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<html>
<head>
<title>
RANMAP - Iterated Weighted Affine Mappings
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
RANMAP <br> Iterated Weighted Affine Mappings
</h1>
<hr>
<p>
<b>RANMAP</b>
is a FORTRAN90 program which
carries out iterated weighted
affine mappings and creates EPS images of the results.
</p>
<p>
The program is interactive, allowing the user to choose
some predefined mappings, including
<ul>
<li>
the cross;
</li>
<li>
the dragon;
</li>
<li>
the fern;
</li>
<li>
the leaf;
</li>
<li>
the Levy dragon;
</li>
<li>
the tree;
</li>
<li>
the triangle;
</li>
<li>
a random mapping;
</li>
<li>
a user-defined mapping;
</li>
</ul>
</p>
<p>
<i>
Thanks to Marc Berger of Carnegie Mellon University for
introducing me to this topic!
</i>
</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">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/eps/eps.html">
EPS</a>,
a data directory which
contains examples of the Encapsulated PostScript format, used to store the
files created by this program.
</p>
<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 = "../../cpp_src/fern_opengl/fern_opengl.html">
FERN_OPENGL</a>,
a C++ program which
uses OpenGL to display the Barnsley fractal fern.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Scott Bailey, Theodore Kim, Robert Strichartz,<br>
Inside the Levy Dragon,<br>
American Mathematical Monthly,<br>
Volume 109, Number 8, October 2002, pages 689-703.
</li>
<li>
Michael Barnsley, Alan Sloan,<br>
A Better Way to Compress Images,<br>
Byte Magazine,<br>
Volume 13, Number 1, January 1988, pages 215-224.
</li>
<li>
Michael Barnsley,<br>
Fractals Everywhere,<br>
Academic Press, 1988,<br>
ISBN: 0120790696,<br>
LC: QA614.86.B37.
</li>
<li>
Michael Barnsley, Lyman Hurd,<br>
Fractal Image Compression,<br>
Peters, 1993,<br>
ISBN: 1568810008,<br>
LC: TA1632.B353
</li>
<li>
Alexander Dewdney,<br>
Mathematical Recreations,<br>
Scientific American,<br>
Volume 262, Number 5, May 1990, pages 126-129.
</li>
<li>
Bernt Wahl, Peter VanRoy, Michael Larsen, Eric Kampman,<br>
Exploring Fractals on the Mac,<br>
Addison Wesley, 1995,<br>
ISBN: 0201626306,<br>
LC: QA614.86.W34.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ranmap.f90">ranmap.f90</a>, the source code;
</li>
<li>
<a href = "ranmap.sh">ranmap.sh</a>,
commands to compile and load the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
A run of the cross data was made for 2000 points.
Files you may copy include:
<ul>
<li>
<a href = "cross_output.txt">cross_output.txt</a>,
the output from the program;
</li>
<li>
<a href = "cross.txt">cross.txt</a>,
the sequence of points generated by random mappings;
</li>
<li>
<a href = "cross.png">cross.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the points;
</li>
</ul>
</p>
<p>
A run of the dragon data was made for 2000 points.
Files you may copy include:
<ul>
<li>
<a href = "dragon_output.txt">dragon_output.txt</a>,
the output from the program;
</li>
<li>
<a href = "dragon.txt">dragon.txt</a>,
the sequence of points generated by random mappings;
</li>
<li>
<a href = "dragon.png">dragon.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the points;
</li>
</ul>
</p>
<p>
A run of the fern data was made for 2000 points.
Files you may copy include:
<ul>
<li>
<a href = "fern_output.txt">fern_output.txt</a>,
the output from the program;
</li>
<li>
<a href = "fern.txt">fern.txt</a>,
the sequence of points generated by random mappings;
</li>
<li>
<a href = "fern.png">fern.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the points;
</li>
</ul>
</p>
<p>
A run of the leaf data was made for 2000 points.
Files you may copy include:
<ul>
<li>
<a href = "leaf_output.txt">leaf_output.txt</a>,
the output from the program;
</li>
<li>
<a href = "leaf.txt">leaf.txt</a>,
the sequence of points generated by random mappings;
</li>
<li>
<a href = "leaf.png">leaf.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the points;
</li>
</ul>
</p>
<p>
A run of the Levy dragon data was made for 2000 points.
