ChapterZero

I’ve had a good day, the kind I imagined that I would have every day when I was in high school thinking about college. The kind I now imagine I will have every day when I’m in grad school…

I spent all day thinking about math, talking about it, doing it. Now I have a new project; I was talking to a friend taking a stochastic processes class. He’s been trying to convince me to take it when it’s offered again, but while I can see that it is a practical subject, and would like to know how to use Markov fields to create realistic images— I won’t be taking it, because it has a lot of probability and statistics. I would read a book on it, but not take a class. Then he told me about a non-linear dynamics class that UH used to offer, and mentioned a neat illustration that the prof gave:

A dog is in the center of an equilateral triangle with three trainers at each corner. When a trainer blows the whistle the dog travels in a straight line toward the trainer; when it reaches half-way, a different trainer (a random one of the other two) blows his whistle.

My project is to: think about this problem and see if I can prove something interesting about the dog’s behavior. Also, to write a program that lets you visualize the dog’s behavior– supposedly it is very interesting.

Here’s a Postscript program that simulates the dog’s travels after 101 whistles: (the conversion really loses a lot of information, but you can see there is a definite pattern; if you download the actual program, you can see it much better)

Possibly relevant posts:

• Bolzano-Weierstrass theorem (2/6/2005)
• Converting to unit fractions (8/30/2004)
• Q: zero crossings and extrema of stationary Gaussian r.v.s (1/7/2008)