Box-counting for young-uns

mark
Mon, 13 Nov 2017 15:27:30 +0000
Quiz or Test Prep

My daughter Audrey learned to compute box-counting dimension when she was two. If you've ever watched a two year old count, though, you know that sometimes they back up and count the same thing two or even three times. As a result, Audrey always computed an estimate $A_{\varepsilon}(E)$ that was close to the actual box-count $B_{\varepsilon}(E)$ but not exact. She certainly never missed anything but could over count by up to a factor of 3.

Write down a string of inequalities relating $A_{\varepsilon}(E)$ to $B_{\varepsilon}(E)$.

Use your inequalities to prove that Audrey still always computed the correct value of the box-counting dimension.