What Are Fractals

The What

Benoit Mandelbrot, who 'discovered' Fractals, died on October 17, 2010.  What fractals are is easier to describe by explaining that they are apparently random mathematical shapes which, however follow a pattern, repeating until the molecular level.  

For example, if you look at a tree; there is the trunk, from the trunk come limbs. If you look at the limb of a tree, it is just like the trunk, and from the limbs grow branches.  If you look at the branches you see, growing from them, in the same pattern that the limbs grow from the trunk and the branches from the limb, are twigs.

This pattern can be reduced to a mathematical formula which can measure previously immeasurable objects, including the coastline of the British Isles, the geometry of a lung or a cauliflower.


Making Music

Synthesizers are programmed by numbers.  Running a mathematical formula through them; primarily a Fractal, will result in unearthly, yet beautiful music. 

Using fractals to create music is based on the fact that all music follows the patterns of fractal motion or  'pink noise', which is somewhere between white noise; which is complete chaos and brown noise, which is too orderly to sound like music.

The mathemusician, (as Phil Thompson, an excellent proponent describes himself) will run the formula, elect the sounds which each of the numbers produces, adds pauses, and there is music.

The Music

Images

We have all seen the incredible images of Fractals, some remarkably beautiful.  We can see them in every day life, in broccoli, a shell.  Although fantastically complex, once they are reduced to a mathematical formula they cease to be confusing unknowable shapes.

Once they can be defined, understood, used, they may still retain their mystical beauty but it is a beauty the mind can comprehend.

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