Chaos - James Gleick [145]
BRANCHING AND CLUMPING, (on facing page). The study of pattern formation, encouraged by fractal mathematics, brought together such natural patterns as the lightning-like paths of an electrical discharge and the simulated aggregation of randomly moving particles (inset).
Where heat diffusion tends to create instability, surface tension creates stability. The pull of surface tension makes a substance prefer smooth boundaries like the wall of a soap bubble. It costs energy to make surfaces that are rough. The balancing of these tendencies depends on the size of the crystal. While diffusion is mainly a large-scale, macroscopic process, surface tension is strongest at the microscopic scales.
Traditionally, because the surface tension effects are so small, researchers assumed that for practical purposes they could disregard them. Not so. The tiniest scales proved crucial; there the surface effects proved infinitely sensitive to the molecular structure of a solidifying substance. In the case of ice, a natural molecular symmetry gives a built-in preference for six directions of growth. To their surprise, scientists found that the mixture of stability and instability manages to amplify this microscopic preference, creating the near-fractal lacework that makes snowflakes. The mathematics came not from atmospheric scientists but from theoretical physicists, along with metallurgists, who had their own interest. In metals the molecular symmetry is different, and so are the characteristic crystals, which help determine an alloy’s strength. But the mathematics are the same: the laws of pattern formation are universal.
Sensitive dependence on initial conditions serves not to destroy but to create. As a growing snowflake falls to earth, typically floating in the wind for an hour or more, the choices made by the branching tips at any instant depend sensitively on such things as the temperature, the humidity, and the presence of impurities in the atmosphere. The six tips of a single snowflake, spreading within a millimeter space, feel the same temperatures, and because the laws of growth are purely deterministic, they maintain a near-perfect symmetry. But the nature of turbulent air is such that any pair of snowflakes will experience very different paths. The final flake records the history of all the changing weather conditions it has experienced, and the combinations may as well be infinite.
BALANCING STABILITY AND INSTABILITY. As a liquid crystallizes, it forms a growing tip (shown in a multiple-exposure photograph) with a boundary that becomes unstable and sends off side-branches (left). Computer simulations of the delicate thermodynamic processes mimic real snowflakes (above).
Snowflakes are nonequilibrium phenomena, physicists like to say. They are products of imbalance in the flow of energy from one piece of nature to another. The flow turns a boundary into a tip, the tip into an array of branches, the array into a complex structure never before seen. As scientists have discovered such instability obeying the universal laws of chaos, they have succeeded in applying the same methods to a host of physical and chemical problems, and, inevitably, they suspect that biology is next. In the back of their minds, as they look at computer simulations of dendrite growth, they see algae, cell walls, organisms budding and dividing.
From microscopic particles to everyday complexity, many paths now seem open. In mathematical physics the bifurcation theory of Feigenbaum and his colleagues advances in the United States and Europe. In the abstract reaches of theoretical physics scientists probe other new issues, such as the unsettled question of quantum chaos: Does quantum mechanics admit the chaotic phenomena of classical mechanics?