Reading: pg. 9-36; 183-233
1. Pick a coastline and compute its box-counting dimension. Comment.
2. Pick a natural fractal and compute its box-counting dimension. Comment.
3. Show that the box-counting dimension of the set A={0,1,1/2,1/3,1/4,...} is 1/2. Show (from the definition) that the Hausdorff dimension of A is zero. Comment.
4. List five physical objects which might be modeled as fractals. What physical significance does their fractal nature have? What physical significance does their fractal dimension have? In what range (scale), roughly, do they appear to be fractal? Are they (statistically) self-similar? If so, what is the physical significance of this?
5. Which is a better definition of a fractal: An object for which the fractal dimension exceeds the topological dimension, or one for which the fractal dimension is not an integer? Which notion of fractal dimension (similarity, compass, box-counting, Hausdorff) is best suited for defining fractals?
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