- New Homework:
Wed 3/17 Fractals, with Chaos Next time: More Chaos! - Upcoming talks and events:
- For those going to the KYMAA
meetings, March 26/27: Let me know your schedule:
- when you'd like to leave,
- when you need to return by, and
- if you'd be willing to drive (gas would be reimbursed).
- This Friday's seminar features a familiar character: me, talking about Global Climate Change!
- For those going to the KYMAA
meetings, March 26/27: Let me know your schedule:
- So what is a fractal? A
couple of things we'll generally see:
- It's a graph that possesses "self-similarity".
- It often possesses a simple and recursive (or iterative) definition.
- Last time, we built fractals deterministically:
- From "sticks" (suggest another)
- From "areas" (suggest another)
- Fractals from Chaos
- Here's a picture derived from a process described in our section on Chaos ("Chaotic Motion", p. 106):
Do you see the fractal?
- The Sierpinski triangle:
- First deterministically: fractals by subtraction
- Now let's introduce a little bit of randomness: Here's a random process that generates Sierpinski's triangle
- Deterministic
fractals: delve into an infinite, dynamic world, created by
a simple mathematical process.
- a simple rule
- repeated over and over and over.... but
- simple rules, intense content!
- Here's the mathematics behind the creation of that beautiful fractal image
- Here's a picture derived from a process described in our section on Chaos ("Chaotic Motion", p. 106):