Not only are fractals beautiful, but they master key features of the “roughness” of nature and culture, including metal fractures, turbulence, financial markets and music. Such complexity is recognised as a key frontier but it can seldom be handled directly. It is often useful – and sometimes even sufficient at first – to begin by studying the roughness of things.
Plato’s list of the sensations of man included heaviness, bigness, hotness, colour, pitch and roughness. Each of these developed into a chapter of physics, except for roughness, which remained a backwater. There was no agreed way of measuring it, and science can begin only when a notion is…
