This is the last week of the TEqb summer bridge program. On Thursday we must make presentations, our group on fractals. I'm in charge of finding a sweet hands on activity for everyone to do, so people don't fall asleep during the group's presentation. In class, this week we are doing complexity, emerging properties, and fractals. Seeing as we are learning about fractals in class, I think it would be impossible not to do any reteaching during the presentation.

On to complexity.  We learned about fractals and how they can be used to explore chaos.  Simply put, fractals are geometric structures that are self-similar.  Fractals have their own dimensions.  Say a fractal is scaled by 1/n. That gives us n copies.  Assuming they are self-similar, the dimension satisfies n^d if scaled by 1/n.  For example, a Sierpinkski Triangle is scaled by 1/2, which yields 4 copies. Therefore, n=2, and n^d=4, which means the dimension is 2.  This can lead to fun fractional dimensions, as in the example of the Koch curve, which has a dimension of about 1.26186.  In the 1980s, a certain man named Barnesly came up with a Collage Theorem which said that any image can be approximated by a fractal.  Microsoft Encarta used fractals to reduce the amount of memory it needed to be stored on a disk to where it could fit on a single cd.  Moving on, it should be stated that the most important thing to know about chaos is that it is not random.  Apparently, Period 3 implies chaos. I don't really quite get that, so feel free to explain it to me.  Chaos has sensitive dependence on initial conditions, a totally disconnected fractal microstructure, and topological transitivity or "wandering orbits." 

So this has been a pretty neat program, getting to know some cool people has been fun. And I guess I'll wrap up this journal. It's been good.