These scientists created jewelry from the striking shapes of chaos theory

These scientists created jewelry from the striking shapes of chaos theory

These chaotic shapes were printed in bronze.
Enlarge / Chaotic shapes 3D printed in bronze represent the first step in the transformation from chaos to manufacturable forms.

F. Bertacchini/PS Pantano/E. Bilotta

A team of Italian scientists has devised a way to turn chaos theory’s striking, complex twisting shapes into real jewelry, according to a new paper published in the journal Chaos. These pieces are not simply inspired by chaos theory; they are created directly from the mathematical principles.

“It was a great pleasure for the whole team to see the chaotic shapes turn into real, polished, shiny, physical jewellery. It was also extremely exciting to touch and wear them,” says co-author Eleonora Bilotta of the University of Calabria. “We think it’s the same joy a scientist feels when her theory takes shape, or when an artist finishes a painting.”

The concept of chaos may suggest complete randomness, but to scientists it denotes systems so sensitive to initial conditions that their output appears random, obscuring their underlying internal rules of order: the stock market, rioting crowds, brain waves during an epileptic seizure, or the weather. In a chaotic system, small effects are amplified by repetition until the system becomes critical. The roots of present-day chaos theory rest on an accidental discovery in the 1960s by mathematician-turned-meteorologist Edward Lorenz.

Lorenz thought the advent of computers offered an opportunity to combine math and meteorology for better weather forecasting. He began constructing a mathematical model of the weather using a series of differential equations representing changes in temperature, pressure, wind speed, and the like. Once he had his skeletal system, he ran a continuous simulation on his computer that would produce a day’s worth of virtual weather every minute. The resulting data resembled naturally occurring weather patterns – nothing ever happened the same way twice, but there was clearly an underlying sequence.

On a wintry day in early 1961, Lorenz decided to take a shortcut. Instead of starting over the whole run, he started halfway through and typed the numbers directly from a previous printout to give the machine its initial state. Then he walked down the hall for a cup of coffee. When he returned an hour later, he found that the new print’s virtual weather deviated so quickly from the previous pattern, rather than exactly duplicating the earlier run, that within just a few virtual “months” all similarity between the two had disappeared . disappeared.

Six decimal places were stored in the computer’s memory. To save space on the print, only three appeared. Lorenz had entered the shorter, rounded numbers, assuming that the difference—one part in a thousand—was insignificant, comparable to a small gust of wind that is unlikely to have much impact on large-scale weather events. But in Lorenz’s particular system of equations, such small variations turned out to be catastrophic.

This is known as sensitive dependence on initial conditions. Lorenz went on to call his discovery “the butterfly effect”: The nonlinear equations governing weather are so incredibly sensitive to initial conditions — that a butterfly flapping its wings in Brazil could theoretically trigger a tornado in Texas. The metaphor is especially striking. To explore this further, Lorenz simplified his complex weather model, focusing on rolling fluid convection in our atmosphere: basically a gas contained in a solid rectangular box with a heat source at the bottom and cooled from above, in which warm air rises and cooler air sinks to the bottom. He simplified some fluid dynamics equations and found that plotting the results of specific parameter values ​​in three dimensions yielded an unusual butterfly-shaped figure.

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