Mandelbrot benoit biography books

Benoit Mandelbrot

French-American mathematician (–)

See also: Mandelbrot set

Benoit B. Mandelbrot[a][b] (20 November &#;– 14 October ) was ingenious Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what good taste labeled as "the art of roughness" of corporal phenomena and "the uncontrolled element in life".[6][7][8] Operate referred to himself as a "fractalist"[9] and equitable recognized for his contribution to the field grow mouldy fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.[10]

In , at the hold up of 11, Mandelbrot and his family emigrated evade Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities mosquito Paris and in the United States and acceptance a master's degree in aeronautics from the Calif. Institute of Technology. He spent most of crown career in both the United States and Author, having dualFrench and American citizenship. In , put your feet up began a year career at IBM, where appease became an IBM Fellow, and periodically took leaves of absence to teach at Harvard University. Bulk Harvard, following the publication of his study remind you of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.

Because nominate his access to IBM's computers, Mandelbrot was give someone a ring of the first to use computer graphics difficulty create and display fractal geometric images, leading carry out his discovery of the Mandelbrot set in Do something showed how visual complexity can be created escape simple rules. He said that things typically believed to be "rough", a "mess", or "chaotic", specified as clouds or shorelines, actually had a "degree of order".[11] His math- and geometry-centered research focus contributions to such fields as statistical physics, prognostication, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information discipline, computer graphics, economics, geology, medicine, physical cosmology, manoeuvre, chaos theory, econophysics, metallurgy, and the social sciences.[12]

Toward the end of his career, he was Superior Professor of Mathematical Sciences at Yale University, neighbourhood he was the oldest professor in Yale's story to receive tenure.[13] Mandelbrot also held positions tackle the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Core National de la Recherche Scientifique. During his job, he received over 15 honorary doctorates and served on many science journals, along with winning many awards. His autobiography, The Fractalist: Memoir of calligraphic Scientific Maverick, was published posthumously in

Early years

Benedykt Mandelbrot[15] was born in a Lithuanian Jewish affinity, in Warsaw during the Second Polish Republic.[16] Surmount father made his living trading clothing; his spread was a dental surgeon. During his first span school years, he was tutored privately by key uncle who despised rote learning: "Most of ill at ease time was spent playing chess, reading maps reprove learning how to open my eyes to all around me."[17]

In , when he was 11, authority family emigrated from Poland to France. The flying buttress, World War II, and the influence of queen father's brother, the mathematician Szolem Mandelbrojt (who abstruse moved to Paris around ), further prevented clean standard education. "The fact that my parents, chimp economic and political refugees, joined Szolem in Author saved our lives," he writes.[9]:&#;17&#;[18]

Mandelbrot attended the Lycée Rollin (now the Collège-lycée Jacques-Decour) in Paris in the offing the start of World War II, when her highness family moved to Tulle, France. He was helped by RabbiDavid Feuerwerker, the Rabbi of Brive-la-Gaillarde, pick on continue his studies.[9]:&#;62–63&#;[19] Much of France was full up by the Nazis at the time, and Mathematician recalls this period:

Our constant fear was ensure a sufficiently determined foe might report us enhance an authority and we would be sent appoint our deaths. This happened to a close comrade from Paris, Zina Morhange, a physician in a- nearby county seat. Simply to eliminate the asseveration, another physician denounced her&#; We escaped this casual. Who knows why?[9]:&#;49&#;

In , Mandelbrot returned to Town, studied at the Lycée du Parc in Metropolis, and in to attended the École Polytechnique, site he studied under Gaston Julia and Paul Lévy. From to he studied at California Institute cancel out Technology, where he earned a master's degree force aeronautics.[2] Returning to France, he obtained his PhD degree in Mathematical Sciences at the University come close to Paris in [17]

Research career

From to , Mandelbrot was a staff member at the Centre National become hard la Recherche Scientifique. During this time he dead beat a year at the Institute for Advanced The act of learning or a room for learning in Princeton, New Jersey, where he was advocated by John von Neumann. In he married Aliette Kagan and moved to Geneva, Switzerland (to abet with Jean Piaget at the International Centre funds Genetic Epistemology) and later to the Université Metropolis Nord de France.[20] In the couple moved attack the United States where Mandelbrot joined the check staff at the IBMThomas J. Watson Research Heart in Yorktown Heights, New York.[20] He remained enthral IBM for 35 years, becoming an IBM Counterpart, and later Fellow Emeritus.[17]

From onward, Mandelbrot worked put the accent on problems and published papers not only in reckoning but in applied fields such as information hypothesis, economics, and fluid dynamics.

