MSRI Mathematics Graphics: Notes for Dave Wright's lectures
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
custom color gradients, tilings with a pattern fill, and
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
- Demonstration graphics from "The Art of Enumeration"
- If you have a PostScript viewer, you may download and view some
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
- Utilities for use on a Linux system to convert small LaTeX
formulas to PNG's ("Portable Net Graphics") for use in web
Requires Perl, Imagemagick and LaTeX. These may aid the
preparation of web slides for presentations.
PostScript Tools and References
PERL script for making PNG's of math formulas. Requires Linux, Perl,
LaTeX, dvips and
convert from the Imagemagick image conversion package.
If problems arise, be sure to check that your original LaTeX
file compiles properly under LaTeX.
- 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
in between TeX comments of the following form:
The "formulaname" can be any word you wish to denote the
formula by. An example file is
- Run the program by the command:
./maketexpng < formulafile.tex
This produces the files
formulaonename.png, etc., one LaTeX and PNG file for
You can delete the little TeX files if you want.
- ps2png: Shell
script for use in converting PostScript files to PNG's.
Requires Linux, amd
convert from the Imagemagick image conversion
Instructions: run the command as in