© Olena Shmahalo/Quanta MagazineA pulsating star in the constellation Lyra generates a unique fractal pattern that hints at unknown stellar processes.
What struck
John Learned about the blinking of KIC 5520878, a bluish-white star 16,000 light-years away, was how artificial it seemed.
Learned, a neutrino physicist at the University of Hawaii, Mānoa, has
a pet theory that super-advanced alien civilizations might send messages by tickling stars with neutrino beams, eliciting Morse code-like pulses. "It's the sort of thing tenured senior professors can get away with," he said. The pulsations of KIC 5520878, recorded recently by NASA's Kepler telescope, suggested that the star might be so employed.
A "variable" star, KIC 5520878 brightens and dims in a six-hour cycle, seesawing between cool-and-clear and hot-and-opaque. Overlaying this rhythm is a second, subtler variation of unknown origin; this frequency interplays with the first to make some of the star's pulses brighter than others. In the fluctuations, Learned had identified interesting and, he thought, possibly intelligent sequences, such as prime numbers (which have been floated as a conceivable basis of extraterrestrial communication). He then found hints that the star's pulses were chaotic.
But when Learned mentioned his investigations to a colleague,
William Ditto, last summer, Ditto was struck by the ratio of the two frequencies driving the star's pulsations.
"I said, 'Wait a minute, that's the golden mean.'"
This irrational number, which begins 1.618, is found in certain spirals, golden rectangles and now the relative speeds of two mysterious stellar processes. It meant that the blinking of KIC 5520878 wasn't an extraterrestrial signal, Ditto realized, but something else that had never before been found in nature: a mathematical curiosity caught halfway between order and chaos called a "strange nonchaotic attractor."
Dynamical systems — such as pendulums, the weather and variable stars — tend to fall into circumscribed patterns of behavior that are a subset of all the ways they could possibly behave. A pendulum wants to swing from side to side, for example, and the weather stays within a general realm of possibility (it will never be zero degrees in summer). Plotting these patterns creates a shape called an "attractor."
Mathematicians in the 1970s used attractors to model the behavior of chaotic systems like the weather, and they found that the future path of such a system through its attractor is extremely dependent on its exact starting point. This sensitivity to initial conditions, known as the butterfly effect, makes the behavior of chaotic systems unpredictable; you can't tell the forecast very far in advance if the flap of a butterfly's wings today can make the difference, two weeks from now, between sunshine and a hurricane. The infinitely detailed paths that most chaotic systems take through their attractors are called "fractals." Zoom in on a fractal, and new variations keep appearing, just as new outcrops appear whenever you zoom in on the craggy coastline of Great Britain. Attractors with this fractal structure are called "strange attractors."
Comment: It is too bad that all scientists don't have such common sense.