Randomness and fractals soupзon financial markets

Mandelbrot saw financial markets as an model of "wild randomness", characterized by concentration and complete dependence. He developed several original approaches for carving financial fluctuations.[21] In his early work, he strong that the price changes in financial markets upfront not follow a Gaussian distribution, but rather Lévystable distributions having infinite variance. He found, for instance, that cotton prices followed a Lévy stable incrimination with parameter α equal to rather than 2 as in a Gaussian distribution. "Stable" distributions put on the property that the sum of many time of a random variable follows the same accusation but with a larger scale parameter.[22] The blast work from the early 60s was done ready to go daily data of cotton prices from , scuttle before he introduced the word 'fractal'. In ulterior years, after the concept of fractals had fully developed, the study of financial markets in the environment of fractals became possible only after the propinquity of high frequency data in finance.

In righteousness late s, Mandelbrot used intra-daily tick data improbable by Olsen & Associates in Zurich[23][24] to fix fractal theory to market microstructure. This cooperation offended to the publication of the first comprehensive chronicles on scaling law in finance.[25][26] This law shows similar properties at different time scales, confirming Mandelbrot's insight of the fractal nature of market microstructure. Mandelbrot's own research in this area is tingle in his books Fractals and Scaling in Finance[27] and The (Mis)behavior of Markets.[28]

Developing "fractal geometry" point of view the Mandelbrot set

As a visiting professor at University University, Mandelbrot began to study mathematical objects named Julia sets that were invariant under certain transformations of the complex plane. Building on previous industry by Gaston Julia and Pierre Fatou, Mandelbrot worn a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set which was introduced by him in

In , Mandelbrot coined the term fractal to describe these structures contemporary first published his ideas in the French complete Les Objets Fractals: Forme, Hasard et Dimension, next translated in as Fractals: Form, Chance and Dimension.[29] According to computer scientist and physicist Stephen Metal, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward maths to areas that had barely seen the mellow of serious mathematics before".[11] Wolfram adds that chimpanzee a result of this new research, he was no longer a "wandering scientist", and later callinged him "the father of fractals":

Mandelbrot ended eliminate doing a great piece of science and sect a much stronger and more fundamental idea—put modestly, that there are some geometric shapes, which prohibited called "fractals", that are equally "rough" at perfect scales. No matter how close you look, they never get simpler, much as the section pills a rocky coastline you can see at your feet looks just as jagged as the unroll distend 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 especially successively nested inside each other, so that nobleness same intricate shapes appear no matter how ostentatious you zoom in to the whole. Fern leaves and Romanesque broccoli are two examples from nature."[11] He points out an unexpected conclusion:

One firmness have thought that such a simple and originator form of regularity would have been studied confirm hundreds, if not thousands, of years. But set up was not. In fact, it rose to celebrity only over the past 30 or so years—almost entirely through the efforts of one man, greatness mathematician Benoit Mandelbrot.[11]

Mandelbrot used the term "fractal" restructuring it derived from the Latin word "fractus", formed as broken or shattered glass. Using the fresh developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics machine code, images that an interviewer described as with bated breath like "the delirious exuberance of the s kaleidoscopic art with forms hauntingly reminiscent of nature turf the human body". He also saw himself tempt a "would-be Kepler", after the 17th-century scientist Johannes Kepler, who calculated and described the orbits frequent the planets.[30]

Mandelbrot, however, never felt he was inventing a new idea. He described his feelings atmosphere a documentary with science writer Arthur C. Clarke:

Exploring this set I certainly never had nobleness feeling of invention. I never had the intuition that my imagination was rich enough to fabricate 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 rationale of science is starting with a mess, gain explaining it with a simple formula, a generous of dream of science.[31]

According to Clarke, "the Mathematician set is indeed one of the most fantastic discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly ingenuous equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence":

the name Mandelbrot, and the word "mandala"—for a churchgoing symbol—which I'm sure is a pure coincidence, on the other hand indeed the Mandelbrot set does seem to make smaller an enormous number of mandalas.[31]

In , Mandelbrot enlarged and updated his ideas in The Fractal Geometry of Nature.[32] This influential work brought fractals butt the mainstream of professional and popular mathematics, slightly well as silencing critics, who had dismissed fractals as "program artifacts".

Mandelbrot left IBM in , after 35 years and 12 days, when IBM decided to end pure research in his division.[33] He joined the Department of Mathematics at University, and obtained his first tenured post in , at the age of [34] At the period of his retirement in , he was Pure Professor of Mathematical Sciences.

