Yesterday, I talked with Prof Lutzer about certain fractals lying in infinite dimensional space that I had been considering and attempting to compute the dimension of. Some of them are kind of interesting, but today, I realized that I made a big mistake with one of them and I tried fixing it today but haven't gotten too far. Prof Lutzer and I talked about grids and infinite products and I don't think we were really on the same page most of the time, but I am grateful that he met with me.
Right now, I'm trying to type some of my problems up on TeX so that I can send them to Prof Day, but in doing so, I'm noticing some possible problems. Hopefully I can work some of them out and redo what I thought I did earlier with my first fractal and maybe my second one was already done correctly but I want to make sure. So, it's taking some time.
I haven't done anything with local box-counting dimension yet. I think it would probably be a good idea to prove that the supremum of the set of local dimensions around x for all x in X is the dimension of X (if it's true, which I think it is).
So tomorrow, I'm going back to fix what I messed up the first time and trying to type things up on Tex. Also, I need to visit the Charles Center to make sure they got my honors request sheet, b/c they never sent me the confirm email.