Benoît Mandelbrot — First rendering of the Mandelbrot Set

1980

Artists: Benoît Mandelbrot · Year: 1980 · Medium: Printed plot of the iteration set of z → z² + c in the complex plane · Substrate: IBM mainframe, printer; later color renderings · Place: Yorktown Heights, New York, USA · Institution: IBM Thomas J. Watson Research Center Benoît Mandelbrot worked for thirty-five years at IBM's Thomas J. Watson Research Center in Yorktown Heights, an unusually free-form institution where mathematicians were permitted to pursue problems that had no obvious industrial application. His problem, from 1963 onward, was the geometry of irregular natural shapes — coastlines, clouds, galaxies, price fluctuations — which classical Euclidean geometry could not describe. He coined the word fractal in 1975 to name the family of objects he was studying. The object now known as the Mandelbrot set had been glimpsed before. Robert Brooks and Peter Matelski had produced a low-resolution sketch of it in a 1978 paper. But it was Mandelbrot's renderings, made at IBM in 1980 at successively higher resolutions and eventually in color, that turned the object into an aesthetic event. The iterative algorithm is elementary — a complex-plane iteration of z → z² + c that determines membership in the set by whether the trajectory stays bounded — but the images it produces, and particularly the recursive self-similarity revealed by zooming into the set's boundary, are visually extraordinary and instantly memorable. Adrien Douady named the set in 1985. By the late 1980s the Mandelbrot set was a commercial graphic in its own right — posters in dorm rooms, screensavers on workstations, a backdrop in science documentaries. Arthur C. Clarke's 1995 television program The Colours of Infinity was dedicated to the set. By the early 1990s a generation of students knew what the set looked like before they knew what a complex number was. The image had escaped the mathematics. The consequence for computer art is that Mandelbrot established, at mass scale, the proposition that mathematical computation could produce images that were self-evidently beautiful without apology or explanation. No mid-century critic would have claimed that a graph of z² + c iteration was an aesthetic object. Mandelbrot showed them. He died in 2010, at eighty-five. The rare mathematician whose work is equally at home in a research seminar and on a dorm-room wall. His IBM colleagues and IBM itself deserve structural credit: the Watson lab's willingness to let a pure mathematician render pictures for two decades is why the images exist. Lore Mandelbrot worked at IBM's Yorktown Heights lab — an unusually free-form research environment where he spent decades on what he eventually named 'fractal geometry.' The set itself had been glimpsed in 1978 by Brooks and Matelski, but Mandelbrot's 1980 renderings — iterative, computationally expensive, and immediately beautiful — made the object legible to a public audience. Adrien Douady named the set after him in 1985. The visual flood that followed — fractal posters, screensavers, early 90s 'computer art' as a shopping-mall category — was, in some ways, the first time a computation became a household aesthetic image. Mandelbrot wrote that he'd always suspected mathematics was visually richer than anyone let on; he lived to see the proof. Sources • Mandelbrot, Benoît — The Fractal Geometry of Nature (Freeman, 1982) • IBM Research archives • Peitgen, Jürgens, Saupe — Chaos and Fractals (Springer, 1992)