He was called the “father of fractals” and “the man who reshaped geometry.” Mathematician and research scientist Benoît Mandelbrot changed the way we view and measure the world and sparked a revolution in numerous areas of science, industry and art.
Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes with uneven contours that could mimic the irregular shapes often found in nature. Fractals are a form of geometric repetition, in which successively smaller copies of a pattern are nested inside each other so that the same intricate shapes appear repeatedly. Mandelbrot believed such irregular shapes were in many ways more natural than the artificially smooth objects of traditional geometry, and that they could have broad applicability.
Fractal geometry made it possible for the first time to measure cloud formations, the contours of coastlines, the clustering of galaxies, even the folds of mammalian brains, in a rigorously quantitative fashion.
Mandelbrot was a restless inquisitor who often strayed from his chosen field of mathematics to investigate how fractals applied to physics, biology, medicine, economics, fluid dynamics and computer graphics. Over the course of his career he developed a reputation as a maverick outsider with a relentless curiosity and a knack for noticing hidden patterns. “He knew everybody, with interests going off in every possible direction,” said David Mumford, a professor emeritus of applied mathematics at Brown University. “Every time he gave a talk, it was about something different.”
During his 35-year career at IBM, Mandelbrot was afforded the freedom to foster his unconventional insights as well as given access to the most advanced information technology. The combination provided the necessary tools to develop an entirely new branch of geometry, which traces back to a question he encountered as a young researcher: How long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks.
On a map, the contours of Britain may appear relatively smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further reveals even more coastline, all the way down to atomic scale. The length of the coastline, in a sense, is infinite.
Mandelbrot’s upbringing was as irregular as the fractal worlds he explored. Born to a Lithuanian Jewish family in Warsaw in 1924, he fled from the Nazis with his family in 1936 — first to Paris and then to the south of France, where he tended horses and fixed tools. As a Polish émigré in France, and then as a French émigré in the US after World War II, his schooling was irregular and discontinuous. He earned a master’s degree in aeronautics at the California Institute of Technology, returned to Paris for his doctorate in mathematics in 1952, then went on to the Institute for Advanced Study in Princeton, New Jersey, where he did research.
In 1958, Mandelbrot took a position at the Thomas J. Watson Research Center in Yorktown Heights, New York, where he was asked to examine the problem of extraneous “noise” in IBM’s electronic transmission lines. He discovered that the noise tended to appear in bunches, with patterns that remained constant whether plotted by the second or by the hour.
There was a larger structure at work. This type of activity — measuring structures and making sense of seeming chaos — would become Mandelbrot’s life’s work. The net result was nothing less than a new geometry of the cosmos.
It wasn’t until Mandelbrot’s 1982 book, The Fractal Geometry of Nature, in which he highlighted the many occurrences of fractal objects in nature, that his insights would receive widespread attention. Each split in a tree — from trunk to limb to branch to twig — is remarkably similar, yet subtle differences provide increasing detail, complexity and insight into the inner workings of the entire tree.
Mandelbrot’s work touched off a revolution in the study of turbulence and disorder across science, industry and art. For millennia, the human heart was believed to beat in a regular, linear fashion, but studies have shown that the true rhythm of a healthy heart fluctuates in a distinctively fractal pattern. Blood is also distributed throughout the body in a fractal manner, and researchers have created mathematical models of blood flows for early detection of cancerous cells.
Fractal-based antennae that pick up the widest range of known frequencies are now used in many wireless devices. Graphic design and image editing programs use fractals to create stunningly lifelike landscapes for films. Climate scientists perform fractal statistical analyses of forests that measure and quantify how much carbon dioxide the world can safely process.
In recognition of his groundbreaking work, Mandelbrot received more than 15 honorary doctorates and numerous awards, including the Barnard Medal for Meritorious Service to Science, past recipients of which include Albert Einstein and Enrico Fermi. Throughout his career, Mandelbrot cherished his role as an outsider who questioned conventional wisdom and remained on the periphery of traditional dogmas.
Even after living in America for decades, he claimed not to know the alphabet, and that having to use a telephone book reduced him to near helplessness. “From the very beginning, his angle has been to show people that they were making faulty assumptions simply because they didn’t have the tools to look beyond them,” noted Mumford.
Mandelbrot died in 2010 at age 85. He often credited his pioneering work on fractal geometry to his own life’s seemingly chaotic pattern. “Every discovery I made while at IBM fell well outside the scope of any university department,” Mandelbrot said. “I did not add new fields because of boredom or coercion, but because of new opportunities.”
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