Fractal Geometry Workshop

Moravian College, June 26-28 2006

Michael Fraboni

mfraboni

moravian

.edu

and

Trisha Moller

trisha.moller

desales

.edu

http://math.moravian.edu/fractals/06Workshop.html

Most of our online material is from an excellent E-book being written by Michael Frame at Yale University. The entire book may be found at http://classes.yale.edu/fractals/ .

Monday, June 26

1. Introduction to Fractals and IFS We introduce fractals with one of the most basic types, the IFS.

Exercise: Decomposing Fractals (pdf)

Lab Exercise: Finding IFS for Fractal Images. Here is some background.

Lab Exercise: Spiral Fractals from IFS. Here is some background.

Lab Exercise: Fractal Folds. Here is some background.

Tuesday, June 27

2. Natural Fractals and Dimensions We discuss ways to measure the complexity of fractals. Generalizing the familiar notion of Euclidean dimension, fractal dimension can be computed from experimental data.

Exercise: Fractals with Geometer's Sketchpad (pdf). Here is the sketchpad file to get you started with the Sierpinski triangle.

Exercise: Geometrically constructing cauliflower (pdf)

Lab Exercise: Dimension by Box-Counting Here is some background.

Exercise: Similarity Dimension Exercises (pdf)

Lab Exercise: Paper Ball and Bean Bag Dimensions. Here is some background.

Lab Exercise: Fingerpaints and Fractals. Here is some background.

Wednesday, June 28

3. The Mandelbrot Set and Julia Sets Some of the most famous and recognizable fractals. An amazing complex picture that results from simple arithmetic.

Lab Exercise: Complex arithmetic.

Exercise: Mandelbrot and Julia set Computations (pdf)

Lab Exercise: Sierpinski Tetrahedron Project.