PBS Nova - Fractals - Hunting the Hidden Dimension.

Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature.
A fractal is "a rough or fragmented geometric shape
that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity.

Fractals: they're famously found in nature and artists have created some incredible renderings as well. Fractals are purely a wonder -- too irregular for Euclidean geometry; iterative and recursive and seemingly infinite. They turn up in food and germs, plants and animals, mountains and water and sky.
http://youtu.be/LemPnZn54Kw