Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life, in Organisms, Cities, Economies, and Companies

by Geoffrey West

it turns out that the pattern of fluctuations in financial markets during an hour of trading is, on average, the same as that for a day, a month, a year, or a decade. They are simply nonlinearly scaled versions of one another. Thus if you are shown a typical plot of the Dow Jones average over some period of time, you can’t tell if it’s for the last hour or for the last five years—the distributions of dips, bumps, and spikes is pretty much the same, regardless of the time frame. In other words, the behavior of the stock market is a self-similar fractal pattern that repeats itself across all timescales following a power law that can be quantified by its exponent or, equivalently, its fractal dimension.