Files you may copy include:
<ul>
<li>
<a href = "levy_dragon_output.txt">levy_dragon_output.txt</a>,
the output from the program;
</li>
<li>
<a href = "levy_dragon.txt">levy_dragon.txt</a>,
the sequence of points generated by random mappings;
</li>
<li>
<a href = "levy_dragon.png">levy_dragon.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the points;
</li>
</ul>
</p>
<p>
A run of the tree data was made for 2000 points.
Files you may copy include:
<ul>
<li>
<a href = "tree_output.txt">tree_output.txt</a>,
the output from the program;
</li>
<li>
<a href = "tree.txt">tree.txt</a>,
the sequence of points generated by random mappings;
</li>
<li>
<a href = "tree.png">tree.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the points;
</li>
</ul>
</p>
<p>
A run of the triangle data was made for 2000 points.
Files you may copy include:
<ul>
<li>
<a href = "triangle_output.txt">triangle_output.txt</a>,
the output from the program;
</li>
<li>
<a href = "triangle.txt">triangle.txt</a>,
the sequence of points generated by random mappings;
</li>
<li>
<a href = "triangle.png">triangle.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the points;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for RANMAP.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CROSS_MAP</b> sets the cross map matrix.
</li>
<li>
<b>DOT_PLOT</b> plots the individual points.
</li>
<li>
<b>DRAGON_MAP</b> sets the dragon map matrix.
</li>
<li>
<b>EPS_FILE_HEAD</b> writes header information to an encapsulated PostScript file.
</li>
<li>
<b>EPS_FILE_TAIL</b> writes trailer information to an encapsulated PostScript file.
</li>
<li>
<b>FERN_MAP</b> sets the fern map matrix.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_SWAP</b> swaps two I4's.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>LEAF_MAP</b> sets the leaf map matrix.
</li>
<li>
<b>LEVY_DRAGON_MAP</b> sets the Levy dragon map matrix.
</li>
<li>
<b>POINT_INSIDE_BOX_2D</b> determines if a point is inside a box in 2D.
</li>
<li>
<b>PS_COLOR_LINE</b> handles the line color.
</li>
<li>
<b>PS_COLOR_LINE_SET</b> sets the line color.
</li>
<li>
<b>PS_COMMENT</b> inserts a comment into the PostScript file.
</li>
<li>
<b>PS_DEFAULT</b> sets the internal settings to their default values
</li>
<li>
<b>PS_FILE_OPEN</b> opens a new version of a PostScript file with a given name.
</li>
<li>
<b>PS_FILE_CLOSE</b> closes a PostScript file.
</li>
<li>
<b>PS_LINE_CLOSED</b> adds the graph of a closed line to a PostScript file.
</li>
<li>
<b>PS_MARK_POINT</b> marks a point with a tiny point.
</li>
<li>
<b>PS_PAGE_HEAD</b> writes header information on a new page.
</li>
<li>
<b>PS_PAGE_TAIL</b> writes tail information at the end of a page.
</li>
<li>
<b>PS_SETTING_INT</b> sets, gets, or prints integer internal PS_WRITE parameters.
</li>
<li>
<b>PS_SETTING_REAL</b> sets, gets, or prints real internal PS_WRITE parameters.
</li>
<li>
<b>R8_SWAP</b> swaps two R8's.
</li>
<li>
<b>R8_TO_BIN_UNEVEN</b> places X in one of several unevenly spaced bins.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8VEC_ASCENDS</b> determines if an R8VEC is (weakly) ascending.
</li>
<li>
<b>RANDOM_MAP</b> randomly applies one of several affine maps to a point.
</li>
<li>
<b>S_EQI</b> is a case insensitive comparison of two strings for equality.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TREE_MAP</b> sets the tree map matrix.
</li>
<li>
<b>TRIANGLE_MAP</b> sets the triangle map matrix.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../g_src.html">
the graphics source codes</a>.
</p>
<hr>
<i>
Last revised on 20 September 2005.
</i>
<!-- John Burkardt -->
</body>
</html>