When viewed from space, the coastline of an island such as Britain, which can be seen it its entirety at a glance, presents a random, jagged appearance. As you approach the island, the large-scale sense of the coastline disappears beyond the horizon allowing you to see finer details of the places where rock meets the sea. But at this close distance, the impression is still the same as the one from space; the coastline looks random and jagged. If you come right up to the rock, nose to nose with the water splashing at your face, you see the same thing; a jagged rock sitting in the water. In nature and the abstract world of geometry, the general appearance of some objects never changes no matter how close or far from the object you are when you view it. An object with this property is called self-similar or...