February 3, 2023

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These scientists have created jewels of amazing forms of chaos theory

Zoom in / The anarchic shapes 3D printed in bronze represent the first step in the shift from chaotic to manufacturable shapes.

F. Bertacchini / PS Pantano / E. Bellotta

A team of Italian scientists has discovered a way to transform the amazing and complex twisted shapes of Chaos Theory In actual jewelry, according to new leaf Published in Chaos Journal. These pieces are not simply inspired by chaos theory. Created directly from its mathematical principles.

“Seeing the messy shapes transformed into real physical jewelry, shimmering and shimmering, was such a treat for the whole team. It was also very exciting to touch and wear them,” she says. said co-author Eleonora Bellotta from the University of Calabria. “We think it’s the same pleasure 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 refers to systems so sensitive to initial conditions that their output appears random, obscuring basic 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 chaos theory today are based on a Serendipitous discovery in the 1960s by a mathematician turned meteorologist Edward Lorenz.

Lorenz believed that the advent of computers provided an opportunity to combine mathematics and meteorology for better weather forecasting. He set out to build a mathematical model of the weather using a set of differential equations that accounted for changes in temperature, pressure, wind speed, and the like. Once he had his skeletal system in place, he would run a continuous simulation on his computer, which would output a virtual weather for one day every minute. The resulting data was like naturally occurring weather patterns — nothing happened the same way twice, but there was clearly an underlying order.

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One winter day early in 1961, Lorenz decided to take a shortcut. Instead of starting the whole thing, he started halfway through, writing the numbers straight from an earlier print to give the machine its initial conditions. Then he walked down the hall to have a cup of coffee. When he returned an hour later, he found that instead of exactly repeating the previous version, the new print showed the default weather diverging so quickly from the previous pattern, that within a few hypothetical “months” all similarity between the two had disappeared.

Six decimal places are stored in the computer’s memory. To save space on the print, only three appeared. Lorenz had inserted the shorter numbers and rounded, assuming that the difference—thousandths of a thousand—was inconsequential, similar to a small puff of wind that is unlikely to have much effect on weather features on a large scale. But In Lorenz’s own system of equations, these small differences proved disastrous.

This is known as a sensitive dependence on initial conditions. Lorenz later called his discovery “The Butterfly Effect“: The nonlinear equations that govern the weather are incredibly sensitive to initial conditions—that a butterfly flapping its wings in Brazil could theoretically cause a tornado in Texas. The metaphor is particularly apt. To investigate further, Lorenz simplified his complex weather model, focusing on Convection of a rolling fluid in our atmosphere: Basically, a gas in a solid rectangular box with a heat source at the bottom and a cooler at the top, where warm air rises to the top and cold air sinks to the bottom.He simplified some fluid dynamics equations and found that plotting the results of parameter values Defined in three dimensions produced an unusual butterfly-shaped shape.