A brief introduction to Fractals

“… a fractal is any pattern that reveals greater complexity as it is enlarged. Thus, fractals graphically portray the notion of 'worlds within worlds' which has obsessed Western culture from its tenth-century beginnings."

The Universe is built on a plan the profound symmetry of which is somehow present in the inner structure of our intellect.

-- Paul Valery

Fractal geometry is a branch of mathematics discovered during the 1970s, by a mathematician working for IBM, named Benoit Mandelbrot. The word “fractal” derives from the Latin adjective fractus, and verb, frangere, to break. Fractals connote fraction, fracture and fragment. They tap into a central quality of nature – the fractured pieces which yet make her whole

Technical fractals are rendered, often quite artistically, on the palette of the computer. They consist of very simple formulas, such as the classic Mandelbrot set, X ← X2 + c, iterated on the complex number plane. To render a mathematical fractal, the same equation is computed over and over for every point on the complex plane, as endless cycles of re-entry. Each time, the final result of the equation is fed back in again as the new starting point. In theory, this continues indefinitely, as the calculation of fractal dimensionality presumes the presence of infinite feedback loops. In practice, iteration continues until either there is a stable endpoint or an artificial cut-off that gives clear indication of where the equation is headed.

When gazing at a mathematical fractal, the territory outside the fractal is out of control. It gallops unpredictably towards infinity at one speed or another, indicated by gradations of colour. By contrast, the territory inside the fractal is ordered. It is relatively stable and settles down to one or more fixed points. The edge between these two realms is what constitutes the actual fractal. Here, in the delicate interface between unbounded and bounded areas, the fractal neither flies out of control nor comes to rest. Instead it self-organizes into an infinitely deep border zone that moves dynamically along with the perspective of the observer

Fractals are a means by which time, or system dynamics, gets etched into form via self-similar, recursive loops that exist on multiple size scales. Fractals exist in the paradoxical space between dimensions, levels and forces of existence. They arise at the interface between processes, at boundary zones where they serve both to connect and separate multiple levels.

Images on this site

All images on this website are created by and copyright of the artist Susan Graves at www.shimmerfire.co.uk and are used with permission.

They depict images of fractals, which are computer generated images.