Fractals
What are fractals?
The textbook definition of a fractal is that it is "A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature" (Source: http://dictionary.reference.com).
|
The basic traits of fractals are self-similarity and recursion. A fractal occurs when you take a mathematical formula that can be repeated infinitely. Each time the formula produces a new result, that result becomes the starting point for the next process.
For example, the picture to the right is a mandelbrot formula fractal. It's an animated .gif where each frame takes you on the journey to multiple levels of a mandelbrot fractal. Notice how each level looks similar to the level above and below it.
|
(Zooming in and out from a mandelbrot fractal)
|
What makes fractals interesting?
(Zooming in and out from a mandelbrot fractal)
|
Fractals are interesting if you're a geek, like me. But, they're interesting beyond that. I could go on and on about how fractals are used in circuitry design, such as the fractal-based antennas used on many cell phones. But, that's boring (to me).
What I find particularly interesting is the way that fractals resemble natural elements and structures. This is something many map-makers have noticed and commented on (before computers, even). This allows my interest in philosophical and theological explorations to take hold of fractals and play with them. One example of that is this essay. In fact, that's why I first generated these fractals that are mesmerizing you right now.
|
Playing with Fractals On Your Own
In the event that you are bored and would like to play with fractals on your own, you can generate a plethora of fractals using FractInt, which has been ported to run on DOS, Windows, and even *nix based operating systems. It was a combination of FractInt and The Gimp that I used to created the images on this page.
Learning more about fractals
The easiest way is to Google it. There's a ton of information on fractals to be found. If you're really desperate, or if your questions are related more to the philosophical nature of the stuff I find interesting, I suppose you could also e-mail me.
Now, feel free to go back to the class website for which this web page was written.