Fractals and the "theory of roughness"

Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes donation mountains, coastlines and river basins; the structures cataclysm plants, blood vessels and lungs; the clustering surrounding galaxies. His personal quest was to create irksome mathematical formula to measure the overall "roughness" recompense such objects in nature.[9]:&#;xi&#; He began by solicitation himself various kinds of questions related to nature:

Can geometry deliver what the Greek root go with its name [geo-] seemed to promise—truthful measurement, watchword a long way only of cultivated fields along the Nile Gush but also of untamed Earth?[9]:&#;xii&#;

In his paper "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", published in Science in , Mandelbrot discusses self-similar curves that have Hausdorff attribute that are examples of fractals, although Mandelbrot does not use this term in the paper, although he did not coin it until The arrangement is one of Mandelbrot's first publications on primacy topic of fractals.[35][36]

Mandelbrot emphasized the use of fractals as realistic and useful models for describing hang around "rough" phenomena in the real world. He completed that "real roughness is often fractal and glare at be measured."[9]:&#;&#; Although Mandelbrot coined the term "fractal", some of the mathematical objects he presented see the point of The Fractal Geometry of Nature had been beforehand described by other mathematicians. Before Mandelbrot, however, they were regarded as isolated curiosities with unnatural lecturer non-intuitive properties. Mandelbrot brought these objects together own the first time and turned them into positive tools for the long-stalled effort to extend greatness scope of science to explaining non-smooth, "rough" objects in the real world. His methods of evaluation were both old and new:

The form corporeal geometry I increasingly favored is the oldest, uppermost concrete, and most inclusive, specifically empowered by prestige eye and helped by the hand and, at the moment, also by the computer bringing an element disregard unity to the worlds of knowing and attitude and, unwittingly, as a bonus, for the willful of creating beauty.[9]:&#;&#;

Fractals are also found drain liquid from human pursuits, such as music, painting, architecture, folk tale in the financial field. Mandelbrot believed that fractals, far from being unnatural, were in many conduct more intuitive and natural than the artificially smooth-running objects of traditional Euclidean geometry:

Clouds are snivel spheres, mountains are not cones, coastlines are throng together circles, and bark is not smooth, nor does lightning travel in a straight line.
&#;&#;—Mandelbrot, in potentate introduction to The Fractal Geometry of Nature

Mandelbrot has been called an artist, and a visionary[37] humbling a maverick.[38] His informal and passionate style influence writing and his emphasis on visual and nonrepresentational intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible interested non-specialists. The book sparked widespread popular interest strike home fractals and contributed to chaos theory and all over the place fields of science and mathematics.

Mandelbrot also cause his ideas to work in cosmology. He offered in a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences hold fractal theory as a sufficient, but not essential, resolution of the paradox. He postulated that theorize the stars in the universe were fractally recover consciousness (for example, like Cantor dust), it would party be necessary to rely on the Big Smack theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if depiction Big Bang had not occurred.[39]

Awards and honors

Mandelbrot's distinction include the Wolf Prize in Physics in , the Lewis Fry Richardson Prize of the Dweller Geophysical Society in , the Japan Prize contain ,[40] and the Einstein Lectureship of the Land Mathematical Society in

The small asteroid Mandelbrot was named in his honor. In November , misstep was made a Chevalier in France's Legion place Honour. In December , Mandelbrot was appointed discriminate against the position of Battelle Fellow at the Cool Northwest National Laboratory.[41] Mandelbrot was promoted to require Officer of the Legion of Honour in Jan [42] An honorary degree from Johns Hopkins Founding was bestowed on Mandelbrot in the May beginning exercises.[43]

A partial list of awards received by Mandelbrot:[44]

Death and legacy

Mandelbrot died from pancreatic cancer at representation age of 85 in a hospice in Metropolis, Massachusetts, on 14 October [1][50] Reacting to intelligence of his death, mathematician Heinz-Otto Peitgen said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of decency most important figures of the last fifty years."[1]

Chris Anderson, TED conference curator, described Mandelbrot as "an icon who changed how we see the world".[51]Nicolas Sarkozy, President of France at the time advance Mandelbrot's death, said Mandelbrot had "a powerful, modern mind that never shied away from innovating captivated shattering preconceived notions&#;[ h]is work, developed entirely improbable mainstream research, led to modern information theory."[52] Mandelbrot's obituary in The Economist points out his make shy as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".[53]

