Thursday, January 1, 2009

FRACTALS: An Introduction

Benoit Mandelbrot's most famous 'Fractal'

In October of 2008, I was watching a television program on PBS, 'The Hidden Dimension' about the life and work of Benoit Mandelbrot, a maverick mathematician who has almost single-handedly rejuvenated how we perceive 'Reality'. I had an 'aha' moment. What I was viewing really began to resonate with many of my own evolving ideas about art, science and Nature ... I soon got hooked on 'fractals'.

Integral to Mandelbrot's 'theory' is an understanding of the underlying 'broken' precision that creates recognizable 'patterns' in Nature that, for lack of better word, 'reverberate' into infinity ....

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." So writes acclaimed mathematician Benoit Mandelbrot in his path-breaking book The Fractal Geometry of Nature. Instead, such natural forms, and many man-made creations as well, are "ROUGH," he says. To study and learn from such roughness, for which he invented the term fractal, Mandelbrot devised a new kind of visual mathematics based on such irregular shapes. Fractal geometry, as he called this new math, is worlds apart from the Euclidean variety of smooth triangles, circles and squares that we all learned in school. It has sparked discoveries in myriad fields, from finance to metallurgy, cosmology to medicine.

Mendelbrot has SHARPENED our vision and given us a new 'tool' to not only investigate but UNDERSTAND this wonderous world around us.

In the spirit of his ground-breaking 'theory', I've created a few of my own computer generated fractals for your viewing pleasure. The fractals that follow are somewhat 'raw' (& 'rough'!). It will be obvious to more sophisticated 'fractal generators' that I've only been 'doodling' with fractals for a couple of months. Even so, I hope my efforts will please. For the layperson, fractals are visually 'generated' by numerical computations using the seemingly 'infinite' 'memory' of the computer. Manipulating 'colour filters' make fractals 'pretty', (or not).

'Fractals' have changed forever how I do SEE. They are visible in the micro of the sub-atomic to the macro of the galaxies ... They're everywhere. And yes - SEEING is BELIEVING.

Are fractals 'ART'? ... well ... that's a very BIG question with many ricochet responses ... Tell me what YOU think ... I'd be interested to know.

My first computer generated 'fractal' ....

I did this using a readily available 'fractal generator' computer programme, without any sense or true understanding of HOW fractals actually 'work'. I just punched in a number of different mathematical 'co-ordinates' and fritzed with the colour filters to see what I would get. After about 2 hours of 'fritzing' I finally settled on the above 'fractal'. It seemed an auspicious 'start' ... I then began to have some REAL 'serious fun' ...

To view an on-line version of the PBS broadcast, and to 'work-play' with an interactive fractal generator, link to:

Update: March 2013 ... I have just discovered apophysis fractal art.  Images galore on Google.
You can download an (addictive) 'generator' here ...

'Northland' - A Fractal Visual Symphony

Fractals in the Abstract ...

SEEING Fractals in Nature ...

Whirlpool Galaxy ( Photo Courtesy of NASA )

MLH Fractals:

The above four fractals were extracted from THIS fractal ...

Series No.2: - Fractals are evident EVERYWHERE in Natur
LOOK and ye shall SEE:

Fractal boogie-woogie