Researchers from the University of Hawaii have discovered with the help of data from the Kepler space telescope that a star oscillates in an interesting pattern.

In a study published in the journal Physical Review Letters, the researchers detailed how they analyzed data from KIC 5520878, tracking the pulses the star made in 30-minute intervals over the course of four years. Within that time period, researchers recorded interesting observations about the star.

KIC 5520878 pulsated in different frequencies. What the researchers discovered was that two of its frequencies occurred at 6.41 and 4.05 hour cycles, pulsating at a 1.58 ratio, which is extremely close to the golden ratio of 1.618. The golden ratio is commonly found in artistic work and in nature, and is an indication of exactness.

Further observation also revealed the pulsating frequencies happened to conform to fractal patterns.

When the oscillations were separated into parts, additional weaker frequencies were identified. Researchers described the weaker frequencies as following a pattern similar to how shorelines appear craggy no matter what distance they were viewed from.

Researchers also found that a power law dependence was present by counting spikes on converted plots where there were heights greater than the specified threshold, which is characteristic of fractal behavior.

The fractal patterns in how the star pulsates is different from the usual ways fractal patterns are observed. In KIC 5520878, the pattern was identified as a factor of time. Researchers suggest that the results of their work can be considered the first example of what is known as a strange nonchaotic attractor, a system displaying fractal patterns but don't exhibit sensitivity to starting conditions like other chaotic systems, such as the weather.

To compare, researchers also observed five other pulsating stars. Mixed results were reported, with three showing pulsating frequencies close to the golden ratio and affinities for fractal patterns while two displayed neither.

At this point, it is still not clear whether the stars' behavior incorporating fractal patterns happens for a reason or not. If it does, then there are other clues regarding the physics of stars awaiting discovery. If not, then the discovery of the golden ratio in pulsating frequencies is a mere coincidence.

Researchers involved in the study include John Lindner, William Ditto, Vivek Kohar, John Learned, Behnam Kia and Michael Hippke.

The golden ratio is observable in flower petals, seed heads, pine cones, tree branches, shells, spiral galaxies, hurricanes, fingers, animal bodies and even DNA molecules.

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