Fractal dimension practice questions:
For each questions that asks what dimension a fractal is, you can answer that they are 0, 1, 2, or 3 dimensional, or you can say that they are between dimension 0 and 1, between dimension 1 and 2 or between dimension 2 and 3. You don't have to know the formula that gives the exact dimension.
If you want to learn about the exact dimension formula, you can read about it here or in the book.
1. I have a mystery shape that is self similar. I have a specific smaller similar copy of my mystery shape where the enlargement scale factor (the scale factor to make the larger copy from the smaller one) is 5.
A. If the mystery shape was 1-D, how many copies of the smaller shape would you need to build the larger shape?
B. If the mystery shape was 2-D, how many copies of the smaller shape would you need to build the larger shape?
C. If the mystery shape was 3-D, how many copies of the smaller shape would you need to build the larger shape?
2. I have a mystery shape that is self similar. I have a specific smaller similar copy of my mystery shape where the enlargement scale factor (the scale factor to make the larger copy from the smaller one) is 5. If I need 25 copies of the smaller shape to build the larger shape, what dimension is my shape?
3. I have a mystery shape that is self similar. I have a specific smaller similar copy of my mystery shape where the enlargement scale factor (the scale factor to make the larger copy from the smaller one) is 5. If I need 15 copies of the smaller shape to build the larger shape, what dimension is my shape?
4. In this Koch curve, circle two pieces that are the same shape as the whole curve, but at a different magnification. For each of your pieces, tell how much (length scale factor) you would need to magnify them to get the whole thing, and how many of them it takes to make the whole thing:
5A. For the circled similar part of this Sierpinski triangle, tell the scale factor needed to enlarge it to the whole triangle, and the number of copies needed to create the whole triangle.
B. Compare the number of copies for this scale factor to the copies needed for a 1D and 2D shape. What does this tell about the fractal dimension of the Sierpinski triangle?
6. In this fractal, circle a piece that is at the same shape as the whole thing, but at a different magnification. For your piece, tell how much (length scale factor) you would need to magnify it to get the whole thing (S), and how many of them it takes to make the whole thing (N). Then tell what dimension this fractal is, or what dimensions it is between.
7. In this fractal, circle a piece that is at the same shape as the whole thing, but at a different magnification. For your piece, tell how much (length scale factor) you would need to magnify it to get the whole thing (S), and how many of them it takes to make the whole thing (N). Then tell what dimension this fractal is, or what dimensions it is between.
8. In this fractal, circle a piece that is at the same shape as the whole thing, but at a different magnification. For your piece, tell how much (length scale factor) you would need to magnify it to get the whole thing (S), and how many of them it takes to make the whole thing (N). Then tell what dimension this fractal is, or what dimensions it is between.
