Visitors can look through a peephole in the wall to see a hidden copy of a 1985 Scientific American issue, which features a colorful picture of the Mandelbrot set on the cover. Samuel explains that she wanted to show the scientific process, which is often outside of public view, and hide the more familiar, multihued image.

Printouts similar to the white series led to the discovery of speckles surrounding the larger set. At first, Mandelbrot thought that the specks might be dirt from the printer. Zooming in to the image with the computer allowed him to clear “ambiguity between mathematics and dirt,” Samuel says.

Mandelbrot sought to understand if those speckles, which he dubbed "islands," were connected to the larger whole. The first time the set was published, in the Annals of the New York Academy of Sciences, the publication’s photo editor removed the dots—likely mistaking them for dust or a printer artifact. Samuels recalls that even years later Mandelbrot would get upset about this error. When he sent the text to colleagues he drew dots in by hand. Later, mathematicians Adrian Douady and John H. Hubbard would mathematically prove that the term "islands" was a misnomer and the speckles were indeed part of the whole.

The exhibit also reveals the work of Mandelbrot's contemporaries. Visitors can turn away from the white series and examine a scrolling printout of two lines crossing each other. Neat handwriting on the top of the printout proclaims it the original. It is the handwriting of Edward N. Lorenz, a meteorologist, mathematician and pioneer of chaos theory. The printout is a visualization of chaos—both lines are from equations that are initially very similar to each other, but over time they become drastically different. Chaos theory explains that it is nearly impossible to make long-term predictions about certain systems—the weather, for example—because they are highly sensitive to small initial perturbations.

The entire exhibit explores the idea that whereas the computer enabled a revolution in mathematics and visual thinking, the interaction of hand, pencil and paper remains vital to understanding and discovery. One section displays sketches and letters from several researchers that show their visual thought processes as they shape and advance theory.

The drawing corner includes four pages covered in blue-ink sketches by Otto Rössler, a German biochemist who works on chaos theory. In these drawings Rössler starts with a dynamic system known as the Lorenz attractor. Then, with pen and paper, he discovers a new type of chaotic attractor. The process of drawing is the process of discovery, Samuel says. Before he put pen to paper, Rössler did not know the equation for the new attractor, but by the fourth page it is clear in his mind. The moment he discovers the final form of his attractor is marked with a green arrow.

The exhibit packs a great amount of information and history into a small space. For this it is notable. But the show also offers a rare opportunity to peek into the workings of renowned math minds.

2 Comments

1. 1. rloldershaw 10:29 AM 12/21/12

   
   It's a fractal world.
   
   For an essay that discusses 80 examples of fractal self-similarity in nature, from subatomic particles to stellar systems to galactic systems, see:
   
   http://www3.amherst.edu/~rloldershaw
   
   The essay is #14 of the Selected Papers (most published).
   
   Robert L. Oldershaw
   Discrete Scale Relativity
   Fractal Cosmology

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2. 2. Mike Round 02:20 PM 12/21/12

   Thanks for the great article and video ...
   
   Here is a project I'm working on regarding the Mandelbrot Set ...
   www.mandelbrotmap.com
   
   Mike Round
   Center for autoSocratic Excellence

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