Challenge Team Abstract
Team Number: 040
School Name: Freedom High School
Area of Science: Mathematics
Project Title: Order! What order?! Fractals and Chaos in Nature
At this point there are more questions in this area than answers and our biggest challenge will be to focus on just one good question.
Chaos is a very general term that covers the set of processes working in most "real" systems. For a long time there was the idea that, if you took "anything" apart and understood what each piece did, you could understand and predict what the "anything" would do in all possible situations. This is called reductionism. But the harder we tried the less the "anything" would behave.
Starting in the 60's, with the growth of computer modeling, it started to appear to a wide range of people that "real" systems were not just hard to predict but impossible. What they discovered was that even very very very small differences in the system, the "anything", would make very large differences in the appearance of the system in a surprisingly short period of time.
We get fractals from a completely different direction. If you take some mathematical expressions or constructions and repeat them over and over, using the answer back into the problem, you can create extreamly complicated images. Again it was in the 60's and later that computers allowed the discovery of these patterns. The complexity of these patterns are now believed to be good models for this roughness or fuzziness of nature.
In this project we would like to shed some light on the ways some fractals and repeating functions react. Some of the questions we hope to explore include:
- does a fractal, like the Mandelbrot Set, display any pattern if we look at intersections of different lines with its edges?
- how sensitive to change are repeating functions or how fast do the changes to the system happen through time?
- can a super computer be used as an interactive tool to help us better understand the fuzziness of natural precesses?
Just as with some of these systems, we may end up in a dramatictly different location from where we thought we would when we started.