These scientists have created jewels from the amazing shapes of chaos theory

These scientists have created jewels from the amazing shapes of chaos theory

Zoom in / Chaotic shapes 3D printed in bronze are the first step in the transformation from chaos to manufacturable shapes.

F. Bertacchini/PS Pantano/E. Bilotta

A team of Italian scientists has discovered a way to turn the amazing and complex shapes of chaos theory into real jewelry, according to a new article published in the journal Chaos. These pieces are not simply inspired by chaos theory; were created directly from his mathematical principles.

“Seeing the chaotic shapes transformed into real, polished, shiny, physical jewels was a great pleasure for the whole team. Touching and wearing them was also extremely exciting,” said 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 might suggest complete randomness, but to scientists it denotes systems that are so sensitive to initial conditions that their production appears random, obscuring the underlying internal rules of order: the stock market, rioting crowds, waves brain during an epileptic fit. , or the weather. In a chaotic system, tiny effects are amplified by repetition until the system becomes critical. The roots of today’s chaos theory lie in a serendipitous discovery in the 1960s by mathematician-turned-meteorologist Edward Lorenz.

Lorenz believed that the advent of computers provided an opportunity to combine mathematics and meteorology for better weather prediction. He set out to build a mathematical model of the weather using a set of differential equations representing changes in temperature, pressure, wind speed and the like. Once he had his skeleton system, he kept a continuous simulation running 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 order.

One winter day in early 1961, Lorenz decided to take a shortcut. Instead of starting the entire run, he started halfway through, typing the numbers directly from a previous printout to give the machine the initial conditions. Then he went down the hall for a cup of coffee. When he returned an hour later, he found that instead of duplicating the previous round exactly, the new printout showed the virtual weather diverging so rapidly from the previous pattern that, in just a few virtual “months,” all similarities between the two had . it disappeared.

Six decimal places were stored in the computer memory. To save space on print, only three have appeared. Lorenz introduced the shorter, rounded numbers, assuming that the difference—one part in a thousand—was insignificant, similar to a small puff of wind unlikely to have a large impact on large-scale weather features. But in Lorenz’s particular system of equations, such small variations proved catastrophic.

This is known as sensitive dependence on initial conditions. Lorenz later called his discovery the “butterfly effect”: the nonlinear equations that govern 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 particularly apt. To investigate further, Lorenz simplified his complex climate model, focusing on the convection of the rolling fluid in our atmosphere: basically, a gas in a rectangular solid box with a heat source at the bottom and cooled at the top, in which warm air rises and cooler air sinks to the bottom. He simplified several fluid dynamics equations and found that plotting the results of specific parameter values ​​in three dimensions produced an unusual butterfly-shaped figure.

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