Math 397 - Fractal Geometry

Welcome to our Fractal Geometry class webpage. This is where I'll post in class demos and handy e-files.

Handouts

• Syllabus
• The latest FractalGeometry packages (Tuesday, November 17)
• Lab 1
• Problems for quiz 1
• Problems for exam 1
• Some box-counting problems
• Digraph fractal lab
• Problems for quiz 3
• Take home exam II

Demos

Most of our demos are created with Mathematica, which we will use extensively.

• Friday, August 17: Scientific American, 1985
• Friday, August 17: Day 1 Pics - Notebook | HTML
• Monday, August 24: Self-similar sets and linear transformations - Notebook | HTML
• Friday, August 28:
  • The IFS determines the attractor
  • The modified deterministic algorithm
• Friday, September 4: More on finding IFSs
• Wednesday, September 9: Testing our algorithms via fractal spirals - Notebook | Fractalina
• Friday, September 18: Last HW problem
• Friday, October 9: Solutions to the take home
• Friday, October 16: Discontinuity of fractal dimension for self-affine sets
• Wednesday, November 18: The self-affine tiles package and boundaries

Assignments

• Friday, August 21:
  • Due Friday, August 28: Chapter 2: 3, 5
  • To think about: Chapter 2: 4, 6, 7, 11
  • Also to think about: Show that the length of the Koch curve is infinite.
• Monday, August 24 (all to think about):
  • Chapter 2: 8, 9
  • Let R be the rectangle with vertices (0,0), (2,0), (2,1), (0,1). Find a linear transformation that reflects R across its main diagonal.
• Wednesday, August 26: Chapter 2 both #11s
  You should email a Mathematica notebook to me with your solution by Wednesday, September 2
• Friday, August 28: The modified algorithm HW
• Wednesday, September 23: Hausdorff metric HW
• Monday, October 20: Self-affine sets HW
• Friday, November 6: Computing digraph dimension HW
• Monday, November 16: Finding a tile