MSRI Mathematics Graphics: Notes for Dave Wright's lectures

Dear friends:

Here we present some notes to accompany the sessions I gave at the Mathematical Graphics Summer Institute sponsored by MSRI, organized and primarily conducted by David Austin, Bill Casselman, and Jim Fix, and held at Reed College. The following table of contents will guide you to the various sections.

PostScript Trickery

In this lecture, I gave examples of how PostScript may be used to produce recursively defined L-system fractals, Euclidean tilings, custom color gradients, tilings with a pattern fill, and mathematical raster and color images.

PostScript Tools

This presents links to the standard references on the PostScript language and most importantly to the home of Ghostview and GSview, programs for viewing PostScript graphics on a PC. You should acquire this software before reading the above notes.

PostScript demo programs

View or download the example PostScript programs, as you wish.

The Art of Enumeration

In the evening lecture, I wanted to give a flavor of the process of enumerating the many beautiful geometrical tessellations that occur in mathematics. In particular, I hoped to give the idea that underlying the beautiful symmetries lie fundamental mathematical structures called groups, and to introduce the process of `programming' some of these groups by means of the equally fundamental structure in computer science called a Finite State Automaton (after the work of Cannon, Epstein, et al.). My main three examples of these sorts of tessellations were the 2-3-5 and 2-3-7 triangle groups of Plato and Klein, resp., the coherent spiral hexagonal circle packings, and a maximal cusp Kleinian group.

Demonstration graphics from "The Art of Enumeration"

If you have a PostScript viewer, you may download and view some of the PostScript graphics connected with the above lecture. These graphics have been "slowed" a little to allow you to see the order in which the tiles are painted. There are some animations here (in GIF or MPEG format), too.

PowerPoint version of `The Art of Enumeration'

The actual PowerPoint slides, unexplained and with little text, but featuring the original artwork Nectarines by J. M. Wright, 2004 Oklahoma State Fair Blue Ribbon winner in painting, high school division.

The maketexpng and ps2png utilities

Utilities for use on a Linux system to convert small LaTeX formulas to PNG's ("Portable Net Graphics") for use in web pages. Requires Perl, Imagemagick and LaTeX. These may aid the preparation of web slides for presentations.

• Ghostscript, Ghostview and GSView: PostScript viewing program.

• Mathematical Illustrations: A Manual of Geometry and PostScript by William Casselman, University of British Columbia.

• The PostScript Language Reference Manual (7.5 Mbyte PDF)

• PostScript Green Book

• PostScript Blue Book

• Thinking in PostScript (by Glenn Reid)

• First Guide to PostScript by Peter J. Weingartner

• maketexpng: PERL script for making PNG's of math formulas. Requires Linux, Perl, LaTeX, dvips and convert from the Imagemagick image conversion package.
  Instructions:
  1. Create a file called something like "formula.tex" which is a basic LaTeX file containing all the formulas you wish to transform into PNG's. Each formula should be enclosed in between TeX comments of the following form:

                 %formula: formulaname
                 ....
                 %endformula
     	    

     The "formulaname" can be any word you wish to denote the formula by. An example file is formula.tex

  2. Run the program by the command:

             ./maketexpng < formulafile.tex
             

     This produces the files formulaonename.tex, formulaonename.png, etc., one LaTeX and PNG file for each formula. You can delete the little TeX files if you want.

  If problems arise, be sure to check that your original LaTeX file compiles properly under LaTeX.
• ps2png: Shell script for use in converting PostScript files to PNG's. Requires Linux, amd convert from the Imagemagick image conversion package.
  Instructions: run the command as in

        ps2png filename.ps
        

  to produce filename.png.