Cantor sets and Connectivity

Well I have not been good at keeping this updated... but that does not mean that we haven't been working hard. We have finally been looking at examples of the sierpinski relatives. At first we looked at things like why are there straight lines. Lately I have been looking at how certain Cantor sets can help determine the connectivity. It does not work in every case, but it is helpful for some, and I think the Cantor sets are interesting. Instead of the usual middle thirds Cantor set that can be related to ternary numbers between 0 and 1, now we have other Cantor sets, often related to base 4 or binary. Since it is already July (eek!) I think the goal now should be to try and writeup what we have done. So the next task is to come up with an outline for a paper. The paper needs to be in LaTex, so the students will have to spend some time figuring that out. I know that this can be very slow! But it will be a good skill for them to develop. They were very fast at figuring out how to generate the Sierpinski relatives with Maple, so perhaps it won't be so bad. I am used to using WinEdt to edit LaTex, but now that I have a Mac I should try to use something else... so that is something I need to do as well. I am really tempted to stay with what is familiar though...

On a somewhat unrelated note, last week I went to a Master's thesis defense for which I was the external examiner. The thesis was on the topological properties (connectedness and disklikeness) of tiles and digit sets. It was very interesting, and reminded me how useful iterated function systems can be. The student used "Beamer" to generate slides with LaTex, so I learned something new! I am glad I asked... I feel like a bit of a loser for not knowing about it already, but I think it will be helpful in the future.

Tomorrow I meet with the students and we will try to come up with an outline for a paper. And I will talk about LaTex.

I really should update this more often, because I have left a lot of details out about what the students have worked on...