A Tribute to Dr. Mandelbrot

What is a fractal? Some would say a fractal is a picture created by a mathematical formula. That is true Others might choose more detail and say    “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole”.  That too is true.

Given the news of loss suffered by the scientific community at the death of Benoit Mandelbrot,  some might say a fractal is a Mandelbrot Set.  They would be correct.  While others before him  had worked with the concept of fractals, it was Mandelbrot who gave them their name, developed the formula for creating, identifying and predicting  them and made their concept accessible to the public at large.

Fellow scientists call him a maverick for his flamboyant style of writing.  I see him as a scientist with a poet’s heart  who put soul into science. More scientifically, Euclidean Geometry concentrated on  smooth surfaces, Dr. Mandelbrot developed a formula that addressed irregular surfaces.

He found fractals occurring in nature,  in clouds, snowflakes, mountain ranges, ferns, even in some vegetables like broccoli and cauliflower.  There you go, another excuse not to eat those less than favorites; just say  you consider them art and your conscience won’t allow you to eat such masterpieces.

Perhaps as great as any of his accomplishments is that he wrote scientific papers in lay language that caused even high school students to be turned on to the concept. Thanks to his presentations,  fractals are now considered  an art form as well as mathematical models.  For those of us  who lack the mathematical aptitude to convert

 Pc:zn+1=zn2+c,    (0, Pc(0), Pc(Pc(0), Pc(Pc(Pc(0))),….) . M={ ………. }

 into a work of art,  there is software designed around Mandelbrot’s formula that will create infinitesimal fractals to boggle the mind and awe the eye. Not only did Mandelbrot create pretty pictures,  he applied  his formula to many fields, including music, architecture, painting and even to the fluctuation of stock prices.

It would not be off the mark to say that the good doctor met his end at the whim of a fractal. It is not a huge stretch of the imagination to perceive cancer as a fractal.  On October 14, 2010, Dr. Benoit Mandelbrot succumbed to pancreatic cancer. He was 85 years old.

The following is an excerpt from his obituary:

For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting a position at Yale, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.

 “He knew everybody, with interests going off in every possible direction,” Professor Mumford said. “Every time he gave a talk, it was about something different.”

 Dr. Mandelbrot traced his work on fractals to a question he first 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 an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.  In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a “fractal dimension,” an insight that has proved useful well beyond the field of cartography.

A  partial list of honors accorded him:

The small asteroid 27500 Mandelbrot was named in his honor.
In November 1990, he was made a Knight in the French Legion of Honour.
In Dec.2005, Mandelbrot was appointed to position of Battelle Fellow at the Pacific Northwest National Laboratory.
Mandelbrot was promoted to Officer of the Legion of Honour in January 2006.
An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises.

Blossoming Fractals

this article was originally pusblished Nov. 18, 2010

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