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Fractal Geometry is a relatively new area of maths related to chaos theory. A fractal image is generated from a chaotic complex number formula. For each pixel in an image, the pixels' position is put in the formula as an input and the formula is repeated several times taking the result of the previous iteration as the new inputs. The color of each pixel depends whether and how quickly the values from the formula tend towards infinity.
Fractal images are often very beautiful and have infinite detail. You can zoom in on parts of the images and never get to the stage where there is no more detail to zoom in on. The most famous Fractal Image is probably the Mandelbrot, named after the mathematician Benoit Mandelbrot. Research into chaotic formulae has had several benefits, including prediction real world events and data compression.
Studying fractal geometry was very difficult until now because only in recent years has there been powerful enough computers to do all the number crunching. There are several programs available for viewing fractal images. I use Fractint. It is a DOS program but it is fast, customizable and free to download.
All of these pictures were created by my using Fractint. They are all custom formulae written by me except for the Lyapunov, which comes with Fractint. The image in the top left of every page on this site is detail from Rob3. Click on the thumbnails for a full size version.
All of my 'Rob' formula are in fracfile.zip (3KB).
