- I've given you a fractal assignment. Give it a try, and get it back to me by Tuesday after Thanksgiving. This is our last assignment!
- We began by talking about some of the fractals we've known: the Fibonacci rabbit tree is fractal, as is the Golden rectangle.
- Some examples you might have seen before:
- We saw how one can create new fractals with rectangles (e.g. the A0 paper fractal)
- We talked about line fractals (where the initiator is a stick) and area fractals (where the initiator is a two-dimensional object).
- We saw and created the classic Koch fractal (a stick fractal)
- We also created an area fractal, based on triangles, called Sierpinski's triangle. Sierpinski's triangle is "infinitely deep".... (You need to listen to the Doors, or Jefferson Airplane, or Jimi Hendrix while studying fractals.)
In each case, there's "the world within the world": that's the most important property of fractals (and my informal definition).
- a simple rule
- repeated over and over and over.... but
- simple rules, intense content! Fantastic creations are a snap.
You might try creating some of your own.
The Koch fractal is this:
- Axiom: f
- Rules: f=f+f--f+f
- Start Angle: 90
- Turn Angle: 60
Let me re-introduce you to Vi Hart, who will talk us through the relationship between Pascal and Sierpinski. She talks really fast, however!
Then we'll try her method to see how, within Pascal, there's Sierpinski....
- even plus even is even
- odd plus odd is even
- even plus odd is odd
- L-System Based Fractals (and a local copy).