Many chaotic patterns and dynamic systems contain such self-similarities across scale, whether in time or in space. Waves, for instance, may break when inches high or 50 feet tall, but they follow the same template: the rear, the curl, the bright splintering of foam.
Like the atmosphere, the ocean is a realm of deterministic chaos. Predictable, periodic patterns can be interrupted by irregularities, complex interactions, and rogue events; meanwhile, what looks like randomness may yield surprisingly rigid rules. The turbulent movements of water are evident in the wavelets that stir the ocean surface and the monstrous, hidden currents roiling the deep sea. Waves may break semi-reliably in certain favored surf spots depending on wind patterns, swell, and underwater topography, but they can also appear unexpectedly, out of the blue. These so-called rogue waves or freak waves may be more than twice as high as waves in the surrounding sea. They can occur in a string of waves or on their own, and have been known to swamp ships and oil rigs. They emerge out of the chaos, a deadly signal.
The mid-20th century articulation of chaos theory, and the discovery of fractal patterns within systems as widely separated as ocean waves and financial markets, revised expectations about the predictability of the physical world in complicated ways. On the one hand, fractal rules could help imitate the real outputs of these dynamic systems. On the other, this insight failed to lead to greater predictability beyond the near-term. Our best guesses remained statistical, not specific.
It seemed there were limits to what we could know about the world, independent of our ability to observe or compute. The blank spaces of the future emerge out of the dynamics of these systems themselves, their jagged geometries.
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