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Benoit Mandelbrot – Manuscripts launches new project October 2012

October 2, 2012
Glynn Edwards

At the beginning of this year, the papers of Benoit Mandelbrot, the father of fractal geometry, were given to SUL’s Dept. of Special Collections. Funding for the first year has been set to begin processing this complex collection. We are happy to announce that Laura Williams has been hired as the project archivist and Christy Smith as the processing assistant. Laura, who has been with the Manuscript’s Division since 2009, is just wrapping up the processing of the Stop AIDS Project Records – another large processing and digitization project. Christy Smith has been in the department since 2000, staring as an assistant to the previous University Archivist, Maggie Kimball. In 2009 she moved to the manuscripts division as a processing assistant on the R. Stuart Hummel Family Papers processing and digitization project.

Benoit Mandelbrot

Benoit Mandelbrot was born in 1924 in Warsaw, Poland. The family moved to Paris in 1936 and, after studies in the United States and France, he completed a Ph.D. in mathematics at the University of Paris in 1952. Mandelbrot spent most of his professional research career at IBM, beginning in 1958; with his appointment as an IBM Fellow in 1974, he was free to investigate problems of his and was able to follow his personal inclination towards interdisciplinary research founded on applied mathematics.

Mandelbrot had begun to focus his attention on fractal mathematics during the 1960s, beginning with his article, “How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,” published in Science (1967). In this article he introduced fractals as part of the solution to a problem that had occupied his attention for some time: How to measure a curve as complex as a geographic coastline? He discussed two salient characteristics of fractals that applied to this problem: self-similarity and “fractional” dimensionality. Self-similarity referred to the persistence of patterns as an observer zoomed in or out of the visualization of a fractal set. Fractional geometry described the quality these sets had mathematically of being “fuzzier” than a line but never completely filling a plane. A few years later, in 1975, Mandelbrot introduced the term “fractal” to describe such mathematical sets. Over the course of his career, until his death in 2010, Mandelbrot tracked down or encouraged myriad applications of fractal geometry as the study of “fuzziness” to fields ranging from engineering and medicine to finance and climate … and to art.

Mandelbrot first rendered a computer-generated image of the set that would be named after him at IBM’s Thomas J. Watson Research Center in 1980. The computer plot produced by a software program revealed the distinctive image of a large vaguely heart-shaped object connected to a smaller spherical object and having a rough, fuzzy border. While this was neither the first mathematical study of this particular mathematical set nor the first visualization of it, Mandelbrot had developed an algorithm that would be the basis of subsequent computer programs used to study and visualize fractals.

Mandelbrot’s work was introduced to a wider readership with the publication of an article about the Mandelbrot Set in Scientific American (1985). Like many other results from applied and recreational mathematics, it appeared in A.K. Dewdney’s “Computer Recreations” column. Dewdney opened by describing the Mandelbrot’s visualization of the set, announcing to his readers that “here is an infinite regress of detail that astonishes us with its variety, its complexity and its strange beauty.” He described Mandelbrot’s work in fractal geometry and how the boundary of the Mandelbrot Set was a fractal exhibiting fractional dimensionality and the recursive quality of self-similarity. The article went on to describe how a computer program could function essentially as a microscope for this geometrical object, allowing the observer to examine its properties in exquisite detail, “like a tourist in a land of infinite beauty.”[A. K. Dewdney, “Computer Recreations: A Computer Microscope Zooms in for a Look at the Most Complex Object in Mathematics,” Scientific American, 253, Aug. 1985: 16-24.]

His memoirs, The Fractalist: Memoir of a Scientific Maverick, was published in 2012.

The Collection

The Benoit Mandelbrot papers (ca. 380 linear feet and 80 gigabytes) include a wide array of materials ranging from the 1930s till his death in 2010. Mandelbrot wrote everything long hand and edited typed drafts in long hand as well. The collection contains manuscripts of his articles and books as well as other publishing states and drafts including notebooks and papers from his school days in France to various versions of his memoirs; correspondence including that with prominent mathematicians; off-prints, original papers and occasional notes by others; hundreds of original renderings and print outs of early fractals and geometric diagrams; posters and other fractal art; audio, video, and still images; artifacts, and computer media including a hard drive received from IBM.