Home Science These scientists created jewelry out of the striking shapes of chaos theory

These scientists created jewelry out of the striking shapes of chaos theory

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

F. Bertacchini/PS Pantano/E. Bilotta

A team of Italian scientists have found a way to change their impressively complex twisted shape. chaos theory According to the actual jewelry new paper Published in Chaos magazine. These works are not simply inspired by chaos theory. They were created directly from that mathematical principle.

“It was a great joy for the whole team to see the chaotic shapes transform into real, sophisticated, lustrous, physical jewellery. , was very exciting.” Co-author Eleonora Bilotta said of the University of Calabria. “We think of it as the same joy a scientist feels when his theory takes shape, or an artist when he finishes a painting.”

The concept of chaos may suggest complete randomness, but to scientists, the system’s output appears random because it is so sensitive to initial conditions that it obscures the underlying rules of internal order. It means the system that is For example, stock markets, rioting crowds, brain waves during epileptic seizures. , or the weather. In a chaotic system, small effects are amplified by repeated repetitions until the system becomes critical. The roots of today’s chaos theory are accidental discovery Mathematician turned meteorologist in the 1960s Edward Lorenz.

Lorenz saw the advent of computers as an opportunity to combine mathematics and meteorology to improve weather forecasting. He set out to build a mathematical model of weather using a set of differential equations that describe changes in temperature, pressure, wind speed, and more. Skeleton Once his system was complete, he kept running simulations continuously on his computer. This will generate a day’s worth of virtual weather every minute. The resulting data resembled naturally occurring weather patterns. The same thing never happened to him twice, but there was clearly an underlying order.

One winter day in early 1961, Lorenz decided to take a shortcut. Instead of starting the whole thing over again, he started halfway through and entered the numbers directly from the previous print to give the machine an initial state. Then he walked down the hallway to drink coffee. When he returned an hour later, he found that the new printout, rather than replicating the previous run exactly, had changed the virtual weather significantly from its previous pattern. found that within hypothetical “months” all similarities between the two were lost. Had disappeared.

Computer memory stored 6 decimal places. Only three are shown to save space on the printout. Lorentz argues that a difference of 1 in 1000 is negligible, and that shorter rounded numbers are assumed to be similar to small winds that are unlikely to significantly affect large-scale weather features. entered.But For certain systems of Lorenz equations, such small fluctuations turned out to be catastrophic.

This is known as sensitive dependence on initial conditions. Lorenz then described his findings as “butterfly effect: The nonlinear equations that govern weather are incredibly sensitive to initial conditions. A flapping butterfly in Brazil could theoretically cause a tornado in Texas. Metaphors are especially apt. For further investigation, Lorenz simplified his complex weather model to focus on rotating fluid convection in the atmosphere. It’s basically a gas in a solid rectangular box that has a heat source at the bottom and is cooled from above, with warm air rising up and cold air sinking down. He simplified some hydrodynamic equations and found that plotting the results for specific parameter values ​​in his three dimensions produced unusual butterfly-shaped figures.

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