Scientists confirm beautiful nano-butterflies, predicted decades ago by Hofstadter

doug hof

IU’s Douglas Hofstadter

Butterflies were in the news last week. Hofstadter butterflies that is – the self-similar patterns of electrons in a magnetic field that Indiana University distinguished professor Douglas Hofstadter predicted to exist in 1976, shortly after Hofstadter had received his Ph.D. in physics from the University of Oregon.

Hofstadter’s nearly 40-year-old prediction of one of the first fractal phenomena in nature – he envisioned an endlessly repeating energy spectrum of electrons in crystal lattices forming butterfly patterns – was confirmed experimentally for the first time by a team of physicists from the U.S. and Japan. At the time he graphed the energy levels, he dubbed the phenomenon as Gplot, and it was a theory he referenced again in his Pulitzer Prize-winning nonfiction work “Gödel, Escher, Bach: an Eternal Golden Braid.”

The confirmation of the Hofstadter Butterfly has implications in any field where nanoscale materials are used and where lighter and faster is the order of the day – think drug delivery, communications, security, optics. Hofstadter at the time didn’t have the benefit of two-dimensional electron systems – the transistor-like structures made from semiconductors – to engineer a test for his theory. But after decades of lab experiments, scientists last week showed how they manufactured nanoscale ripples on two two-dimensional lattices of graphene coupled to hexagonal boron nitride. In case you’re wondering, the ripples were twenty-trillionths of a meter high (0.2 angstroms).


Columbia University engineers created this image illustration of a butterfly departing from a graphene pattern formed on the top of an atomically thin boron nitride substrate. Electron energy in the structure exhibits the butterfly like a self-recursive fractal quantum spectrum.

So now physicists and engineers have the best ever access to experimenting within the fractal spectrum, and the ability to tune in or tune out varying degrees of freedom within this self-repeating spectrum, all in order to better understand the behavior of electrons in a magnetic field. The work also confirms, if not once again, that Hofstadter is one of Indiana University’s greatest intellectual treasures.

An undergraduate mathematician who grew up around Stanford where his father was a Nobel Prize-winning physicist, Hofstadter is a distinguished professor in cognitive science and comparative literature in IU’s College of Arts and Sciences. He is director of the Center for Research on Concepts and Cognition. He and his students work within the Fluid Analogies Research Group, which is referred as FARG and the students as FARGonauts, and, as he’s stated before, their work is “perpetually in search of beauty.”

It’s been during that search that Hofstadter has helped generate a cadre of thinkers who’ve gone out into the world and proven over and over again how proud Indiana University Bloomington should be to have such a unique polymath, a true Renaissance man, at its campus. These FARGonauts and other students of Hofstadter, conducting research, inventing, writing and teaching around the globe, are IU’s reward.

One of them, who remains here at IU, is Donald Byrd, a senior scientist and adjunct professor in the School of Informatics and Computing at the forefront of computational music study. He’s designed music programs like SMUT and Nightingale; was a designer and software developer for the Kurzweil 250, which is recognized as one of the first synthesizers to convincingly reproduce the sounds of acoustic instruments; and his work on online music information retrieval is cutting edge.

classic hofstadter butterfly

The classic Hofstadter Butterfly from Hofstadter’s 1975 PhD dissertation.

Another is David Chalmers, a Distinguished Professor of Philosophy at Australian National University, where he founded the Centre for Consciousness, and a professor of philosophy at New York University. And Robert French is a cognitive scientist who is now research Director at the French National Center for Scientific Research, the largest fundamental science agency in Europe.

Computer scientist Melanie Mitchell, a professor at Portland State University, in 2009 published the high-successful book “Complexity: A Guided Tour.” called it one of the 10 best science books of that year, and Phi Beta Kappa honor society agreed, recognizing Mitchell with it 2010 best book award.

Scott A. Jones received his Bachelor of Science in computer science while working with Hofstadter and then went on in the 1980s to invent one of the first types of voicemail while co-founding Boston Technology. Still an Indiana resident and a global entrepreneur, Jones has been featured in various media, from MTV to USA Today.

The list could go on, and will go on, and many of the freshest faces leaving FARG are being grabbed up by Google – like Eric Nichols and Abhijit Mahabal – and other tech research companies. Together, as a collective, they give Indiana University a unique presence in the domain where technology and the human mind intersect, and that’s all because Hofstadter calls IU and Bloomington home.

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