A butterfly flaps its wings and scientists make jewelry

The further out in time, the more unreliable a weather forecast. That's because small variations in initial weather conditions can completely change the entire system, making it unpredictable. Put another way, in the "butterfly effect," an insect can flap its wings and create a microscopic change in initial conditions that leads to a hurricane halfway around the world.

This chaos is seen everywhere, from weather to labor markets to brain dynamics. And now, in the journal Chaos, by AIP Publishing, researchers from the University of Calabria explored how to turn the twisting, fractal structures behind the science into jewelry with 3D printing.

The jewelry shapes are based on the Chua circuit, a simple electronic system that was the first physical, mathematical, and experimental proof of chaos. Instead of an ordinary circuit, which produces an oscillating current, Chua's circuit results in oscillations that never repeat.

"These chaotic configurations, called strange attractors, are complex structures that had never been observed before," said author Eleonora Bilotta. "The depictions of such structures are strikingly beautiful, continually shifting when the point of view is changing. Jewelry seemed to be the best way to interpret the beauty of chaotic shapes."

At first, the team tried to employ goldsmiths to create prototypes of the twisting, arcing patterns. But the chaotic forms proved too difficult to manufacture with traditional methods. In contrast, additive printing allows for the necessary detail and structure. By 3D-printing the jewelry, the team created a counter-mold for a goldsmith to use as a cast.

"Seeing the chaotic shapes transformed into real, polished, shiny, physical jewelry was a great pleasure for the whole team. Touching and wearing them was also extremely exciting," said Bilotta. "We think it is the same joy that a scientist feels when her theory takes form, or when an artist finishes a painting."

The jewelry can also be used as an educational tool, providing students the ability to develop their scientific knowledge and artistic creativity. By building Chua's circuit, they can manipulate chaos and discover the extreme sensitivity to initial conditions. While designing the jewelry before sending it to be printed, they can tweak the parameters to generate different shapes according to personal taste.

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Chaos theory provides hints for controlling the weather

Under a project led by the RIKEN Center for Computational Science, researchers have used computer simulations to show that weather phenomena such as sudden downpours could potentially be modified by making small adjustments to certain variables in the weather system. They did this by taking advantage of a system known as a "butterfly attractor" in chaos theory, where a system can have one of two states -- like the wings of a butterfly -- and that it switches back and forth between the two states depending on small changes in certain conditions.

While weather predictions have reached levels of high accuracy thanks to methods such as supercomputer-based simulations and data assimilation, where observational data is incorporated into simulations, scientists have long hoped to be able to control the weather. Research in this area has intensified due to climate change, which has led to more extreme weather events such as torrential rain and storms.

There are methods at present for weather modification, but they have had limited success. Seeding the atmosphere to induce rain has been demonstrated, but it is only possible when the atmosphere is already in a state where it might rain. Geoengineering projects have been envisioned, but have not been carried out due to concerns about what unpredicted long-term effects they might have.

As a promising approach, researchers from the RIKEN team have looked to chaos theory to create realistic possibilities for mitigating weather events such as torrential rain. Specifically, they have focused on a phenomenon known as a butterfly attractor, proposed by mathematician and meteorologist Edward Lorentz, one of the founders of modern chaos theory. Essentially, this refers to a system that can adopt one of two orbits that look like the wings of a butterfly, but can change the orbits randomly based on small fluctuations in the system.

To perform the work, the RIKEN team ran one weather simulation, to serve as the control of "nature" itself, and then ran other simulations, using small variations in a number of variables describing the convection -- how heat moves through the system -- and discovered that small changes in several of the variables together could lead to the system being in a certain state once a certain amount of time elapsed.

According to Takemasa Miyoshi of the RIKEN Center for Computational Science, who led the team, "This opens the path to research into the controllability of weather and could lead to weather control technology. If realized, this research could help us prevent and mitigate extreme windstorms, such as torrential rains and typhoons, whose risks are increasing with climate change."

"We have built a new theory and methodology for studying the controllability of weather," he continues. "Based on the observing system simulation experiments used in previous predictability studies, we were able to design an experiment to investigate predictability based on the assumption that the true values (nature) cannot be changed, but rather that we can change the idea of what can be changed (the object to be controlled)."

Looking to the future, he says, "In this case we used an ideal low-dimensional model to develop a new theory, and in the future we plan to use actual weather models to study the possible controllability of weather."

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