Summary of Class

We talked about a lot of interesting things. I was most excited about the Julia. I thought that even though at the time, it seemed like the hardest thing to understand, it was the thing that I walked away with the best understanding of. Not to mention, I was able to get Mathematica to cooperate with me and made a lot of beautiful pictures, many of which I did not share. One I particularly love occurs at c=0.253930+0.000480i. You can see a good rendering of it here. My graph in Mathematica does not capture as many points, but it is still nice.

Dimension is the thing I get asked about the most by non-math knowers in the world. I still don't know what to tell them. I know what is going on, but it is hard to bring outside the precise definition and talk about it in terms anyone would understand. The major question is how does mathematical dimension compare with the dimensions we think of with respect to the definition of the universe and what impact do fractal dimensions have on that understanding. It's hard to relate what we know with what we experience.

We looked at such a wide variety of fractals that I get the impression that if you doctor the ingredients a certain way, you can make a fractal out of anything. I was watching my creamer mix with my coffee the other day, the basic cliche, and realized how much I got out of this class.

I think that one of the things that gave me the best advantage was sitting down creating my weekly summaries. It really helped to solidify what we were talking about and give me a better grasp when the conversation continued. I felt like I did not need to be reminded very much of things we had already discussed, because they were preserved in my mind in a concrete way.