What Are Fractals?

The term, fractal (derived from the Latin, fractus, meaning 'broken' or 'fractured'), was coined by Polish-born, French/American mathematician Benoit Mandelbrot (20 November 1924 - 14 October 2010), in 1975.

A fractal is a rough or fragmented geometric shape that is too irregular to be easily described through the language of traditional Euclidean geometry (triangle, square, circle). They occur naturally in the world in the form of: clouds, snow flakes, coastlines, tree branches, river networks, mountain ranges, crystals, lightning, cauliflower florets, blood vessel systems, ocean waves and more.

In computing, each fractal shape has a mathematical formula which describes it (e.g. zn+1 = zn2 + c) and may involve a complex number, the sum of which might keep iterating (feeding into) itself, becoming either more and more complex - into infinity - or to nothing. Each iteration can give rise to a point of colour (or black) on a computer or TV screen and, therefore, the outcome of the formulae can be manipulated not only into shapes but into fantastical 3D moving pictures.

Many fractal shapes are named after the discoverer of such formulae, e.g. Mandelbrot, Julia, Sierpinski, Koch, Menger etc. Fractals may appear similar (not the same) at all levels of magnification and because of this they are often considered to be infinitely complex. The degree of infinity may depend upon whether the fractal is Classified as possessing the property of Exact, Quasi or Statistical Self-Similarity. Statistical self-similarity is the **weakest type of self-similarity, which sees fractals occur naturally in the world. (**In these instances, we would not expect to see ever-decreasing snowflakes or trees etc).

Whilst Mandelbrot is affectionately recognised as the father of fractals and the creator of the Mandelbrot set (1979), much earlier than this, the Julia set was postulated - but never seen - by Gaston Julia (February 3, 1893 - March 19, 1978). In fact, roots of the concept of fractals can be traced back to the 17th century.

2-dimensional Mandelbrot fractal images have been with us since 1980. However, 3-dimensional fractals have only been realised since 2009. There are now numerous fractal-generating programmes available and, with ever-increasing processing power, we are seeing for the first time some incredible fractal imagery through combining 'hybrids' of the five main types of generated fractals:

Escape-time fractals (or 'orbitals'): Mandelbrot and Julia Sets,
Iterated function systems (IFS): Koch snowflake, Menger sponge,
Random Fractals: the landscape, Brownian Motion,
Strange Attractors,

The fractal world is so vast - infinite in fact - that no single video or group of videos can give the casual observer any idea of what can be produced with the software. Fractals as Art

If you would like to know more about fractals, please visit FractalForums.com or read the many tutorials online, such as: