756:. The latter work from the early 60s was done with daily data of cotton prices from 1900, long before he introduced the word 'fractal'. In later years, after the concept of fractals had matured, the study of financial markets in the context of fractals became possible only after the availability of high frequency data in finance. In the late 1980s, Mandelbrot used intra-daily tick data supplied by Olsen & Associates in Zurich to apply fractal theory to market microstructure. This cooperation led to the publication of the first comprehensive papers on scaling law in finance. 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 presented in his books
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837:, 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". 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":
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Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental ideaâput 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
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in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess", or "chaotic", such as clouds or shorelines, actually had a "degree of order". His math- and geometry-centered research included contributions to such fields as
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had been previously described by other mathematicians. Before
Mandelbrot, however, they were regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to
999:
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." Although
Mandelbrot coined the term "fractal", some of the mathematical objects he presented in
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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
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Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics computer code, images that an interviewer described as looking
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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 yearsâalmost entirely through the efforts of one man, the mathematician Benoit
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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
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at the time of
Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions is work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot's obituary in
846:
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.
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as an example of "wild randomness", characterized by concentration and long-range dependence. He developed several original approaches for modelling financial fluctuations. In his early work, he found that the price changes in
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Mandelbrot has been called an artist, and a visionary and a maverick. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made
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equal to 1.7 rather than 2 as in a
Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger
962:. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature. He began by asking himself various kinds of questions related to nature:
580:: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me." In 1936, when he was 11, the family emigrated from Poland to France. The move,
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588:(who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.
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is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally
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Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the
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Mandelbrot, B. (1959) Variables et processus stochastiques de Pareto-Levy, et la repartition des revenus. Comptes rendus de l'Académie des
Sciences de Paris, 249, 613â615.
996:, 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.
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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,
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MĂŒller, U. A.; Dacorogna, M. M.; DavĂ©, R. D.; Pictet, O. V.; Olsen, R. B.; Ward, J. R. (28 June 1995). "FRACTALS AND INTRINSIC TIME â A CHALLENGE TO ECONOMETRICIANS".
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prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional
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accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.
576:. His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised
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2016:
919:. This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "
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357:" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of
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deliver what the Greek root of its name seemed to promiseâtruthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?
646:. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics. Returning to France, he obtained his
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Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division. He joined the
Department of Mathematics at
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obituary stated that "he added the middle initial himself, though it does not stand for a middle name", an assertion that is supported by his obituary in
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622:, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why?
518:. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography,
407:. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.
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said: "f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years."
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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.
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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.
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1560:"Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature"
909:"âfor a religious symbolâwhich I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas.
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theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.
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Mandelbrot, however, never felt he was inventing a new idea. He described his feelings in a documentary with science writer Arthur C. Clarke:
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with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist
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ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in
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extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new:
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Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of
Britain?"
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MĂŒller, Ulrich A.; Dacorogna, Michel M.; Olsen, Richard B.; Pictet, Oliver V.; Schwarz, Matthias; Morgenegg, Claude (December 1990).
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796:, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the
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1513:(63 min video film, interviews with BenoĂźt Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990.
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Mandelbrot, B. (1961) Stable
Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517â543.
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Mandelbrot, B. (1964) Random walks, fire damage amount and other
Paretian risk phenomena. Operations Research, 12, 582â585.
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post in 1999, at the age of 75. At the time of his retirement in 2005, he was
Sterling Professor of Mathematical Sciences.
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From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as
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2591:"Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis"
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Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot)
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614:, to continue his studies. Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period:
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Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79â106.
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Recording of the ceremony on 11 September 2006 at which Mandelbrot received the insignia for an Officer of the
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502:, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the
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Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains,
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on the subject of the financial markets which includes his critique of the "efficient market" hypothesis.
1600: â Counterintuitive observation that the coastline of a landmass does not have a well-defined length
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points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".
1116:. Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006. An honorary degree from
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of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.
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Michael Frame, "Benoit B. Mandelbrot", Biographical Memoirs of the National Academy of Sciences (2014)
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Opening Lecture of the XXXIXth International Conference of the Applied Econometrics Association (AEA)
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with broad interests in the practical sciences, especially regarding what he labeled as "the art of
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690:. In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the
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748:. He found, for example, that cotton prices followed a LĂ©vy stable distribution with parameter
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Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of
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2884:"How long is the coast of Britain? Statistical self-similarity and fractional dimension"
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1112:. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the
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Fractals are also found in human pursuits, such as music, painting, architecture, and
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How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
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Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E
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3293:"Medal i WykĆad im. WacĆawa SierpiĆskiego | Polskie Towarzystwo Matematyczne"
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is in his opinion "The deepest and most realistic finance book ever published".
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was named in his honor. In November 1990, he was made a Chevalier in France's
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to describe these structures and first published his ideas in the French book
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curator, described Mandelbrot as "an icon who changed how we see the world".
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2236:"Web of Stories â BenoĂźt Mandelbrot â Family background and early education"
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Mandelbrot, BenoĂźt (February 1999). "A Multifractal Walk down Wall Street".
701:. He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow
345:(20 November 1924 â 14 October 2010) was a Polish-born French-American
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1568:, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.
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384:. He spent most of his career in both the United States and France, having
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3068:(Press release). Pacific Northwest National Laboratory. 16 February 2006.
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3126:"Six granted honorary degrees, Society of Scholars inductees recognized"
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Gefter, Amanda (25 June 2008). "Galaxy Map Hints at Fractal Universe".
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are two examples from nature." He points out an unexpected conclusion:
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at the International Centre for Genetic Epistemology) and later to the
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The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward
1390:(Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot
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Multifractals and 1/Æ Noise: Wild Self-Affinity in Physics (1963â1976)
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2298:"BenoĂźt Mandelbrot, Novel Mathematician, Dies at 85 (Published 2010)"
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Mandelbrot, BenoĂźt; Bernard Sapoval; Daniel Zajdenweber (May 1998).
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Mandelbrot, BenoĂźt; Bernard Sapoval; Daniel Zajdenweber (May 1998).
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in English. When speaking in French, Mandelbrot pronounced his name
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In 1936, at the age of 11, Mandelbrot and his family emigrated from
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Fractals and Scaling in Finance: Discontinuity, Concentration, Risk
1269:, on 14 October 2010. Reacting to news of his death, mathematician
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was bestowed on Mandelbrot in the May 2010 commencement exercises.
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702:
464:
350:
1444:
The Misbehavior of Markets: A Fractal View of Financial Turbulence
1238:
WacĆaw SierpiĆski medal of the Polish Mathematical Society (2005)
5763:
5566:
4828:
4780:
1262:
906:
821:
460:
432:
153:
5834:
5401:
4716:
1609: â A measure of the long-range dependence of a time series
959:
931:
719:
584:, and the influence of his father's brother, the mathematician
569:
369:
66:
1787:
1738:
1065:
in the universe were fractally distributed (for example, like
2267:"Benoit Mandelbrot (1924â2010) â ojciec geometrii fraktalnej"
604:
600:
1632: â French pioneer in mathematical economics (1870-1946)
5535:
1796:
1062:
955:
927:
848:
631:
3645:
2588:
1747:
1521:(re-published by Films for the Humanities & Sciences,
873:, who calculated and described the orbits of the planets.
