(5 pts)

This assignment is a follow up to the Generate your own carpet IFS assignment. Your mission is:

Use the box-counting techniques to compute the box-counting dimension of your personal carpet.

To be clear, you are *not* asked to compute the similarity dimension, though the two should probably agree. Itâ€™s still not particularly hard, though; the main point is the write up. Be sure to:

- Identify an appropriate sequence (\varepsilon_n) of mesh sizes decreasing to zero,
- Find the corresponding expression for N_{\varepsilon_n}(E), and
- Simplify \displaystyle \frac{\log N_{\varepsilon_n(E)}}{\varepsilon_n} so you can compute the limit.