A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox.
Lake Navisha, Kenya
Eleuthera Island, Bahamas
Sandy Cay, Great Bahamas
Lake Nasser: Egypt
Rivers forming tree-like figures on the desert of Baja California, Mexico. Photograph courtesy Adriana Franco/National Geographic