6287:
Members of the United States National Academy of Sciences
2619:
1778:
1729:
1692:
to the "i" (i.e. "Ăź") in his first name, as is usual for
691:
396:
276:
3062:"Mandelbrot joins Pacific Northwest National Laboratory"
2378:"'Fractal' mathematician BenoĂźt Mandelbrot dies aged 85"
776:, Mandelbrot began to study mathematical objects called
662:
From 1949 to 1958, Mandelbrot was a staff member at the
6282:
Members of the Norwegian Academy of Science and Letters
2875:
1684:
1682:
1602:
Pages displaying short descriptions of redirect targets
1061:, resolution of the paradox. He postulated that if the
3473:"BenoĂźt Mandelbrot: Fractals and the art of roughness"
1427:
14 December 2001 by Benoit Mandelbrot and F.J. Damerau
913:
In 1982, Mandelbrot expanded and updated his ideas in
626:
In 1944, Mandelbrot returned to Paris, studied at the
403:, and periodically took leaves of absence to teach at
1808:
1781:
1759:
1732:
901:
complexity?" Clarke also notes an "odd coincidence":
555:, (4:11) Benoit Mandelbrot interview, Part 1 of 144,
2858:"BenoĂźt Mandelbrot, Novel Mathematician, Dies at 85"
1911:
1799:
1793:
1790:
1784:
1750:
1744:
1741:
1735:
1679:
768:
Developing "fractal geometry" and the Mandelbrot set
2744:
Arthur C Clarke â Fractals â The Colors Of Infinity
2565:"The Wandering Scientist Turned Father of Fractals"
1775:
1772:
1726:
1723:
1533:Mandelbrot, BenoĂźt; Taleb, Nassim (23 March 2006).
1209:
Medaglia della Presidenza della Repubblica Italiana
395:citizenship. In 1958, he began a 35-year career at
3437:. Singapore: World Scientific Publishing Company.
2970:(1). American Mathematical Society. Archived from
2795:"BenoĂźt Mandelbrot âą IBM: background and policies"
2716:"Benoit Mandelbrot Influenced Art and Mathematics"
2697:, by BenoĂźt Mandelbrot; W H Freeman and Co, 1977;
2277:. Instytut Fizyki Uniwersytetu JagielloĆskiego: 50
1912:
1477:
1476:Hudson, Richard L.; Mandelbrot, BenoĂźt B. (2004).
2411:Divine proportion: Phi in art, nature and science
1446:, 2006 by Benoit Mandelbrot and Richard L. Hudson
1438:Fractals and Chaos: The Mandelbrot Set and Beyond
1123:A partial list of awards received by Mandelbrot:
6158:
3573:, a three-dimensional Mandelbrot-set projection.
2474:Cont, Rama (15 May 2010). "Mandelbrot, Benoit".
2448:. Interviewed by Anthony Barcellos. BirkhaĂŒser.
1452:The Fractalist, Memoir of a Scientific Maverick.
1030: âMandelbrot, in his introduction to
833:. According to computer scientist and physicist
678:. In 1955 he married Aliette Kagan and moved to
520:The Fractalist: Memoir of a Scientific Maverick
6237:Fellows of the American Statistical Association
3272:"American Philosophical Society Member History"
2067:The Fractalist: Memoir of a Scientific Maverick
1874:
1872:
1688:In his autobiography, Mandelbrot did not add a
1656: â Extensions of the concept of randomness
1644: â System with multiple fractal dimensions
1535:"A focus on the exceptions that prove the rule"
1532:
1470:The Fractalist: Memoir of a Scientific Maverick
827:Les Objets Fractals: Forme, Hasard et Dimension
6272:Institute for Advanced Study visiting scholars
6217:Deaths from pancreatic cancer in Massachusetts
3578:Video fly-through an animated Mandelbulb world
3344:"Mandelbrot, father of fractal geometry, dies"
1878:
1847:"BenoĂźt Mandelbrot, Mathematician, Dies at 85"
1371:, 1997 by Benoit B. Mandelbrot and R.E. Gomory
1159:Fellow of the American Statistical Association
591:Mandelbrot attended the Lycée Rollin (now the
6342:Members of the American Philosophical Society
5551:
4732:
4124:
3631:
3378:[Sarkozy pays homage to Mandelbrot].
2186:list includes specific sciences mentioned in
1621: â Term in geometry and fractal analysis
1097:in 2003, and the Einstein Lectureship of the
3486:Fractals in Science, Engineering and Finance
3435:Benoit Mandelbrot: A Life in Many Dimensions
1869:
1069:), it would not be necessary to rely on the
865:like "the delirious exuberance of the 1960s
720:Randomness and fractals in financial markets
664:Centre National de la Recherche Scientifique
516:Centre National de la Recherche Scientifique
3314:"BenoĂźt Mandelbrot, fractals pioneer, dies"
3096:announcement of promotion of Mandelbrot to
2964:Proceedings of Symposia in Pure Mathematics
2826:"BenoĂźt Mandelbrot the Maverick, 1924â2010"
2264:
2060:
2058:
2056:
2054:
2052:
2050:
2048:
2046:
1638: â High school mathematics competition
1582: â Signal with equal energy per octave
5558:
5544:
4739:
4725:
4138:
4131:
4117:
3638:
3624:
3603:
3432:
3154:
2881:
2761:
2669:
2644:
2436:
2339:
2190:, the Prelude, p. xvi, and p. 26
2157:
2155:
2153:
2151:
2149:
2064:
2014:
1840:
1838:
1836:
1393:
1335:
666:. During this time he spent a year at the
37:
6227:Fellows of the American Geophysical Union
6207:California Institute of Technology alumni
3525:
3155:Mandelbrot, Benoit B. (2 February 2006).
3132:. Johns Hopkins University. 7 June 2010.
2737:
2735:
2629:
2432:
2430:
2121:
2088:
2086:
1879:Lesmoir-Gordon, Nigel (17 October 2010).
1668: â Discrete probability distribution
1128:2004 Best Business Book of the Year Award
16:French-American mathematician (1924â2010)
6232:Fellows of the American Physical Society
3246:Norwegian Academy of Science and Letters
2539:
2408:
2370:
2043:
1220:Norwegian Academy of Science and Letters
1212:MĂ©daille de Vermeil de la Ville de Paris
1036:
875:
802:
6112:List of fractals by Hausdorff dimension
2951:
2562:
2335:
2333:
2331:
2295:
2161:
2146:
1844:
1833:
1164:Fellow of the American Physical Society
811:, during his acceptance speech for the
6159:
3551:Collection of Mathematics Interviews,
3545:Interview (1 January 1981, Ithaca, NY)
3497:
3433:Frame, Michael; Cohen, Nathan (2015).
3026:
2995:
2823:
2817:
2732:
2427:
2246:from the original on 11 September 2011
2092:
2083:
1893:from the original on 17 September 2013
938:Fractals and the "theory of roughness"
522:, was published posthumously in 2012.
6247:French emigrants to the United States
5539:
4720:
4112:
3619:
3252:from the original on 10 November 2013
3222:from the original on 20 November 2020
3106:from the original on 20 November 2020
2957:"Mandelbrot's Vision for Mathematics"
2805:from the original on 8 September 2011
2786:
2199:
2162:Wolfram, Stephen (22 November 2012).
1945:
1816:
1114:Pacific Northwest National Laboratory
800:which was introduced by him in 1979.
784:under certain transformations of the
553:Family background and early education
504:Pacific Northwest National Laboratory
494:Toward the end of his career, he was
284:Pacific Northwest National Laboratory
6197:21st-century American mathematicians
6182:20th-century American mathematicians
3324:from the original on 22 October 2012
3148:
3072:from the original on 12 January 2009
2882:Mandelbrot, Benoit B. (5 May 1967).
2838:from the original on 18 October 2010
2713:
2695:Fractals: Form, Chance and Dimension
2609:– via Elsevier Science Direct.
2552:on 11 July 2021 – via JOC.com.
2540:Davidson, Clive (15 December 1997).
2476:Encyclopedia of Quantitative Finance
2473:
2390:from the original on 18 October 2010
2358:from the original on 3 December 2013
2328:
2316:from the original on 21 January 2017
2227:
2215:from the original on 22 October 2014
2015:Mandelbrot, Benoit (February 2010),
1990:"Remembering the Father of Fractals"
1933:participating institution membership
1857:from the original on 18 October 2010
1322:Fractals: Form, Chance and Dimension
1303:has remarked that Mandelbrot's book
1076:
831:Fractals: Form, Chance and Dimension
819:In 1975, Mandelbrot coined the term
6317:Polish people of Lithuanian descent
4879:Measure-preserving dynamical system
4761:
3376:"Sarkozy rend hommage Ă Mandelbrot"
3008:from the original on 22 August 2009
2945:
2714:Ivry, Benjamin (17 November 2012).
2563:Muldoon, Oliver (14 October 2019).
2514:. Newscientist.com. 19 April 1997.
2296:Hoffman, Jascha (16 October 2010).
2017:"Fractals and the art of roughness"
1996:from the original on 8 January 2018
1845:Hoffman, Jascha (16 October 2010).
1432:Gaussian Self-Affinity and Fractals
1252:
905:the name Mandelbrot, and the word "
634:, and in 1945 to 1947 attended the
13:
6302:20th-century Polish mathematicians
6242:Fellows of the Econometric Society
6202:21st-century French mathematicians
6187:20th-century French mathematicians
3035:
3002:Hunting the Hidden Dimension, NOVA
2824:Tenner, Edward (16 October 2010).
2751:on 31 May 2017 – via YouTube
2747:, 25 December 2010, archived from
2518:from the original on 21 April 2010
2455:from the original on 27 April 2015
2265:GoĆÄ
b-Meyer, Zofia (Spring 2011).
1594: â Probability theory concept
1155:Fellow, American Geophysical Union
657:
564:Benedykt Mandelbrot was born in a
382:California Institute of Technology
126:California Institute of Technology
14:
6358:
6094:How Long Is the Coast of Britain?
5447:Oleksandr Mykolayovych Sharkovsky
3559:Video animation of Mandelbrot set
3535:Mandelbrot relates his life story
3452:
3388:from the original on 28 July 2013
3136:from the original on 17 June 2010
3102:(in French). Legifrance.gouv.fr.
2933:from the original on 13 July 2015
2864:. 17 October 2010. Archived from
2205:"The Genius of the Unpredictable"
1598:How Long is the Coast of Britain?
1418:10.1038/scientificamerican0299-70
6292:Officers of the Legion of Honour
6262:IBM Research computer scientists
6192:21st-century American economists
6177:20th-century American economists
4977:
4969:
4746:
3186:"View/Search Fellows of the ASA"
1951:Longman Pronunciation Dictionary
1768:
1719:
1511:Fractals: An Animated Discussion
1081:Mandelbrot's awards include the
695:Thomas J. Watson Research Center
650:in Mathematical Sciences at the
547:
538:
6327:Wolf Prize in Physics laureates
4558:/ John Frederick Grassle (2013)
3500:"Obituaries: Benoit Mandelbrot"
3400:
3368:
3336:
3306:
3285:
3264:
3234:
3208:
3178:
3118:
3084:
3054:
3020:
2989:
2850:
2755:
2707:
2688:
2663:
2647:Fractals and Scaling in Finance
2638:
2613:
2582:
2556:
2533:
2500:
2467:
2402:
2289:
2258:
2193:
2180:
2098:"BenoĂźt Mandelbrot (1924â2010)"
2031:
1662: â Financial modeling term
1615: â Term in decision theory
1342:. San Francisco: W.H. Freeman.
1310:
1152:High School Spelling Bee (1940)
788:. Building on previous work by
758:Fractals and Scaling in Finance
688:Université Lille Nord de France
508:Université Lille Nord de France
6312:Naturalized citizens of France
6118:The Fractal Geometry of Nature
5212:RabinovichâFabrikant equations
2996:Jersey, Bill (24 April 2005).
2765:The Fractal Geometry of Nature
2595:Journal of Banking and Finance
2484:10.1002/9780470061602.eqf01006
2342:"The Wolf Prizes for Physics,
2008:
1982:
1967:
1939:
1905:
1711:
1449:Mandelbrot, Benoit B. (2010).
1339:The Fractal Geometry of Nature
1336:Mandelbrot, BenoĂźt B. (1983).
1329:The Fractal Geometry of Nature
1227:American Philosophical Society
1048:The Fractal Geometry of Nature
1032:The Fractal Geometry of Nature
1003:The Fractal Geometry of Nature
984:in 1967, Mandelbrot discusses
916:The Fractal Geometry of Nature
829:, later translated in 1977 as
807:Mandelbrot speaking about the
595:) in Paris until the start of
525:
1:
4268:Ernest John Christopher Polge
3566:Video animation of Mandelbulb
3463:Mathematics Genealogy Project
2441:Interview of B. B. Mandelbrot
1827:
1374:Mandelbrot, Benoit B. (1997)
1315:
1299:Best-selling essayist-author
1099:American Mathematical Society
1059:sufficient, but not necessary
6347:Recipients of Franklin Medal
5565:
3407:BenoĂźt Mandelbrot's obituary
3042:Laureates of the Japan Prize
2911:10.1126/science.156.3775.636
2672:The (Mis)behavior of Markets
2607:10.1016/0378-4266(90)90009-Q
2542:"Wildly Random Market Moves"
1881:"BenoĂźt Mandelbrot obituary"
1459:, Division of Random House.
1384:, 1959â1997, 1 November 1998
1382:Fractales, hasard et finance
1305:The (Mis)Behavior of Markets
1091:European Geophysical Society
950:; the structures of plants,
762:The (Mis)behavior of Markets
674:, where he was sponsored by
668:Institute for Advanced Study
593:CollÚge-lycée Jacques-Decour
512:Institute for Advanced Study
498:of Mathematical Sciences at
7:
6134:Chaos: Making a New Science
4947:Poincaré recurrence theorem
3242:"Gruppe 1: Matematiske fag"
2762:Mandelbrot, BenoĂźt (1982).
2670:Mandelbrot, Benoit (2004).
2645:Mandelbrot, Benoit (1997).
2344:A Maverick's Apprenticeship
2340:Mandelbrot, BenoĂźt (2002).
2187:
2065:Mandelbrot, Benoit (2012).
2037:
1572:
1475:
1041:Section of a Mandelbrot set
1012:purpose of creating beauty.
772:As a visiting professor at
603:, France. He was helped by
599:, when his family moved to
372:, Poland, to France. After
10:
6363:
6322:University of Paris alumni
6307:Polish emigrants to France
6222:Ăcole Polytechnique alumni
4942:PoincarĂ©âBendixson theorem
3553:Cornell University Library
3426:
3318:United Press International
2437:Mandelbrot, B. B. (1984).
2351:. Imperial College Press.
2203:(NovemberâDecember 2004).
1654:Seven states of randomness
1592:Fractional Brownian motion
1206:Lewis Fry Richardson Medal
893:According to Clarke, "the
699:Yorktown Heights, New York
18:
6252:Harvard University people
6085:
6009:
5958:
5929:
5845:
5815:
5797:
5638:
5573:
5495:
5312:
5294:Swinging Atwood's machine
5239:
5177:
5047:
5034:
4986:
4967:
4937:KrylovâBogolyubov theorem
4917:
4814:
4754:
4637:
4498:
4363:
4284:William Hayward Pickering
4228:
4159:Ephraim Katchalski-Katzir
4147:
4066:
4015:
3924:
3863:
3788:
3681:
3654:
3468:Mandelbrot's page at Yale
1953:(3rd ed.). Longman.
1920:Oxford English Dictionary
1818:[bÉnwamÉÌdÉlbÊot]
1484:. New York: Basic Books.
1147:Charles Proteus Steinmetz
1085:for Physics in 1993, the
930:, and obtained his first
638:, where he studied under
546:
537:
532:
333:
302:
290:
264:
243:
236:
181:
175:(m. 1955â2010; his death)
167:
136:
116:
96:
77:
52:
36:
29:
6332:Yale Sterling Professors
6297:20th-century Polish Jews
6277:Jewish French scientists
5202:LotkaâVolterra equations
5026:Synchronization of chaos
4829:axiom A dynamical system
3498:Taylor, Richard (2011).
3478:17 February 2014 at the
2768:. W H Freeman & Co.
2721:The Jewish Daily Forward
2164:"The Father of Fractals"
1673:
1267:Cambridge, Massachusetts
1131:AMS Einstein Lectureship
1118:Johns Hopkins University
89:Cambridge, Massachusetts
6337:Yale University faculty
5187:Double scroll attractor
4952:Stable manifold theorem
4859:False nearest neighbors
4425:/ Keith J. Sainsbury /
3796:Pierre-Gilles de Gennes
3412:24 October 2010 at the
2188:Hudson & Mandelbrot
2169:The Wall Street Journal
2038:Hudson & Mandelbrot
1925:Oxford University Press
1696:. He included "B" as a
1430:Mandelbrot, Benoit B.,
6126:The Beauty of Fractals
5227:Van der Pol oscillator
5207:MackeyâGlass equations
4839:Box-counting dimension
4596:Emmanuelle Charpentier
4215:Frank Sherwood Rowland
2439:"Mathematical People,
1636:Mandelbrot Competition
1509:and Cornelia Zahlten:
1261:at the age of 85 in a
1241:WĆadysĆaw Orlicz Prize
1143:Natural Sciences Award
1042:
1035:
1014:
972:
911:
891:
881:
862:
844:
816:
624:
574:Second Polish Republic
449:information technology
5377:Svetlana Jitomirskaya
5284:Multiscroll attractor
5129:Interval exchange map
5082:Dyadic transformation
5067:Complex quadratic map
4909:Topological conjugacy
4844:Correlation dimension
4819:Anosov diffeomorphism
4027:Pablo Jarillo-Herrero
3648:Wolf Prize in Physics
3047:17 April 2016 at the
2868:on 31 December 2018.
2478:. pp. eqf01006.
2409:Hemenway, P. (2005).
2040:, Prelude, page xviii
1694:the French given name
1301:Nassim Nicholas Taleb
1257:Mandelbrot died from
1245:Wolf Foundation Prize
1040:
1026:
1009:
992:that are examples of
964:
903:
886:
879:
857:
839:
806:
735:Gaussian distribution
682:(to collaborate with
672:Princeton, New Jersey
616:
399:, where he became an
6072:Lewis Fry Richardson
6067:Hamid Naderi Yeganeh
5857:Burning Ship fractal
5789:Weierstrass function
5387:Edward Norton Lorenz
4701:John Michael Wallace
3816:Joseph H. Taylor Jr.
3216:"APS Fellow Archive"
2782:on 30 November 2015.
2413:. Psychology Press.
2209:Yale Alumni Magazine
1235:Sven Berggren-Priset
1087:Lewis Fry Richardson
958:; the clustering of
742:stable distributions
5830:Space-filling curve
5807:Multifractal system
5690:Space-filling curve
5675:Sierpinski triangle
5347:Mitchell Feigenbaum
5289:Population dynamics
5274:HĂ©nonâHeiles system
5134:Irrational rotation
5087:Dynamical billiards
5072:Coupled map lattice
4932:Liouville's theorem
4864:Hausdorff dimension
4849:Conservative system
4834:Bifurcation diagram
4685:/ Kazuo Hagimoto /
4524:Tadamitsu Kishimoto
4254:Jacques-Louis Lions
3755:Albert J. Libchaber
3751:Mitchell Feigenbaum
3672:Giuseppe Occhialini
3518:2011PhT....64f..63T
3320:. 16 October 2010.
2903:1967Sci...156..636M
2546:Journal of Commerce
2386:. 17 October 2010.
2114:2010Natur.468..378G
1992:. 22 October 2010.
1923:(Online ed.).
1666:ZipfâMandelbrot law
1642:Multifractal system
1410:1999SciAm.280b..70M
1397:Scientific American
1289:President of France
1104:The small asteroid
990:Hausdorff dimension
853:Romanesque broccoli
680:Geneva, Switzerland
652:University of Paris
636:Ăcole Polytechnique
417:statistical physics
159:ZipfâMandelbrot law
131:University of Paris
121:Ăcole Polytechnique
6057:Aleksandr Lyapunov
6037:Desmond Paul Henry
6001:Self-avoiding walk
5996:Percolation theory
5640:Iterated function
5581:Fractal dimensions
5525:Santa Fe Institute
5392:Aleksandr Lyapunov
5222:Three-body problem
5109:Gingerbreadman map
4996:Bifurcation theory
4874:Lyapunov stability
4663:Robert A. Weinberg
4645:Robert G. Gallager
4590:Steven D. Tanksley
4576:Theodore Friedmann
4479:Victor A. McKusick
4437:Masatoshi Takeichi
4385:Timothy R. Parsons
4381:John B. Goodenough
4375:Kimishige Ishizaka
4350:Jack L. Strominger
4346:W. Wesley Peterson
4326:Hiroyuki Yoshikawa
4322:Joseph Engelberger
4298:Edward F. Knipling
4031:Allan H. MacDonald
4002:Charles H. Bennett
3980:Robert P. Kirshner
3970:Juan Ignacio Cirac
3356:on 19 October 2010
2977:on 9 December 2006
2953:Devaney, Robert L.
2862:The New York Times
2302:The New York Times
2176:on 25 August 2017.
2069:. Pantheon Books.
1851:The New York Times
1547:on 23 October 2010
1499:Heinz-Otto Peitgen
1271:Heinz-Otto Peitgen
1247:for Physics (1993)
1199:LĂ©gion d'honneur (
1191:Japan Prize (2003)
1043:
1022:Euclidean geometry
882:
817:
774:Harvard University
710:information theory
612:Brive-la-Gaillarde
586:Szolem Mandelbrojt
496:Sterling Professor
469:physical cosmology
405:Harvard University
6154:
6153:
6100:Coastline paradox
6077:WacĆaw SierpiĆski
6062:Benoit Mandelbrot
5986:Fractal landscape
5894:Misiurewicz point
5799:Strange attractor
5680:Apollonian gasket
5670:Sierpinski carpet
5533:
5532:
5397:BenoĂźt Mandelbrot
5362:Martin Gutzwiller
5352:Peter Grassberger
5235:
5234:
5217:Rössler attractor
4965:
4964:
4869:Invariant measure
4791:Lyapunov exponent
4714:
4713:
4683:Masataka Nakazawa
4677:Christopher Field
4562:Yasuharu Suematsu
4506:Shun-ichi Iwasaki
4465:Peter Shaw Ashton
4405:Benoit Mandelbrot
4399:Andrzej Tarkowski
4219:Elias James Corey
4106:
4105:
3946:Maximilian Haider
3881:Bertrand Halperin
3875:Masatoshi Koshiba
3871:Raymond Davis Jr.
3822:BenoĂźt Mandelbrot
3810:Valentine Telegdi
3806:Maurice Goldhaber
3800:David J. Thouless
3769:Riccardo Giacconi
3745:Philippe NoziĂšres
3721:Martin Lewis Perl
3707:Gerardus 't Hooft
3697:Kenneth G. Wilson
3646:Laureates of the
3597:Benoit Mandelbrot
3588:Benoit Mandelbrot
3561:, zoom factor 10.
3527:10.1063/1.3603925
3459:Benoit Mandelbrot
3444:978-981-4366-06-9
3420:(21 October 2010)
3157:"Vita and Awards"
2897:(3775): 636â638.
2674:. Profile Books.
2656:978-1-4757-2763-0
2076:978-0-307-38991-6
1960:978-1-4058-8118-0
1931:(Subscription or
1586:Fractal dimension
1527:978-0-7365-0520-8
1491:978-0-465-04355-2
1465:978-0-307-38991-6
1434:, Springer: 2002.
1349:978-0-7167-1186-5
1259:pancreatic cancer
1077:Awards and honors
988:curves that have
921:program artifacts
733:did not follow a
731:financial markets
726:financial markets
712:, economics, and
608:David Feuerwerker
566:Lithuanian Jewish
562:
561:
453:computer graphics
337:
336:
303:Doctoral students
238:Scientific career
31:Benoit Mandelbrot
6354:
6017:Michael Barnsley
5884:Lyapunov fractal
5742:SierpiĆski curve
5695:Blancmange curve
5560:
5553:
5546:
5537:
5536:
5505:Butterfly effect
5417:Itamar Procaccia
5367:Brosl Hasslacher
5264:Elastic pendulum
5192:Duffing equation
5139:KaplanâYorke map
5057:Arnold's cat map
5045:
5044:
5021:Stability theory
5006:Dynamical system
5001:Control of chaos
4981:
4973:
4957:Takens's theorem
4889:Poincaré section
4759:
4758:
4741:
4734:
4727:
4718:
4717:
4552:C. Grant Willson
4340:Marc Van Montagu
4314:Takashi Sugimura
4248:Xavier Le Pichon
4193:Donald Henderson
4189:Georges Vendryes
4133:
4126:
4119:
4110:
4109:
3976:James D. Bjorken
3960:Jacob Bekenstein
3895:François Englert
3761:Herbert Friedman
3717:Leon M. Lederman
3711:Victor Weisskopf
3668:George Uhlenbeck
3640:
3633:
3626:
3617:
3616:
3607:
3579:
3567:
3531:
3529:
3492:FT.com interview
3448:
3421:
3404:
3398:
3397:
3395:
3393:
3372:
3366:
3365:
3363:
3361:
3352:. Archived from
3340:
3334:
3333:
3331:
3329:
3310:
3304:
3303:
3301:
3299:
3289:
3283:
3282:
3280:
3278:
3268:
3262:
3261:
3259:
3257:
3244:(in Norwegian).
3238:
3232:
3231:
3229:
3227:
3212:
3206:
3205:
3203:
3201:
3192:. Archived from
3182:
3176:
3175:
3173:
3171:
3165:
3159:. Archived from
3152:
3146:
3145:
3143:
3141:
3122:
3116:
3115:
3113:
3111:
3094:LĂ©gion d'honneur
3088:
3082:
3081:
3079:
3077:
3058:
3052:
3039:
3033:
3032:
3024:
3018:
3017:
3015:
3013:
2998:"A Radical Mind"
2993:
2987:
2986:
2984:
2982:
2976:
2961:
2949:
2943:
2942:
2940:
2938:
2888:
2879:
2873:
2872:
2854:
2848:
2847:
2845:
2843:
2821:
2815:
2814:
2812:
2810:
2790:
2784:
2783:
2778:. Archived from
2759:
2753:
2752:
2739:
2730:
2729:
2724:. Archived from
2711:
2705:
2692:
2686:
2685:
2667:
2661:
2660:
2642:
2636:
2635:
2633:
2617:
2611:
2610:
2601:(6): 1189â1208.
2586:
2580:
2579:
2577:
2575:
2560:
2554:
2553:
2548:. Archived from
2537:
2531:
2528:
2525:
2523:
2510:, 19 April 1997"
2504:
2498:
2497:
2471:
2465:
2464:
2462:
2460:
2454:
2447:
2434:
2425:
2424:
2406:
2400:
2399:
2397:
2395:
2374:
2368:
2367:
2365:
2363:
2357:
2350:
2337:
2326:
2325:
2323:
2321:
2293:
2287:
2286:
2284:
2282:
2262:
2256:
2255:
2253:
2251:
2231:
2225:
2224:
2222:
2220:
2197:
2191:
2184:
2178:
2177:
2172:. Archived from
2159:
2144:
2143:
2125:
2090:
2081:
2080:
2062:
2041:
2035:
2029:
2028:
2027:on 14 April 2016
2023:, archived from
2012:
2006:
2005:
2003:
2001:
1986:
1980:
1976:LĂ©gion d'honneur
1971:
1965:
1964:
1943:
1937:
1936:
1928:
1916:
1909:
1903:
1902:
1900:
1898:
1876:
1867:
1866:
1864:
1862:
1842:
1822:
1820:
1811:
1806:
1805:
1802:
1801:
1798:
1795:
1792:
1789:
1786:
1783:
1780:
1777:
1774:
1762:
1757:
1756:
1753:
1752:
1749:
1746:
1743:
1740:
1737:
1734:
1731:
1728:
1725:
1715:
1709:
1686:
1603:
1556:
1554:
1552:
1543:. Archived from
1495:
1483:
1440:, 9 January 2004
1421:
1353:
1253:Death and legacy
1201:Legion of Honour
1195:John Scott Award
1110:Legion of Honour
1106:27500 Mandelbrot
978:", published in
880:A Mandelbrot set
813:LĂ©gion d'honneur
744:having infinite
676:John von Neumann
551:
550:
542:
530:
529:
359:fractal geometry
292:Doctoral advisor
206:
188:LĂ©gion d'honneur
176:
128:
84:
63:20 November 1924
62:
60:
43:Mandelbrot at a
41:
27:
26:
6362:
6361:
6357:
6356:
6355:
6353:
6352:
6351:
6212:Chaos theorists
6157:
6156:
6155:
6150:
6081:
6032:Felix Hausdorff
6005:
5969:Brownian motion
5954:
5925:
5848:
5841:
5811:
5793:
5784:Pythagoras tree
5641:
5634:
5630:Self-similarity
5574:Characteristics
5569:
5564:
5534:
5529:
5497:
5491:
5437:Caroline Series
5332:Mary Cartwright
5314:
5308:
5259:Double pendulum
5241:
5231:
5180:
5173:
5099:Exponential map
5050:
5036:
5030:
4988:
4982:
4975:
4961:
4927:Ergodic theorem
4920:
4913:
4904:Stable manifold
4894:Recurrence plot
4810:
4764:
4750:
4745:
4715:
4710:
4705:Ronald M. Evans
4691:Karl Deisseroth
4687:Gero Miesenböck
4659:Bert Vogelstein
4655:Martin A. Green
4633:
4614:Max Dale Cooper
4600:Jennifer Doudna
4572:Yutaka Takahasi
4494:
4441:Erkki Ruoslahti
4423:Akira Fujishima
4391:Tim Berners-Lee
4359:
4354:Don Craig Wiley
4240:W. Jason Morgan
4224:
4183:Theodore Maiman
4169:Willem J. Kolff
4143:
4137:
4107:
4102:
4062:
4043:Anne L'Huillier
4023:Rafi Bistritzer
4011:
4006:Gilles Brassard
3940:Anton Zeilinger
3932:John F. Clauser
3920:
3905:Daniel Kleppner
3885:Anthony Leggett
3859:
3828:Vitaly Ginzburg
3784:
3779:Stephen Hawking
3741:Conyers Herring
3735:Theodore Maiman
3677:
3662:Chien-Shiung Wu
3650:
3644:
3577:
3565:
3480:Wayback Machine
3455:
3445:
3429:
3424:
3414:Wayback Machine
3405:
3401:
3391:
3389:
3374:
3373:
3369:
3359:
3357:
3342:
3341:
3337:
3327:
3325:
3312:
3311:
3307:
3297:
3295:
3291:
3290:
3286:
3276:
3274:
3270:
3269:
3265:
3255:
3253:
3240:
3239:
3235:
3225:
3223:
3214:
3213:
3209:
3199:
3197:
3196:on 16 June 2016
3184:
3183:
3179:
3169:
3167:
3164:(Word document)
3163:
3153:
3149:
3139:
3137:
3130:gazette.jhu.edu
3124:
3123:
3119:
3109:
3107:
3090:
3089:
3085:
3075:
3073:
3060:
3059:
3055:
3051:. japanprize.jp
3049:Wayback Machine
3040:
3036:
3025:
3021:
3011:
3009:
2994:
2990:
2980:
2978:
2974:
2959:
2950:
2946:
2936:
2934:
2886:
2880:
2876:
2856:
2855:
2851:
2841:
2839:
2822:
2818:
2808:
2806:
2791:
2787:
2776:
2760:
2756:
2741:
2740:
2733:
2728:on 2 June 2013.
2712:
2708:
2693:
2689:
2682:
2668:
2664:
2657:
2643:
2639:
2631:10.1.1.197.2969
2618:
2614:
2587:
2583:
2573:
2571:
2561:
2557:
2538:
2534:
2521:
2519:
2506:
2505:
2501:
2494:
2472:
2468:
2458:
2456:
2452:
2445:
2435:
2428:
2421:
2407:
2403:
2393:
2391:
2376:
2375:
2371:
2361:
2359:
2355:
2348:
2338:
2329:
2319:
2317:
2294:
2290:
2280:
2278:
2263:
2259:
2249:
2247:
2232:
2228:
2218:
2216:
2198:
2194:
2185:
2181:
2160:
2147:
2123:10.1038/468378a
2091:
2084:
2077:
2063:
2044:
2036:
2032:
2013:
2009:
1999:
1997:
1988:
1987:
1983:
1972:
1968:
1961:
1944:
1940:
1930:
1910:
1906:
1896:
1894:
1877:
1870:
1860:
1858:
1843:
1834:
1830:
1825:
1809:
1771:
1767:
1760:
1722:
1718:
1716:
1712:
1687:
1680:
1676:
1671:
1648:Self-similarity
1630:Louis Bachelier
1601:
1575:
1550:
1548:
1540:Financial Times
1503:Hartmut JĂŒrgens
1492:
1350:
1318:
1313:
1285:Nicolas Sarkozy
1255:
1250:
1232:Science for Art
1137:Caltech Service
1079:
1055:Olbers' paradox
1029:
940:
871:Johannes Kepler
867:psychedelic art
835:Stephen Wolfram
770:
754:scale parameter
724:Mandelbrot saw
722:
660:
658:Research career
610:, the Rabbi of
548:
533:External videos
528:
500:Yale University
489:social sciences
363:self-similarity
329:
286:
281:
272:Yale University
260:
228:
223:
218:
213:
208:
207:
192:
191:
177:
174:
173:
163:
129:
124:
123:
117:Alma mater
112:
92:
86:
82:
81:14 October 2010
73:
64:
58:
56:
48:
32:
23:
17:
12:
11:
5:
6360:
6350:
6349:
6344:
6339:
6334:
6329:
6324:
6319:
6314:
6309:
6304:
6299:
6294:
6289:
6284:
6279:
6274:
6269:
6264:
6259:
6254:
6249:
6244:
6239:
6234:
6229:
6224:
6219:
6214:
6209:
6204:
6199:
6194:
6189:
6184:
6179:
6174:
6169:
6152:
6151:
6149:
6148:
6143:
6138:
6130:
6122:
6114:
6109:
6104:
6103:
6102:
6089:
6087:
6083:
6082:
6080:
6079:
6074:
6069:
6064:
6059:
6054:
6049:
6047:Helge von Koch
6044:
6039:
6034:
6029:
6024:
6019:
6013:
6011:
6007:
6006:
6004:
6003:
5998:
5993:
5988:
5983:
5982:
5981:
5979:Brownian motor
5976:
5965:
5963:
5956:
5955:
5953:
5952:
5950:Pickover stalk
5947:
5942:
5936:
5934:
5927:
5926:
5924:
5923:
5918:
5913:
5908:
5906:Newton fractal
5903:
5898:
5897:
5896:
5889:Mandelbrot set
5886:
5881:
5880:
5879:
5874:
5872:Newton fractal
5869:
5859:
5853:
5851:
5843:
5842:
5840:
5839:
5838:
5837:
5827:
5825:Fractal canopy
5821:
5819:
5813:
5812:
5810:
5809:
5803:
5801:
5795:
5794:
5792:
5791:
5786:
5781:
5776:
5771:
5769:Vicsek fractal
5766:
5761:
5756:
5751:
5750:
5749:
5744:
5739:
5734:
5729:
5724:
5719:
5714:
5709:
5708:
5707:
5697:
5687:
5685:Fibonacci word
5682:
5677:
5672:
5667:
5662:
5660:Koch snowflake
5657:
5652:
5646:
5644:
5636:
5635:
5633:
5632:
5627:
5622:
5621:
5620:
5615:
5610:
5605:
5600:
5599:
5598:
5588:
5577:
5575:
5571:
5570:
5563:
5562:
5555:
5548:
5540:
5531:
5530:
5528:
5527:
5522:
5520:Predictability
5517:
5512:
5507:
5501:
5499:
5493:
5492:
5490:
5489:
5487:Lai-Sang Young
5484:
5482:James A. Yorke
5479:
5477:Amie Wilkinson
5474:
5469:
5464:
5459:
5454:
5449:
5444:
5439:
5434:
5429:
5424:
5419:
5414:
5412:Henri Poincaré
5409:
5404:
5399:
5394:
5389:
5384:
5379:
5374:
5369:
5364:
5359:
5354:
5349:
5344:
5339:
5334:
5329:
5324:
5318:
5316:
5310:
5309:
5307:
5306:
5301:
5296:
5291:
5286:
5281:
5279:Kicked rotator
5276:
5271:
5266:
5261:
5256:
5251:
5249:Chua's circuit
5245:
5243:
5237:
5236:
5233:
5232:
5230:
5229:
5224:
5219:
5214:
5209:
5204:
5199:
5194:
5189:
5183:
5181:
5178:
5175:
5174:
5172:
5171:
5169:Zaslavskii map
5166:
5164:Tinkerbell map
5161:
5156:
5151:
5146:
5141:
5136:
5131:
5126:
5121:
5116:
5111:
5106:
5101:
5096:
5095:
5094:
5084:
5079:
5074:
5069:
5064:
5059:
5053:
5051:
5048:
5042:
5032:
5031:
5029:
5028:
5023:
5018:
5013:
5011:Ergodic theory
5008:
5003:
4998:
4992:
4990:
4984:
4983:
4968:
4966:
4963:
4962:
4960:
4959:
4954:
4949:
4944:
4939:
4934:
4929:
4923:
4921:
4918:
4915:
4914:
4912:
4911:
4906:
4901:
4896:
4891:
4886:
4881:
4876:
4871:
4866:
4861:
4856:
4851:
4846:
4841:
4836:
4831:
4826:
4821:
4815:
4812:
4811:
4809:
4808:
4803:
4801:Periodic point
4798:
4793:
4788:
4783:
4778:
4773:
4767:
4765:
4762:
4756:
4752:
4751:
4744:
4743:
4736:
4729:
4721:
4712:
4711:
4709:
4708:
4694:
4680:
4669:Katalin KarikĂł
4666:
4652:
4641:
4639:
4635:
4634:
4632:
4631:
4624:Yoshio Okamoto
4621:
4618:Jacques Miller
4607:
4593:
4583:
4569:
4566:C. David Allis
4559:
4549:
4542:Nicholas Lydon
4531:
4520:Dennis Ritchie
4513:
4510:Peter Vitousek
4502:
4500:
4496:
4495:
4493:
4492:
4485:Dennis Meadows
4482:
4475:Robert E. Kahn
4468:
4461:Peter GrĂŒnberg
4454:
4444:
4430:
4427:John H. Lawton
4416:
4409:James A. Yorke
4402:
4388:
4378:
4367:
4365:
4361:
4360:
4358:
4357:
4343:
4329:
4311:
4304:Charles K. Kao
4301:
4291:
4288:Arvid Carlsson
4281:
4278:Kary B. Mullis
4271:
4261:
4251:
4232:
4230:
4226:
4225:
4223:
4222:
4212:
4205:Luc Montagnier
4186:
4175:Henry Beachell
4172:
4165:David Turnbull
4162:
4155:John R. Pierce
4151:
4149:
4145:
4144:
4136:
4135:
4128:
4121:
4113:
4104:
4103:
4101:
4100:
4093:
4088:
4083:
4078:
4073:
4067:
4064:
4063:
4061:
4060:
4054:
4040:
4037:Giorgio Parisi
4034:
4019:
4017:
4013:
4012:
4010:
4009:
3999:
3989:
3983:
3973:
3963:
3957:
3943:
3928:
3926:
3922:
3921:
3919:
3918:
3915:Peter GrĂŒnberg
3908:
3902:
3888:
3878:
3867:
3865:
3861:
3860:
3858:
3857:
3851:
3844:Yakir Aharonov
3841:
3835:
3832:Yoichiro Nambu
3825:
3819:
3813:
3803:
3792:
3790:
3786:
3785:
3783:
3782:
3772:
3758:
3748:
3738:
3724:
3714:
3700:
3689:Michael Fisher
3685:
3683:
3679:
3678:
3676:
3675:
3665:
3658:
3656:
3652:
3651:
3643:
3642:
3635:
3628:
3620:
3614:
3613:
3608:
3594:
3585:
3574:
3562:
3556:
3542:
3539:Web of Stories
3532:
3495:
3489:
3483:
3482:(TED address).
3470:
3465:
3454:
3453:External links
3451:
3450:
3449:
3443:
3428:
3425:
3423:
3422:
3399:
3367:
3335:
3305:
3284:
3263:
3233:
3207:
3177:
3166:on 2 July 2007
3147:
3117:
3083:
3053:
3034:
3019:
2988:
2944:
2874:
2849:
2816:
2799:Web of Stories
2785:
2774:
2754:
2731:
2706:
2687:
2680:
2662:
2655:
2637:
2612:
2581:
2555:
2532:
2508:"New Scientist
2499:
2492:
2466:
2426:
2419:
2401:
2369:
2327:
2288:
2257:
2240:Web of Stories
2226:
2192:
2179:
2145:
2082:
2075:
2042:
2030:
2007:
1981:
1966:
1959:
1947:Wells, John C.
