Review for Week of Mar 6

It helped this week to talk a little bit about the coverings we are building for our triangle to realize that we are squeezing. I mention this on last weeks review, but to be fair - I was not following last week. Somehow, this week I put together what we are doing with this. It helps that we reached our punchline about the theorems that we were looking at on Monday, so I had some idea what we were doing while we were doing it. Sometimes I like to be surprised, and sometimes, I like to know what's going on.

What is interesting is that we are looking at these factors (the S_'s) and the value that undoes the contractions and that we can show that the relationship between the factors, the size of our cover and the definition of dimension forces that there always exists a unique dimension for every fractal. These is really comforting to the intuitive understanding of dimension where little else in this class is. I also think it helped me understand the contraction by seeing how the inverse works, and thinking of everything from a backward direction.

I also found it interesting to note that you can get all the info about the parent from the child. This was not true about the popcycle. The stick was not the same. So this is something that works for fractal attractors that is not necessarily true of other geometric shapes.

Lots of "interesting" this week.