Math Circles on Fractals |
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- Homework exercises you might try for the first week.
- Homework exercises for the second week.
- Homework exercises for the third week.
- Test at the end.

- LECTURE 1 -
*The Koch curve and Sierpinski triangle; fractals and non-fractals*- Paul Bourke Fractals and Chaos pages containing many examples of fractals.
- Self Similarity of a coastline.
- Fractals in Wikipedia; the free web encyclopedia.

- LECTURE 2 -
*Fractal dimension and the Chaos game*- The Cantor Set
- The Cantor Set and Menger Sponge [Paul Bourke]
- Description of the Chaos Game
- Chaos Game for the Sierpinski triangle [Shodor].
- Chaos Game for the Sierpinski triangle [Univ Bremen].
- Relatives of Sierpinski - Game [Univ Bremen].
- Chaos Game using a graphical Iterated Function System editor.
- Fractal trees, etc.
- Fractal coastline
- Fractal landscapes

- LECTURE 3 -
*Iterating functions; complex numbers*- Nonlinear Web applet [Boston University] displays cobweb diagrams for the quadratic and cosine maps.
- Iteration of the Logistic Map [Andy Burbanks]
- Chaos Lab [University of Bremen] displays cobweb diagrams for the logistic map.
- An introduction to complex numbers
- Dave's Short course on complex numbers

- LECTURE 4 -
*Julia and Mandelbrot sets*- Filled-in Julia set applet [Shodor]
- Filled-in Julia set applet (Beware: the positive imaginary axis points downwards; for instructions see their Mandelbrot set) [tzingaro]
- Mandelbrot and filled-in Julia sets [Boston University]
- Mandelbrot and Julia sets [Mark McClure]
- The Julia set trip [Evgeny Demidov]
- XaoS real-time interactive fractal zoomer for Windows and Mac OS 9 (but not Mac OS X)

[Thomas Marsh and Jan Hubicka] The tutorials are good. Read:- Help->Tutorials->Math behind fractals->Whole story
- Help->Tutorials->An introduction to fractals->Mandelbrot set
- Help->Tutorials->An introduction to fractals->Julia set

- OTHER LINKS
- A Fractals Unit for Elementary and Middle School Students by Cynthia Lanius.
- The Fract-ED Information Pages, an introductory fractal tutorial for high school or college entry-level students.

- LOTS MORE REFERENCES AND LINKS from a university course I gave.

This page was last updated on 5 September 2013 by W. Gilbert