These scientists have created a collection of surprising figures based on chaos theory

A team of Italian scientists has pioneered a path-breaking process by shaping the complex twisting shapes of chaos theory into actual jewelry, according to a new paper published in the journal Chaos. These parts were not only inspired by chaos theory; they were created directly from their mathematical principles.

“Seeing the dark figures transformed into a real, polished, shiny, body ornament was a great pleasure for the whole team. Touching and losing it was also very exciting,” said co-author Eleonora Bilotta of the University of Calabria. “We think it is the same joy that a scientist feels when it is formed or when an artist paints.”

The concept of chaos may suggest complete randomness, but to scientists, it means systems so sensitive in their initial conditions that their outputs appear random, obscuring the internal rules of order: stock markets, rioting crowds, brain waves in an epileptic seizure. or the weather In a chaotic system, small effects are amplified through repetition until a critical system is reached. The roots of today’s chaos theory rest on a serendipitous discovery in the 1960s by mathematician-turned-meteorologist Edward Lorenz.

Lorenz saw the advent of computers as an opportunity to combine mathematics and meteorology for better weather forecasting. He set out to construct a mathematical model of the weather using a set of differential equations representing changes in temperature, pressure, wind speed, and the like. When he had his skeleton system, he kept a continuous simulation running on his computer that would produce one day’s worth of virtual weather every minute. From there the data is similar to naturally occurring weather patterns – nothing ever happened the same way twice, but there was clearly an underlying order.

One winter morning in 1961, Lorenz decided to take a short break. Instead of going through the whole thing, he started in the middle, typing the correct numbers from the previous printout to give the machine its initial conditions. Then he walked into the hall for a cup of coffee. When he returned an hour later, he found that, instead of nearly duplicating the previous run, the new virtual storm printout had so rapidly faded from the previous model that, within a few virtual “months,” there was every resemblance between the two. disappeared

Six decimal places are stored in the computer’s memory. As a space in the printout, only three appeared. Lorenz had entered shorter round numbers if a difference of one part in a thousand was inexplicable, like a small gust of wind which is unlikely to have much effect on the characteristics of large storms. But in Lorenz’s particular system of equations, such small variations proved disastrous.

This is known as a sensitive dependence on the initial conditions. Lorenz later called his discovery the “butterfly effect”: the nonlinear equations that govern the weather have such an incredible sensitivity to the initial conditions that a butterfly flapping its wings in Brazil theoretically fits a Texas hurricane best. To investigate further, Lorenz simplified his complex model of weather, focusing on the fluid convection in our atmosphere: basically, gas in a solid rectangular box with a hot spring at the bottom and a cooler on top, in which hot air rises to the top and cooler air sinks to the bottom. He simplified a few fluid dynamics equations and found that by plotting the results of specific modulus values ​​in three dimensions, he formed an unusual butterfly shape.