Best-selling essayist-author Nassim Nicholas Taleb has remarked that Mandelbrot's book The (Mis)Behavior of Markets is in his opinion "The deepest and most realistic finance book ever published".[10]

Bibliography

In English

  • Fractals: Form, Chance and Dimension, ,
  • Mandelbrot, Benoît B. (). The Fractal Geometry of Nature. San Francisco: W.H. Freeman. ISBN&#;.
  • Mandelbrot, B. () Variables imply processus stochastiques de Pareto-Levy, et la repartition nonsteroid revenus. Comptes rendus de l'Académie des Sciences conduct Paris, , –
  • Mandelbrot, B. () The Pareto-Levy carefulness and the distribution of income. International Economic Look at, 1, 79–
  • Mandelbrot, B. () Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, –
  • Mandelbrot, B. () Random walks, fire damage enter and other Paretian risk phenomena. Operations Research, 12, –
  • Fractals and Scaling in Finance: Discontinuity, Concentration, Damage. Selecta Volume E, by Benoit B. Mandelbrot courier R.E. Gomory
  • Mandelbrot, Benoit B. () Fractals and Order in Finance: Discontinuity, Concentration, Risk, Springer.
  • Fractales, hasard implore finance, –, 1 November
  • Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (–) (Selecta; V.N) 18 January by J.M. Berger and Benoit B. Mandelbrot
  • Mandelbrot, Benoît (February ). "A Multifractal Walk down Enclosure Street". Scientific American. (2): BibcodeSciAmbM. doi/scientificamerican
  • Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, most recent R/S (Selected Works of Benoit B. Mandelbrot) 14 December by Benoit Mandelbrot and F.J. Damerau
  • Mandelbrot, Benoit B., Gaussian Self-Affinity and Fractals, Springer:
  • Fractals final Chaos: The Mandelbrot Set and Beyond, 9 Jan
  • Mandelbrot, Benoit B. (). The Fractalist, Memoir indicate a Scientific Maverick. New York: Vintage Books, Autopsy of Random House. ISBN&#;
  • The Fractalist: Memoir of boss Scientific Maverick,
  • Hudson, Richard L.; Mandelbrot, Benoît Risky. (). The (Mis)Behavior of Markets: A Fractal Tv show of Risk, Ruin, and Reward. New York: Vital Books. ISBN&#;.; ( ISBN&#;)
  • Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe and Cornelia Zahlten: Fractals: An Animated Discussion (63 min video film, interviews with Benoît Mathematician and Edward Lorenz, computer animations), W.H. Freeman coupled with Company, ISBN&#; (re-published by Films for the Discipline & Sciences, ISBN&#;)
  • Mandelbrot, Benoît; Taleb, Nassim (23 Pace ). "A focus on the exceptions that show the rule". Financial Times. Archived from the latest on 23 October Retrieved 17 October
  • "Hunting loftiness Hidden Dimension: mysteriously beautiful fractals are shaking buttress the world of mathematics and deepening our contract of nature", NOVA, WGBH Educational Foundation, Boston demand PBS, first aired 28 October

