WertPerch Fractals Page

Fractals are complex geometric shapes that commonly exhibit the property of self-similarity. The term fractal was coined by the Polish-born mathematician Benoit Mandelbrot. Since its introduction in 1975, the concept of the fractal has given rise to a new system of geometry that has had a significant impact not only on mathematics but also on such diverse fields as physical chemistry, physiology, and fluid mechanics. (On the plus side, they're also pretty and fun!)

A self-similar object is one whose component parts resemble the whole. This reiteration of irregular details or patterns occurs at progressively smaller scales and can continue indefinitely, so that each part of each part, when magnified, will look basically like the object as a whole. This fractal phenomenon can be readily seen in such objects as snowflakes and tree barks. As you magnify them more, the same structures can be seen. Although not all fractals, in nature or maths, are self-similar, most do show this property.

Simply put, fractal images are created by taking a simple formula and calculating a result, which is then fed back into the formula. That result is then fed in, and so on. This repetition ("iteration") is carried out until a predetermined point is reached, then the outcome is plotted on a graph. Sure, there is a far more complex explanation, but I'm no mathematician. In fact, the very thought of M-m-maths is terrifying to me.... You want a better explanation? Look elsewhere! Try the Fractint home page, or Simon's page. (His final year dissertation is on the subject!!)

The thing which fascinates me is that so many of the images produced are very much like natural shapes. When considering the Mandelbrot Set (in particular), the 'lake' is actually infinitely long. No matter how deeply you zoom in, it just keeps going. Scary...

The background on this page and the examples below were produced with the aid of Fractint, a fractal generator for the PC (although versions have been produced for Unix, too!)

All these images are in Kevin's .PAR (ZIPped) - those with yellow names have full-size (640x480) images attached. I will eventually put all the full-sized images on the site, too, when I can be bothered. These thumbnails are all Fractint gifs, so do contain the info need to generate them in larger sizes!