Fractals

Mandelbrot Set

A fractal zoom on a mandelbrot set, finishing on a dendrite area

The Fingerprint of God
Fibonacci Sequence - An amazing insight into the detailed architecture of Creation.

Arthur C. Clarke presents this unusual documentary on the mathematical discovery of the Mandelbrot Set (M-Set) in the visually spectacular world of fractal geometry. This show relates the science of the M-Set to nature in a way that seems to identify the hand of God in the design of the universe itself. Dr. Mandelbrot in 1980 discovered the infinitely complex geometrical shape called the Mandelbrot Set using a very simple equation with computers and graphics.

The Mandelbrot set is probably the most famous of all fractals. Its distinctive spiny pear shape is what many people think of when they think of fractals. It is an extremely complex and beautiful fractal, yet it is one of the simplest to calculate. Its formula, expressed in complex numbers, is simply "Z = Z * Z + C". Yet this simple formula, applied iteratively to every pixel in the image, produces an image so complex and detailed that the length of its boundary is infinite. An image so complex that within just a few minutes of starting to zoom in on its tendrils, explorers almost invariably find themselves seeing a part of the set which no person has ever seen before. On the Program, we consider how the repetitive nature of fractals can be used in our personal and organisational lives. By repeating a small action on a regular basis, we can bring about sustainable change within a system - in our families, our communities and our organisations.