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

According to a new paper published in the journal Chaos, a team of Italian scientists have figured out how to turn chaos theory’s impressively complex twisted shapes into real jewelry. These works are not simply inspired by chaos theory. They were created directly from that mathematical principle.

Co-author Eleonora Bilotta from the University of Calabria said, “It was a great joy for the whole team to see the chaotic shapes transformed into real, sophisticated, lustrous physical jewelry. “We thought it was the same joy a scientist feels when his theory takes shape, or an artist when he finishes a painting.” thinking about.”

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 lie in his accidental discovery in the 1960s by mathematician-turned-meteorologist 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 over the whole thing, 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 for coffee. When he returned an hour after his, he found that rather than exactly replicating his previous run, the new printout showed that the hypothetical weather had deviated very rapidly from its previous pattern. and 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 named his discovery the “butterfly effect”. The nonlinear equations that govern weather are incredibly sensitive to initial conditions, and a flapping butterfly in Brazil could theoretically trigger 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 an unusual butterfly-shaped figure.