Questions on African Fractals ch 1-2


1)     pp. 3-4 What is a cultural design theme? What examples do we find in Chinese and American societies?

2)     pp. 5-6 Does the presence of a particular geometric design prove that the artisans who produced it understand the underlying mathematics?

3)     pp. 6 How is the theory of Karl Popper used in this context? Why?

4)     pp. 8-9 Who invented the first fractal? How did he do it?

5)     pp. 9-10 The Cantor set and the Koch curve appear to be very different shapes; explain what they have in common.

6)     p. 11 Explain the differences in the two Koch fractals produced by using different seed shapes.

7)     pp. 12-13 What is the length of the Koch curve? Why?

8)     pp. 12-14 How was Hausdorff able to come up with a better measure for fractals?

9)     pp. 12-15 What did Mandelbrot see in common between the empirical work of Hurst and the abstract mathematics of Cantor?

10)pp. 12-16 How are fractals used to model nature?

11)pp. 12,17 What is the difference between passive and active lines in fractal modeling?

12)pp. 18 What is the potential danger in discussing fractals in African culture?

13)pp. What are the 5 essential components of fractal geometry? What is the relationship between recursion and scaling?

14)pp. 3-5, 20 Why look to architecture for cultural design themes? (hint: the answer is not explicit in the book, you have to think about this one).

15)pp. 21-24 Explain the fractal aspects of the architecture of Logone-Birni.

16)pp. 22-24 What evidence shows that the scaling structure is intentional, and not merely the result of unconscious social dynamics?

17)pp. 24-25 Explain the fractal aspects of the architecture of the Bamileke.

18)pp. 26-29 Explain the fractal aspects of the architecture of the Ba-ila.

19)pp. 26-29 What knowledge system is connected to the front-back scaling? What knowledge system is connected to the inside-outside nesting?

20)pp. 29-31 Explain the fractal aspects of the architecture of Mokoulek.

21)pp. What is the significance of the square building at the center of Mokoulek?

22)pp. 32 In what way do the swirls of circular buildings in Labbezanga resemble the fractal in figure 2.5b?

23)pp. 32-34 What symbolic meaning does the fractal structure of Nankani architecture convey?

24)pp. 34-38 Critique the following sentence: “While European cities have streets arranged in orderly grids, African city streets have no order at all, they are nothing but chaos.”