.png</a>,
</li>
<li>
<a href = "mandelbrot_201_201_21.png">mandelbrot_201_201_21.png</a>,
</li>
<li>
<a href = "mandelbrot_401_401_21.png">mandelbrot_401_401_21.png</a>,
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 10 August 2009.
</i>
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