|
| Unlike the gasket, these shapes are not made of exact reduced
copies of themselves. |
| However, there are ways in which the part is similar to the whole. |
| For example, we might look at the distribution of the number and size of holes. |
| On the left we see the holes cut out in forming the fractal on the left above. There are |
| 1 hole (red) of side length 1/2, |
| 3 holes (green) of side length 1/4, |
| 9 holes (dark blue) of side length 1/8, |
| 27 holes (light blue) of side length 1/16, |
| and so on. |
|
| Expecting a power law fit,
on the right
below we plot the Log of the number of holes of side length L against Log(1/L). |
|
| The red dots are the
plot for the entire shape, the blue dots are the plot for the lower left corner. |
| (The other two
occupied corners have the same distribution.) |
| Even though the parts are not scaled copies of the
whole, distributions associated with the parts are scaled copies of distributions associated with
the whole. |
