"Beehive Pools" is part of a Mandelbrot set. Mathematician Benoit Mandelbrot introduced a set of equations in 1975 that impressed artists more than scientists. That's because his equations--called fractals--become amazing geometrical pictures. The Mandelbrot set is a fractal. Fractals are self-similar structures, containing patterns within patterns. Fractal-like structures are found in nature in clouds, mountain ranges and coastlines. In fractals, the basic shape occurs infinitely many times in the set, an example of the self-similarity of fractals. If you were to magnify a fractal, it would reveal small-scale details similar to the large-scale characteristics. However, at magnified scales, the small-scale details would not be identical to the whole. In fact, the Mandelbrot set is infinitely complex, yet the process of generating it is based on an extremely simple equation involving complex numbers. Here we see infinitely many fabulous patterns, including miniature copies of the whole set, spidery filaments, pools and lagoons of color, devilish pitchforks and complicated spirals. This image was made using the KPT Fractal Explorer plug-in for Adobe Photoshop. The colors have been chosen to emphasize the structure and detail of the M-set, rather than to make an artistic statement.
Image credit: Frances Griffin