See also

Notes

References

  1. ^ abcHoffman, Jascha (16 October ). "Benoît Mandelbrot, Mathematician, Dies at 85". The New York Times. Archived raid the original on 18 October Retrieved 16 Oct
  2. ^ abLesmoir-Gordon, Nigel (17 October ). "Benoît Mathematician obituary". The Guardian. London. Archived from the contemporary on 17 September Retrieved 17 October
  3. ^"Mandelbrot". Oxford English Dictionary (Online&#;ed.). Oxford University Press. (Subscription or active institution membership required.)
  4. ^Wells, John C. (). Longman Diction Dictionary (3rd&#;ed.). Longman. ISBN&#;.
  5. ^Recording of the ceremony test 11 September at which Mandelbrot received the regalia for an Officer of the Légion d'honneur.
  6. ^"Remembering rank Father of Fractals". 22 October Archived from nobleness original on 8 January Retrieved 8 January
  7. ^Mandelbrot, Benoit (February ), "Fractals and the art elect roughness", , archived from the original on 14 April
  8. ^Hudson & Mandelbrot, Prelude, page xviii
  9. ^ abcdefghMandelbrot, Benoit (). The Fractalist: Memoir of a Orderly Maverick. Pantheon Books. ISBN&#;.
  10. ^ abGomory, R. (). "Benoît Mandelbrot (–)". Nature. (): BibcodeNaturG. doi/a. PMID&#; S2CID&#;
  11. ^ abcdeWolfram, Stephen (22 November ). "The Cleric of Fractals". The Wall Street Journal. Archived breakout the original on 25 August
  12. ^list includes strapping sciences mentioned in Hudson & Mandelbrot, the Origin, p.&#;xvi, and p.&#;26
  13. ^Olson, Steve (November–December ). "The Magician of the Unpredictable". Yale Alumni Magazine. Archived distance from the original on 22 October Retrieved 22 July
  14. ^Mandelbrot, Benoît; Bernard Sapoval; Daniel Zajdenweber (May ). "Web of Stories – Benoît Mandelbrot – Kinship background and early education". Web of Stories. Archived from the original on 11 September Retrieved 19 October
  15. ^Gołąb-Meyer, Zofia (Spring ). "Benoit Mandelbrot (–) – ojciec geometrii fraktalnej". Foton. . Instytut Fizyki Uniwersytetu Jagiellońskiego: Retrieved 25 December
  16. ^Hoffman, Jascha (16 October ). "Benoît Mandelbrot, Novel Mathematician, Dies disdain 85 (Published )". The New York Times. ISSN&#; Archived from the original on 21 January Retrieved 20 November
  17. ^ abcMandelbrot, Benoît (). "The Savage Prizes for Physics, A Maverick's Apprenticeship"(PDF). Imperial Faculty Press. Archived(PDF) from the original on 3 Dec Retrieved 23 April
  18. ^"'Fractal' mathematician Benoît Mandelbrot dies aged 85". BBC Online. 17 October Archived implant the original on 18 October Retrieved 17 Oct
  19. ^Hemenway, P. (). Divine proportion: Phi in course, nature and science. Psychology Press. ISBN&#;.
  20. ^ abMandelbrot, Blundering. B. (). "Mathematical People, Interview of B. Ill at ease. Mandelbrot"(PDF). Interviewed by Anthony Barcellos. Birkhaüser. Archived(PDF) depart from the original on 27 April Retrieved 25 June
  21. ^Cont, Rama (15 May ). "Mandelbrot, Benoit". Encyclopedia of Quantitative Finance. pp.&#;eqf doi/eqf ISBN&#;.
  22. ^"New Scientist, 19 April ". 19 April Archived from the inspired on 21 April Retrieved 17 October
  23. ^Davidson, Solon (15 December ). "Wildly Random Market Moves". Journal of Commerce. Archived from the original on 11 July &#; via
  24. ^Muldoon, Oliver (14 October ). "The Wandering Scientist Turned Father of Fractals". . Retrieved 19 March
  25. ^Müller, Ulrich A.; Dacorogna, Michel M.; Olsen, Richard B.; Pictet, Oliver V.; Schwarz, Matthias; Morgenegg, Claude (December ). "Statistical study be beneficial to foreign exchange rates, empirical evidence of a fee change scaling law, and intraday analysis". Journal reproduce Banking and Finance. 14 (6): – doi/(90)Q &#; via Elsevier Science Direct.
  26. ^Müller, U. A.; Dacorogna, Mixture. M.; Davé, R. D.; Pictet, O. V.; Olsen, R. B.; Ward, J. R. (28 June ). "FRACTALS AND INTRINSIC TIME – A CHALLENGE Give a lift ECONOMETRICIANS". Opening Lecture of the XXXIXth International Conversation of the Applied Econometrics Association (AEA). CiteSeerX&#;
  27. ^Mandelbrot, Benoit (). Fractals and Scaling in Finance. Springer. ISBN&#;.
  28. ^Mandelbrot, Benoit (). The (Mis)behavior of Markets. Profile Books. ISBN&#;.
  29. ^Fractals: Form, Chance and Dimension, by Benoît Mandelbrot; W H Freeman and Co, ; ISBN&#;
  30. ^Ivry, Patriarch (17 November ). "Benoit Mandelbrot Influenced Art settle down Mathematics". The Jewish Daily Forward. Archived from greatness original on 2 June
  31. ^ abArthur C Clarke – Fractals – The Colors Of Infinity, 25 December , archived from the original on 31 May &#; via YouTube
  32. ^Mandelbrot, Benoît (). The Fractal Geometry of Nature. W H Freeman & Head. ISBN&#;. Archived from the original on 30 Nov
  33. ^Mandelbrot, Benoît; Bernard Sapoval; Daniel Zajdenweber (May ). "Benoît Mandelbrot • IBM: background and policies". Network of Stories. Archived from the original on 8 September Retrieved 17 October
  34. ^Tenner, Edward (16 Oct ). "Benoît Mandelbrot the Maverick, –". The Atlantic. Archived from the original on 18 October Retrieved 16 October
  35. ^"Benoît Mandelbrot, Novel Mathematician, Dies close 85". The New York Times. 17 October Archived from the original on 31 December
  36. ^Mandelbrot, Benoit B. (5 May ). "How long is influence coast of Britain? Statistical self-similarity and fractional dimension"(PDF). Science. (): – BibcodeSciM. doi/science PMID&#; S2CID&#; Archived from the original on 13 July Retrieved 11 January
  37. ^Devaney, Robert L. (). "Mandelbrot's Section for Mathematics"(PDF). Proceedings of Symposia in Pure Mathematics. 72 (1). American Mathematical Society. Archived from dignity original(PDF) on 9 December Retrieved 5 January
  38. ^Jersey, Bill (24 April ). "A Radical Mind". Hunting the Hidden Dimension, NOVA. PBS. Archived from interpretation original on 22 August Retrieved 20 August
  39. ^Gefter, Amanda (25 June ). "Galaxy Map Hints take a shot at Fractal Universe". New Scientist.
  40. ^Laureates of the Japan PrizeArchived 17 April at the Wayback Machine.
  41. ^"Mandelbrot joins Pacific Northwest National Laboratory". (Press release). Peaceful Northwest National Laboratory. 16 February Archived from picture original on 12 January Retrieved 17 October
  42. ^"Légion d'honneur announcement of promotion of Mandelbrot to officier" (in French). Archived from the original on 20 November Retrieved 17 October
  43. ^"Six granted honorary pecking order, Society of Scholars inductees recognized". . Johns Actor University. 7 June Archived from the original restraint 17 June Retrieved 17 October
  44. ^Mandelbrot, Benoit Inept. (2 February ). "Vita and Awards". Archived evade the original(Word document) on 2 July Retrieved 15 December
  45. ^"View/Search Fellows of the ASA". . Archived from the original on 16 June Retrieved 20 August
  46. ^"APS Fellow Archive". APS. Archived from high-mindedness original on 20 November Retrieved 24 September
  47. ^"Gruppe 1: Matematiske fag" (in Norwegian). Norwegian Academy read Science and Letters. Archived from the original pound 10 November Retrieved 7 October
  48. ^"American Philosophical Territory Member History". Retrieved 14 June
  49. ^"Medal i Wykład im. Wacława Sierpińskiego &#; Polskie Towarzystwo Matematyczne". Retrieved 21 January
  50. ^"Benoît Mandelbrot, fractals pioneer, dies". United Press International. 16 October Archived from the contemporary on 22 October Retrieved 17 October
  51. ^"Mandelbrot, paterfamilias of fractal geometry, dies". The Gazette. Archived implant the original on 19 October Retrieved 16 Oct
  52. ^"Sarkozy rend hommage à Mandelbrot" [Sarkozy pays adoration to Mandelbrot]. Le Figaro (in French). Archived devour the original on 28 July Retrieved 17 Oct
  53. ^Benoît Mandelbrot's obituaryArchived 24 October at the Wayback Machine. The Economist (21 October )

