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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. According to the author, "to play the chaos game quickly, you need a computer with a graphics screen and a random number generator, but in principle a sheet of paper and" what will work as well?

2. What is a measure of some property of a piece of software or its specifications?

3. What were used to address deep issues in theoretical physics according to the author in Chapter 8, "Images of Chaos"?

4. What science deals with the visible, orderly outcomes of self-organization and the common principles behind similar patterns?

5. From what institution did Heinz-Otto Peitgen earn his Ph.D.?

Short Essay Questions

1. How is Mitchell Feigenbaum described? What was his early life like, according to the author?

2. How is the Taylor-Couette flow defined?

3. Describe the career of Heinz-Otto Peitgen. Where is Peitgen from?

4. What is the definition of a bifurcation diagram?

5. How are the Navier-Stokes equations defined? For whom are they named?

6. Describe the Julia set. How is it related to the Fatou set?

7. How does the author describe the evolution of chaos in Chapter 8, "Images of Chaos"?

8. How are Feigenbaum constants defined?

9. How did Barnsley's approach differ from that of Richter and Peitgen in Chapter 8, "Images of Chaos"?

10. Who is Michael Barnsley? How is his early career described in Chapter 8, "Images of Chaos"?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Describe the early life of Benoit Mandelbrot and Mandelbrot's work as a mathematician. How did WWII affect the education Mandelbrot received?

Essay Topic 2

Describe and discuss Edward Lorenz and his weather simulator at MIT. What effects did the weather simulator create? What led to the machine's breakdowns?

Essay Topic 3

Describe Mitchell Feigenbaum and Michael Barnsley. How did the two mathematicians meet and what discoveries arose from their conversations?

(see the answer keys)

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