I'm not just talking about the Mandelbrot Set (which is pretty sweet on it's own), but fractal geometry nature (hey that's the name of a book). A straight forward example of this principle can be observed by the coastline of Great Britain (or any other coastline). Suppose we wanted to measure the length of the coast line of Britain. We get out a map and a protractor, use the map key to make the points of the protractor something like 200 km apart, and take the protractor for a walk around the island. We would get something like 2,400 km (thanks wikipedia!). Now, if we get a bigger map and take step sizes of 50 km, down from the 200 km. The length of the coastline now increases to something closer to 3,500 km.
One of the characteristics of fractal geometry is self-similarity. Using our coastline example, if I were to present you with a random piece of coastline, you would be unable to tell me if you were looking at a kilometer, ten kilometers, or a million kilometers (assuming there aren't any recognizable landmarks or manmade structures). This type of property shows up everywhere in nature. Mountains, clouds, our blood vessels. NOVA produced a fantastic documentary, Hunting the Hidden Dimension, that covers the topic nicely.
Mandelbrot also wrote a book Fractals and Scaling In Finance: Discontinuity, Concentration, Risk. As a mathematician/economist, I have always pondered on these types of things, but my recent exploration into python hacking (specifically with Flask), I decided to build a little game that explores this property. I've gathered historical stock prices from a few public companies, and then I randomly choose 50 days, 50 weeks, or 50 months of data. The data is then plotted, but with out either axis. The user is prompted to guess the weather the data comes from 50 days, weeks or months. Right now, that's all it does, but I do intend eventually store people's responses and to get an idea of whether people can guess any better than random.
skien.cc (pronounced skīəns) is the personal website of Erik Taubeneck. I am a mathematician/economist/statistician by schooling, a data scientist by trade, and a python hacker by night. This is my very first project for skien.cc, so don't be surprised when you don't find much here. I fully intend to build more small projects like this up here, and write blog posts. In fact, I intend to write a fairly detailed blog post about how I build this little project. But, for now, you can fork me on github and check out the code for this project.