Each complex number can be represented as a point on a two-dimensional plane. When x becomes a complex number, the formula can produce the Mandelbrot set. If the equation starts heading off into infinity, the computer stops the equation with that point. The point is then labelled chaotic, and is assigned a colour, depending on how quickly it broke out from stability. If the point, however, does not break into infinity within a preset number of steps, it is labelled stable, and usually coloured black.
Fractal geometry provides a new way to explore and measure nature.
Mandelbrot was the first to realise their usefulness to the scientific world. The first use of fractals was in the solving of noise problems during data transmission. Mandelbrot studied the noise found during such transmissions, and found that they were fractals. The noise was self-similar. Within the jagged line of the noise, there were similar lines.