Mathematica notebook about self-similar fractals

Mathematica version ( is a Mathematica notebook I created that discusses fractal dimension, the Koch Snowflake, the Sierpinski Gasket, and the Menger Sponge. It includes an introduction and three problems for the user to solve. If you don't have Mathematica installed on your machine, you can download a free copy of Math Reader that will allow you to read (but not execute) Mathematica files. The file looks best under the Mac front-end for Mathematica because the PC and SGI versions don't support subscript and superscript characters.

HTML version (fractals.html)
Thanks to Terry Robb and his amazing nb2html program, there is also an HTML version of that will allow you to view its contents directly in your Web browser without any extra software. The HTML version retains the look and feel of the original while making the notebook (including all the output and graphics it generates) easily accessible to anyone with a Web browser.
RIFS v. 1.1

Random Iterated Functions Systems (for lack of a better name) plots the attractors of four iterated function systems (gasket, crystal, leaf, and fern) using one of four coloring methods (black and white, by transform, random, and blend). You can control the number of iterations and the update interval, and the program has Auto Clear and Show Elapsed Time options.

Random Iterated Functions Systems is freely distributable e-mail ware. If you like it or have any suggestions, send a message to me at <>. You get bonus points if you make me laugh or wax philosophical. RIFS.exe was written in Microsoft Visual Basic 3. It should run under any version of Windows. This package includes the source code that's responsible for setting the transforms and plotting and coloring points.

  1. Download the program (~238 KB, last updated August 10, 1997).
  2. Extract all the files in the .ZIP file into a new directory (e.g. C:\RIFS) using WinZip.
  3. If you don't have it already, copy VBRUN300.DLL to C:\WINDOWS\SYSTEM. Otherwise, you can delete it.
  4. Run RIFS.exe and send me e-mail.
L-systems (turtle graphics on steroids)

Some images I created with FractInt and the instructions file for drawing them.
Book announcement

Description of Dr. Richard M. Crownover's textbook, Introduction to Fractals and Chaos. While I was in Dr. Crownover's Math 316 class at the University of Missouri-Columbia, I did a project entitled "Periods Associated with Bulbs of the MSet: A Pattern." Dr. Crownover was also my advisor for my honors project in mathematics in which I compared encirclement, electrostatic equipotential curves, and binary decomposition as methods of representing the underlying dynamics of Julia sets. One of these days, I'd like to post both projects on the Web.

Recommended links to fractal-related papers, software, images, and Web pages at other sites.
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Brian Marston <>