Fractals are a geometric patterns that repeat themselves at smaller scales to produce self-similar irregular shapes and that cannot be represented by classical Euclidian geometry.

For instance, take this classic Mandelbrot set z^2+c.  When you zoom in on smaller areas you will see the same basic shape repeating itself.  As you explore different fractals you will discover many repeating shapes.

The mathematics behind fractals had been explored as early as the 17th century, but they could not be visualized until the advent of computer technology due to the calculation intensive nature of plotting fractals.

The word fractal was originally coined by the Benoit B. Mandelbrot in 1975 and is derived from the Latin word fractus meaning broken or fractured. Mandelbrot was the first to plot fractals using computers while he was working at IBM. His work with fractals was based on the earlier work of many other mathematicians including Gaston Julia.

There are also many objects in nature that have the self-similar properties of fractals such as snow flakes, crystals, lightning, river networks, systems of blood vessels and even mountain ranges.