Benoit B. [n 1] Mandelbrot [n 2] (20 November 1924 – 14
October 2010) was a Polish-born, French and American mathematician and
polymath with broad interests in the practical sciences, especially
regarding what he labeled as "the art of roughness" of physical
phenomena and "the uncontrolled element in life".[6][7][8] He referred
to himself as a "fractalist".[9] He is recognized for his contribution
to the field of fractal geometry, which included coining the word
"fractal", as well as developing a theory of "roughness and
self-similarity" in nature.[10]
In 1936, while he was a child, Mandelbrot's family emigrated to France
from Warsaw, Poland. After
Contents 1 Early years 2 Research career 2.1 Randomness in financial markets 2.2 Developing "fractal geometry" and the Mandelbrot set 2.3 Fractals and the "theory of roughness" 3 Awards and honors 4 Death and legacy 5 Bibliography 5.1 in English 5.2 In French 6 References in popular culture 7 See also 8 Notes 9 References 10 Bibliography 11 Further reading 12 External links Early years[edit]
Mandelbrot was born in
Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why?[9]:49 In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc
in Lyon, and in 1945 to 1947 attended the École Polytechnique, where
he studied under
Mandelbrot speaking about the Mandelbrot set, during his acceptance
speech for the
In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, Fractals: Form, Chance and Dimension.[22] According to mathematics scientist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics … to areas that had barely seen the light of serious mathematics before."[11] Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals": Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.[11] Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesco broccoli are two examples from nature."[11] He points out an unexpected conclusion: One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.[11] Mandelbrot used the term "fractal" as it derived from the Latin word
"fractus", defined as broken or shattered glass. Using the newly
developed
A Mandelbrot set Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke: Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.[24] According to Clarke, "the
the name Mandelbrot, and the word "mandala"—for a religious
symbol—which I'm sure is a pure coincidence, but indeed the
Mandelbrot left
Can geometry deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?[9]:xii In his paper titled How Long Is the Coast of Britain? Statistical
Self-Similarity and Fractional Dimension published in Science in 1967
Mandelbrot discusses self-similar curves that have Hausdorff dimension
that are examples of fractals, although Mandelbrot does not use this
term in the paper, as he did not coin it until 1975. The paper is one
of Mandelbrot's first publications on the topic of fractals.[27][28]
Mandelbrot emphasized the use of fractals as realistic and useful
models for describing many "rough" phenomena in the real world. He
concluded that "real roughness is often fractal and can be
measured."[9]:296 Although Mandelbrot coined the term "fractal", some
of the mathematical objects he presented in The
The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer … bringing an element of unity to the worlds of knowing and feeling … and, unwittingly, as a bonus, for the purpose of creating beauty.[9]:292 Fractals are also found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry: Clouds are not spheres, mountains are not cones, coastlines are not
circles, and bark is not smooth, nor does lightning travel in a
straight line.
—Mandelbrot, in his introduction to The
Section of a Mandelbrot set Mandelbrot has been called a work of art, and a visionary[29] and a
maverick.[30] His informal and passionate style of writing and his
emphasis on visual and geometric intuition (supported by the inclusion
of numerous illustrations) made The
2004 Best Business Book of the Year Award
AMS Einstein Lectureship
Barnard Medal
Caltech Service
Death and legacy[edit] Wikinews has related news:
Mandelbrot died from pancreatic cancer at the age of 85 in a hospice
in
Fractals: Form, Chance and Dimension, 1977
The
In French[edit] La forme d'une vie. Mémoires (1924-2010) by Benoît Mandelbrot (Author), Johan-Frédérik Hel Guedj (Translator) References in popular culture[edit] In 2004, the American singer-songwriter
See also[edit] External video Family background and early education, (4:11) Benoit Mandelbrot interview, Part 1 of 144, Web of Stories[44] "How Long is the Coast of Britain?"
Louis Bachelier
Zipf-Mandelbrot law
Seven states of randomness
Skewness risk
Kurtosis risk
Self-similarity Self-affinity Hurst exponent Fractional Brownian motion Multifractal system 1/f noise Mandelbrot Competition Notes[edit] ^ a b In his autobiography, Mandelbrot did not add a circumflex to the "i" (i.e. "î") in his first name. He included "B" as a middle initial. His New York Times obituary stated that "he added the middle initial himself, though it does not stand for a middle name",[1] an assertion that is supported by his obituary in The Guardian.[2] However, other sources conjecture that he intended his middle initial B to recursively stand for Benoit B. Mandelbrot, thereby including a fractal (his mathematical discovery) in his own name, as a mathematical joke.[3] ^ Pronounced /ˈmændəlbrɒt/ MAN-dəl-brot in English.[4] When speaking in French, Mandelbrot pronounced his name [bənwa mɑ̃dɛlbʁot].[5] References[edit] ^ a b c Hoffman, Jascha (16 October 2010). "Benoît Mandelbrot,
Mathematician, Dies at 85". The New York Times. Retrieved 16 October
2010.
^ a b Lesmoir-Gordon, Nigel (17 October 2010). "Benoît Mandelbrot
obituary". The Guardian. London. Retrieved 17 October 2010.
^ Selinker, Mike (18 October 2010). "Never Trend Away: Jonathan
Coulton on Benoit Mandelbrot". Wired.
^ "Mandelbrot".
Bibliography[edit] Hudson, Richard L.; Mandelbrot, Benoît B. (2004). The (Mis)Behavior
of Markets: A
Further reading[edit] Mandelbrot, Benoit B. (2010). The Fractalist, Memoir of a Scientific
Maverick. New York: Vintage Books, Division of Random House.
ISBN 978-0-307-38991-6
Mandelbrot, Benoît B. (1983). The
External links[edit] Wikimedia Commons has media related to Benoît Mandelbrot. Wikiquote has quotations related to: Benoit Mandelbrot
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