Many people know Benoît Mandelbrot from the computer screensavers of a pre-LCD era. Others have a deeper understanding of his mathematics, the repeating geometries that earned him the sobriquet Father of Fractals. Less appreciated, though, is the process underlying his work: Mandelbrot relied as much for guidance on visual imagery as whiteboard formulae. Primitive computer printouts were his maps to uncharted mathematical terrain, their dot-matrix patterns a "here be dragons" for the exploration of dynamical systems and chaos theory.
In 2008, fascinated by the interplay between imagery and scientific investigation, art historian Nina Samuel spent two weeks interviewing Mandelbrot in his Cambridge, Massachusetts home. After Mandelbrot passed away in 2010, she was allowed entry to his office, collecting some 300 printouts, sketches and notebook scribbles now on display in The Islands of Benoît Mandelbrot: Fractals, Chaos, and the Materiality of Thinking, an exhibition at the Bard Graduate Center in Manhattan.
"There is such an organic quality to these images," said Samuel. "These are the images the scientists used when they were working, and not what was found on magazine covers or popularized in screensavers."
The exhibition runs until Jan. 27, but for readers not fortunate enough to visit, Samuel took Wired on a guided virtual tour. Each entry is followed by links to high-resolution versions of the images.
Becoming the Mandelbrot Set
The image below comes from a series of 120 prints, some composed of seemingly stray dots and others almost completely blank, that preceded Mandelbrot's discovery of the fractal set that bears his name (visualized above, as produced by a modern pattern generator).
"If you look at the shadows, you can see the resemblance," Samuel said of the early image. "Later on, he could have seen the shapes that became famous." But at the time, Mandelbrot saw only an undefined something, a hint of what needed next to be done.
"Mandelbrot would never say that an image was a proof, but an image would lead to conjecture, open up the imagination, and then you could prove something with formulas," said Samuel.
Images: 1) Geek3/Wikimedia Commons [high-resolution] 2) Benoît Mandelbrot and Mark Laff, programmer. Collection Aliette Mandelbrot. [high-resolution]