A fractal is generally "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. Roots of mathematical interest on fractals can be traced back to the late 19th Century, the term however was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion. [...]
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns. [Wikipedia]
If you have an spare hour on your hands, I heartily recommend this episode of PBS' Nova on Fractals: Hunting the Hidden Dimension on the discovery of fractals and their manifestation in ; further info can be found on their accompanying website.
For a mind-blowing demonstration of a fractal's scale, explore the infinite detail of a Mandelbrot set as you zoom to a magnification of 250,000,000x.