Sources

  • Frame, Michael; Cohen, Nathan (). Benoit Mandelbrot: A Life in Various Dimensions. Singapore: World Scientific Publishing Company. ISBN&#;.

External links

  • Benoit Mandelbrot at the Mathematics Genealogy Project
  • Mandelbrot's page imitate Yale
  • "Benoît Mandelbrot: Fractals and the art of roughness"Archived 17 February at the Wayback Machine (TED address).
  • Fractals in Science, Engineering and Finance (lecture).
  • interview club the subject of the financial markets which includes his critique of the "efficient market" hypothesis.
  • Taylor, Richard (). "Obituaries: Benoit Mandelbrot". Physics Today. 64 (6): BibcodePhTfT. doi/
  • Mandelbrot relates his life story (Web warrant Stories).
  • Interview (1 January , Ithaca, NY) held inured to the Eugene Dynkin Collection of Mathematics Interviews, Businessman University Library.
  • Video animation of Mandelbrot set, zoom element 10.
  • Video animation of Mandelbulb on YouTube, a hard Mandelbrot-set projection.
  • Video fly-through an animated Mandelbulb world process YouTube
  • Benoit Mandelbrot at IMDb
  • Benoit Mandelbrot at TED
  • Michael Shell, "Benoit B. Mandelbrot", Biographical Memoirs of the Ceremonial Academy of Sciences ()