Not only are fractals beautiful, but they master key features of the 鈥渞oughness鈥� 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 鈥� and sometimes even sufficient at first 鈥� to begin by studying the roughness of things.
Plato鈥檚 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 quantified.
Fractals have provided the first proper measure of roughness. Measurements proposed earlier failed because they implicitly assumed that roughness was an insignificant, mild disturbance when in fact it is wild and hard to deal with. The fractal geometry of roughness is set to expand rapidly and carve itself an increasingly central role.
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