Dimension and Fractals

The homework assignment: [html] [Postscript] [Gif Image].
The shape I asked you to compute the dimension of: [Gif Image] [Postscript]. (Warning: The postscript file is rather large: 1.3 MB. The gif file is only 12kB and thus will load a lot faster.)
Solutions to the homework: [html] [Gif Image ] [Postscript ].

Bob Devaney, a math prof at Boston University, has put together an excellent set of information on Chaos in the Classroom. He has a very clear discussion of self-similarity and dimension. One of the examples he uses is the Sierpinski Triangle, the shape whose dimension you've been asked to figure out for homework.
A very clear introduction to fractals: A Fractals Lesson. Highly recommended!
There are many, many sites with pictures of fractals. A large list of such sites can be found here: Mathematical Art, Graphics, Chaos and Fractals.
Another page with a discussion of The Sierpinski Triangle.
The Sierpinski triangle is closely related to Pascal's Triangle. Here's a neat java applet that helps one see the patterns in Pascal's triangle.
And here's non-java based interface that produces nice-looking Pascal's Triangles.

If you have any questions about the class or the content of this web page, please feel free to email me at dfeldman@landau.ucdavis.edu.
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