MLA 31500

Natural Sciences Elective

Order and Chaos in the Natural World

Spring Quarter 2008

CLASS NOTES

EIGHTH CLASS

May 17, 2008

I. STEWART, CHAPTER 11: THE TEXTURE OF REALITY

1. In what respects would Benoit Mandelbrot appear to be unrepresentative of someone doing “normal mathematics?”

2. What is a fractal? What are the defining properties of a fractal? How do we recognize a fractal? Is the word a noun or an adjective? (And, are these four different questions?)

3. What are examples of systems that exhibit fractal behavior or fractal structure? What insights about such systems are gained when their fractal character is recognized?

4. Does a common sponge have a fractal structure? How would you decide?

5. Is there a connection between fractals and properties of the logistic map? If so, what is that connection?

6. What is the relevance of the study of fractals to the study of dynamical systems?

II. LORENZ, CHAPTER 5: WHAT ELSE IS CHAOS?

1. What, if anything, does Lorenz’s account of fractals add to what is already described by Stewart?

2. “Complex behavior (or structure) can result from simple recipes.” How does the Mandelbrot set illustrate this proposition? How and why might this be an important principle in nature?

3. Suppose that you decide that two objects are fractals. How would you decide whether or not the fractal structures of the objects are similar?

4. James Gleick suggests on page 108 of his book Chaos that the human circulatory system has a fractal structure. What would be the advantage or benefit of such a geometry?

LINKS:

Return to Course Page: mla315spring2008.htm

Return to Peter Vandervoort's Home Page: pov.html

Go to the home page of the Department of Astronomy and Astrophysics

of the University of Chicago: http://astro.uchicago.edu/