RANMAP
Iterated Weighted Affine Mappings

RANMAP is a FORTRAN90 program which carries out iterated weighted affine mappings and creates EPS images of the results.

The program is interactive, allowing the user to choose some predefined mappings, including

• the cross;
• the dragon;
• the fern;
• the leaf;
• the Levy dragon;
• the tree;
• the triangle;
• a random mapping;
• a user-defined mapping;

Thanks to Marc Berger of Carnegie Mellon University for introducing me to this topic!

Licensing:

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

Languages:

RANMAP is available in a FORTRAN90 version.

Related Data and Programs:

EPS, a data directory which contains examples of the Encapsulated PostScript format, used to store the files created by this program.

FERN, a MATLAB program which uses MATLAB graphics to display the Barnsley fractal fern.

FERN_OPENGL, a C++ program which uses OpenGL to display the Barnsley fractal fern.

Reference:

1. Scott Bailey, Theodore Kim, Robert Strichartz,
   Inside the Levy Dragon,
   American Mathematical Monthly,
   Volume 109, Number 8, October 2002, pages 689-703.
2. Michael Barnsley, Alan Sloan,
   A Better Way to Compress Images,
   Byte Magazine,
   Volume 13, Number 1, January 1988, pages 215-224.
3. Michael Barnsley,
   Fractals Everywhere,
   Academic Press, 1988,
   ISBN: 0120790696,
   LC: QA614.86.B37.
4. Michael Barnsley, Lyman Hurd,
   Fractal Image Compression,
   Peters, 1993,
   ISBN: 1568810008,
   LC: TA1632.B353
5. Alexander Dewdney,
   Mathematical Recreations,
   Scientific American,
   Volume 262, Number 5, May 1990, pages 126-129.
6. Bernt Wahl, Peter VanRoy, Michael Larsen, Eric Kampman,
   Exploring Fractals on the Mac,
   Addison Wesley, 1995,
   ISBN: 0201626306,
   LC: QA614.86.W34.

Source Code:

• ranmap.f90, the source code;

Examples and Tests:

A run of the cross data was made for 2000 points. Files you may copy include:

• cross.txt, the output from the program;
• cross.txt, the sequence of points generated by random mappings;
• cross.png, a PNG image of the points;

A run of the dragon data was made for 2000 points. Files you may copy include:

• dragon.txt, the output from the program;
• dragon.txt, the sequence of points generated by random mappings;
• dragon.png, a PNG image of the points;

A run of the fern data was made for 2000 points. Files you may copy include:

• fern.txt, the output from the program;
• fern.txt, the sequence of points generated by random mappings;
• fern.png, a PNG image of the points;

A run of the leaf data was made for 2000 points. Files you may copy include:

• leaf.txt, the output from the program;
• leaf.txt, the sequence of points generated by random mappings;
• leaf.png, a PNG image of the points;

A run of the Levy dragon data was made for 2000 points. Files you may copy include:

• levy_dragon.txt, the output from the program;
• levy_dragon.txt, the sequence of points generated by random mappings;
• levy_dragon.png, a PNG image of the points;

A run of the tree data was made for 2000 points. Files you may copy include:

• tree.txt, the output from the program;
• tree.txt, the sequence of points generated by random mappings;
• tree.png, a PNG image of the points;

A run of the triangle data was made for 2000 points. Files you may copy include:

• triangle.txt, the output from the program;
• triangle.txt, the sequence of points generated by random mappings;
• triangle.png, a PNG image of the points;

List of Routines:

• MAIN is the main program for RANMAP.
• CH_CAP capitalizes a single character.
• CROSS_MAP sets the cross map matrix.
• DOT_PLOT plots the individual points.
• DRAGON_MAP sets the dragon map matrix.
• EPS_FILE_HEAD writes header information to an encapsulated PostScript file.
• EPS_FILE_TAIL writes trailer information to an encapsulated PostScript file.
• FERN_MAP sets the fern map matrix.
• GET_UNIT returns a free FORTRAN unit number.
• I4_SWAP swaps two I4's.
• I4_UNIFORM returns a scaled pseudorandom I4.
• LEAF_MAP sets the leaf map matrix.
• LEVY_DRAGON_MAP sets the Levy dragon map matrix.
• POINT_INSIDE_BOX_2D determines if a point is inside a box in 2D.
• PS_COLOR_LINE handles the line color.
• PS_COLOR_LINE_SET sets the line color.
• PS_COMMENT inserts a comment into the PostScript file.
• PS_DEFAULT sets the internal settings to their default values
• PS_FILE_OPEN opens a new version of a PostScript file with a given name.
• PS_FILE_CLOSE closes a PostScript file.
• PS_LINE_CLOSED adds the graph of a closed line to a PostScript file.
• PS_MARK_POINT marks a point with a tiny point.
• PS_PAGE_HEAD writes header information on a new page.
• PS_PAGE_TAIL writes tail information at the end of a page.
• PS_SETTING_INT sets, gets, or prints integer internal PS_WRITE parameters.
• PS_SETTING_REAL sets, gets, or prints real internal PS_WRITE parameters.
• R8_SWAP swaps two R8's.
• R8_TO_BIN_UNEVEN places X in one of several unevenly spaced bins.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8VEC_ASCENDS determines if an R8VEC is (weakly) ascending.
• RANDOM_MAP randomly applies one of several affine maps to a point.
• S_EQI is a case insensitive comparison of two strings for equality.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TREE_MAP sets the tree map matrix.
• TRIANGLE_MAP sets the triangle map matrix.

You can go up one level to the graphics source codes.