In physics and mathematics, deterministic chaos denotes behavior so complex and unpredictable that it appears to be random; but in fact, it is the consequence of so-called deterministic nonlinear equations, for which the present situation exactly predicts the future behavior. The subtlety of chaos means that the slightest change in the present situation produces enormous changes in the subsequent behavior, and thus the long-range future is unpredictable. Phenomena such as turbulence in fluids, including weather, obey equations that are predictable for short times but not for long ones, as small perturbations magnify rapidly.
When Feigenbaum began his career in the early 1970s, the term “chaos theory” did not exist. Generations of scientists dating back to Isaac Newton had worked on problems related to the predictability of complex systems, such as the orbits of the planets in the solar system. By the middle of the 20th century, physicists and mathematicians—inspired by the pioneering work of the French physicist and mathematician Henri Poincaré—had succeeded in characterizing chaotic states, often enabled by computers, by framing such questions as geometric problems. But the boundary between regular and chaotic behavior remained fuzzy, particularly as it applied to real physical systems.
Feigenbaum stepped into this foggy arena, developing methods capable of computationally modelling the period-doubling transition to chaos, which proceeds in a series of geometrically focused steps that remain similar when scaled across orders of magnitude, an example of so-called fractal geometry. He first studied a simple iterated algebraic equation known as the logistic map, and was later able to demonstrate that these steps are “universal:” all physical systems that become chaotic via this period-doubling route to chaos exhibit the same behavior. Feigenbaum also found that this behavior is determined by two universal constants, now known as the Feigenbaum constants.
Working with Albert N. Libchaber, a Rockefeller colleague, Feigenbaum showed that this universal behavior occurred in a low-temperature fluid dynamics experiment. For this work, Feigenbaum and Libchaber won the prestigious Wolf Prize in Physics, in 1986. The universal behavior they described was later seen in many real-world examples, from electrical circuits to biological systems.