Fractals are objects with dimensions that cannot be expressed as whole numbers - for example, a curve with the fractal dimension 1.3 is something between a line (euclidean dimension 1) and a plane (euclidean dimension 2). Fractals have three typical characteristics: They are infinitely complex, they show signs of self-similarity on all scales of magnification, and they contain areas of order and chaos.

Although the first fractal objects were discovered by mathematicians around 1870 and many more were conceived in the decades afterwards, they were considered intriguing but exceptional cases - mathematical irregularities that had little to do with the real world. It took about a hundred years before Benoit Mandelbrot found the common bond between all those seemingly unrelated cases and integrated them into the new field of fractal geometry in 1977. Mandelbrot also realized that fractals actually describe the real world much better than traditional mathematical models do - tree trunks are not perfect cylinders, the Earth is not a perfect sphere, the orbits of the planets are not perfect ellipsoids, etc. And as the weather forecast teaches us, nature also is not predictable on large timescales but shows chaotic behavior. "Reality is fractal", Mandelbrot discovered [BM77].

The Mandelbrot Set >