Math 215. Fractals and computer graphics. Spring 1998.

  Course description: This hands on course surveys fractal geometry with applications to chaos theory and related computer software. You will learn about the mathematics behind the fractal images shown below (among others), and how to use software that produces them. The course will meet in the social sciences computer lab in Harkness, and enrollment is limited to 25. For a soon to be published account of previous offerings of this course written for other educators, see Ravenel's paper, A software driven undergraduate fractal course.  Here is a photo of of the meeting on teaching courses about fractals at Yale in December, 1997. Click here for the catalog description of Math 215.

Prequisites: One semester of calculus (Math 141, 161, 171 or equivalent AP credit) is required, and computer literacy is highly desirable.

Time and place: Monday and Wednesday, 2:00-3:15, Harkness 114. This room has a computer at every desk. Click here for computer instructions relevant to this course.

Spring 1998 schedule of Math courses.
 

 
  Instructor: Professor Douglas C. Ravenel

• Office: Hylan 918
• Office hours: Monday 3:30-5:00 , Wednesday 10:00-12:00, and by appointment.
• Phone: 54413
• Email: drav@harpo.math.rochester.edu

Teaching Assistant: Usman Raza Alim

• Phone: 43752
• Email: ua001f@uhura.cc.rochester.edu
• Help session: Tuesday 4:50-6:05 pm, Harkness 114.

Text: Encounters with Chaos by Denny Gulick (McGraw-Hill 1992). A copy will soon be on reserve in Carlson Library.

Material to be covered: Most of Chapters 1, 2 and 4 of Gulick.  The main topics are discrete dynamics, the Mandelbrot and Julia sets, and iterated fucntion systems.
 
 
 

Grading:
Your course grade will be based on eight group homework assignments. These are to be done by groups of up to three people.   Each should result in a printed paper with computer generated illustrations, some of which may be animated.  I am open to suggestions for alternative experiments for each of these topics.  Contact me a week or more before an assignment is due if you want to try something different.
Class attendance is mandatory and your final grade will be discounted by 1% for each unexcused absence after January 21. Homework assignments are due at classtime unless otherwise noted and late assignments will not be accepted.

Software:
We will make substantial use of Fractint, an omnibus program that can quickly produce any fractal image you can think of. It will be the work horse program for this course and you should familiarize yourself with it as soon as possible. It comes with extensive online help. On the web you can find copy of the help manual and extensive information about Fractint commands. It has a formula mode and an L-systems mode, both of which enable you to create new types of fractals. Fractint runs under DOS, Windows and Unix, but I know of no comparable software for the Macintosh.
We will also use FDESIGN, a mouse driven program for experimenting with IFS attractors.
 

 
 
  Other resources:

• Here is the course reading list; see also the Fractint Bibliography, the Julia and Mandelbrot Set Bibliography, the Chaotic Bibliography, the Fractal Music Bibliography, and References on Chaos and Fractals.
• Chaos under Control is a Macintosh software package written by Michael Frame and David Peak, who wrote a book by the same name.
• Ken Monks (a friend of mine who also teaches a course like this one) has a list of Fractals and Chaos software. Monks, Frame, Mandelbrot, Devaney and myself can all be seen in the Yale photo.
• Andrew Ho's Chaos Introduction and Andreas Kassler's Fractal Image Compression page.
• There is a Usenet newsgroup about fractals; mathematics and software, sci.fractals. The sci.fractals FAQ is a useful list of answers to frequently asked questions about fractals.
• The Spanky Fractal Database is a collection of programs, images, and other material all relating to the subject of Fractals.
• Fractal Pictures & Animations, a collection .of images and animations, plus fractal FAQs and 2-D/3-D fractal explorer, and other sites with pictures of the Mandelbrot set.
• There are also other fractal sites on the web. Here is Infoseek's list of fractal sites.

Note to students: This page is a work in progress. You should reload it frequently to keep up with developments in the course. The revision date is always indicated at the bottom of the page. It is especially important to consult the lecture notes frequently.
 

The pictures on this page are details of the Mandelbrot set and were downloaded from the Beauty of Chaos site.

This page was last revised on February 12, 1998.

The web address for this page is http://www.math.rochester.edu/courses/current/MTH215/index.html