Seventh Homework Set Answers

5. (a) Because the generator has three segents, the number of segments in each iteration is a power of 3.

For example, the second iteration consists of 32 segments and the third iteration consists of 33 = 27 segments.

We count 27 segments, so this picture is of the third iteration.

(b) The turning points are the endpoints of the 9th and 18th segments. Thus they are (.25,.75) and (.75,.25).

(c) The coarse Hölder exponents are

Log(.75)/Log(.25) ≈ 0.2075 , Log(.5)/Log(.5) = 1, and Log(.75)/Log(.25)

Not all these are equal, so this generator is multifractal.

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