Tuesday, October 19, 2010

Goodbye to a great mathematician

A couple days ago, I read that famous mathematician Benoit Mandelbrot passed away. If you are not a math nerd or a math hobbyist, you probably have never heard of him before. If you are, however, interested in the fascinating aspects of weird geometries and crazy sequences, you probably worship the man. He is credited with inventing fractal geometry, a branch of mathematics that deals with fractals. I will try my best to go briefly over them, but forgive me if I am not able to clearly explain the idea.

In my precalculus class in high school, there were some forbidden (i.e. chapters we were not going to cover in the class) chapters at the back of the book. One day, I flipped through some of them just out of curiosity. I felt a lot like Harry Potter stealthily walking around the forbidden forest. One of these forbidden chapters talked about something called fractals. This intrigued me a lot. I knew what fractions were (thanks to my third grade math teacher), but what kind of  a beast was this fractal?

I talked to my math teacher and he was nice enough to let me borrow a DVD on fractals. Fractals are, roughly put, geometrical entities that have infinite complexity at all levels of magnification. No matter how far you zoom into the object, you will keep unraveling more and more layers of complexity. The coastline of Britain is often used as an example of this. From the sky, it looks more or less uniform, but as you get closer and closer to it, you begin to see all the jagged edges, coves, etc. They also have a property called self-similarity, which basically means that small sections of a fractal share shape and other features with the fractal as a whole.This video illustrates both of these properties: (it shows the Mandelbrot set, named in honor of the man.)

Fractal geometry has been successfully used to calculate Cloud dynamics, formation of galaxy clusters and predict market fluctuations. Combined with cutting-edge computer technology, fractals have also been used to create stunning visual effects in movies.

Goodbye sir, and thank you for inspiring and captivating us.

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