1938:
1904:
1868:
1831:
1829:
1826:
1824:
1823:
1710:
1702:New York Times
1698:middle initial
1677:
1675:
1672:
1670:
1669:
1663:
1657:
1651:
1645:
1639:
1633:
1627:
1622:
1616:
1610:
1607:Hurst exponent
1604:
1595:
1589:
1583:
1576:
1574:
1571:
1570:
1569:
1557:
1530:
1496:
1490:
1473:
1467:
1447:
1441:
1435:
1428:
1422:
1391:
1385:
1379:
1372:
1366:
1363:
1360:
1357:
1354:
1348:
1333:
1325:
1317:
1314:
1312:
1309:
1281:TED conference
1277:Chris Anderson
1254:
1251:
1249:
1248:
1242:
1239:
1236:
1233:
1230:
1225:Member of the
1223:
1218:Member of the
1216:
1213:
1210:
1207:
1204:
1197:
1192:
1189:
1188:IBM Fellowship
1186:
1181:
1178:
1172:
1170:Franklin Medal
1167:
1161:
1156:
1153:
1150:
1144:
1138:
1135:
1132:
1129:
1125:
1078:
1075:
974:In his paper "
939:
936:
895:Mandelbrot set
809:Mandelbrot set
798:Mandelbrot set
769:
766:
721:
718:
714:fluid dynamics
659:
656:
560:
559:
557:Web of Stories
544:
543:
535:
534:
527:
524:
412:Mandelbrot set
335:
334:
331:
330:
328:
327:
322:
317:
312:
306:
304:
300:
299:
294:
288:
287:
282:
280:
279:
274:
268:
266:
262:
261:
259:
258:
253:
247:
245:
241:
240:
234:
233:
226:Franklin Medal
185:
183:
179:
178:
171:
169:
165:
164:
162:
161:
156:
151:
146:
144:Mandelbrot set
140:
138:
137:Known for
134:
133:
118:
114:
113:
111:
110:
107:
104:
100:
98:
94:
93:
87:
85:(aged 85)
79:
75:
74:
65:
54:
50:
49:
45:TED conference
42:
34:
33:
30:
21:Mandelbrot set
15:
9:
6:
4:
3:
2:
6359:
6348:
6345:
6343:
6340:
6338:
6335:
6333:
6330:
6328:
6325:
6323:
6320:
6318:
6315:
6313:
6310:
6308:
6305:
6303:
6300:
6298:
6295:
6293:
6290:
6288:
6285:
6283:
6280:
6278:
6275:
6273:
6270:
6268:
6267:IBM employees
6265:
6263:
6260:
6258:
6255:
6253:
6250:
6248:
6245:
6243:
6240:
6238:
6235:
6233:
6230:
6228:
6225:
6223:
6220:
6218:
6215:
6213:
6210:
6208:
6205:
6203:
6200:
6198:
6195:
6193:
6190:
6188:
6185:
6183:
6180:
6178:
6175:
6173:
6170:
6168:
6165:
6164:
6162:
6147:
6144:
6142:
6139:
6136:
6135:
6131:
6128:
6127:
6123:
6120:
6119:
6115:
6113:
6110:
6108:
6105:
6101:
6098:
6097:
6095:
6091:
6090:
6088:
6084:
6078:
6075:
6073:
6070:
6068:
6065:
6063:
6060:
6058:
6055:
6053:
6050:
6048:
6045:
6043:
6040:
6038:
6035:
6033:
6030:
6028:
6025:
6023:
6020:
6018:
6015:
6014:
6012:
6008:
6002:
5999:
5997:
5994:
5992:
5989:
5987:
5984:
5980:
5977:
5975:
5974:Brownian tree
5972:
5971:
5970:
5967:
5966:
5964:
5961:
5957:
5951:
5948:
5946:
5943:
5941:
5938:
5937:
5935:
5932:
5928:
5922:
5919:
5917:
5914:
5912:
5909:
5907:
5904:
5902:
5901:Multibrot set
5899:
5895:
5892:
5891:
5890:
5887:
5885:
5882:
5878:
5877:Douady rabbit
5875:
5873:
5870:
5868:
5865:
5864:
5863:
5860:
5858:
5855:
5854:
5852:
5850:
5844:
5836:
5833:
5832:
5831:
5828:
5826:
5823:
5822:
5820:
5818:
5814:
5808:
5805:
5804:
5802:
5800:
5796:
5790:
5787:
5785:
5782:
5780:
5777:
5775:
5772:
5770:
5767:
5765:
5762:
5760:
5757:
5755:
5752:
5748:
5747:Z-order curve
5745:
5743:
5740:
5738:
5735:
5733:
5730:
5728:
5725:
5723:
5720:
5718:
5717:Hilbert curve
5715:
5713:
5710:
5706:
5703:
5702:
5701:
5700:De Rham curve
5698:
5696:
5693:
5692:
5691:
5688:
5686:
5683:
5681:
5678:
5676:
5673:
5671:
5668:
5666:
5665:Menger sponge
5663:
5661:
5658:
5656:
5653:
5651:
5650:Barnsley fern
5648:
5647:
5645:
5643:
5637:
5631:
5628:
5626:
5623:
5619:
5616:
5614:
5611:
5609:
5606:
5604:
5601:
5597:
5594:
5593:
5592:
5589:
5587:
5584:
5583:
5582:
5579:
5578:
5576:
5572:
5568:
5561:
5556:
5554:
5549:
5547:
5542:
5541:
5538:
5526:
5523:
5521:
5518:
5516:
5515:Edge of chaos
5513:
5511:
5508:
5506:
5503:
5502:
5500:
5494:
5488:
5485:
5483:
5480:
5478:
5475:
5473:
5472:Marcelo Viana
5470:
5468:
5465:
5463:
5462:Audrey Terras
5460:
5458:
5457:Floris Takens
5455:
5453:
5450:
5448:
5445:
5443:
5440:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5415:
5413:
5410:
5408:
5405:
5403:
5400:
5398:
5395:
5393:
5390:
5388:
5385:
5383:
5380:
5378:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5357:Celso Grebogi
5355:
5353:
5350:
5348:
5345:
5343:
5340:
5338:
5337:Chen Guanrong
5335:
5333:
5330:
5328:
5325:
5323:
5322:Michael Berry
5320:
5319:
5317:
5311:
5305:
5302:
5300:
5297:
5295:
5292:
5290:
5287:
5285:
5282:
5280:
5277:
5275:
5272:
5270:
5267:
5265:
5262:
5260:
5257:
5255:
5252:
5250:
5247:
5246:
5244:
5238:
5228:
5225:
5223:
5220:
5218:
5215:
5213:
5210:
5208:
5205:
5203:
5200:
5198:
5197:Lorenz system
5195:
5193:
5190:
5188:
5185:
5184:
5182:
5176:
5170:
5167:
5165:
5162:
5160:
5157:
5155:
5152:
5150:
5147:
5145:
5144:Langton's ant
5142:
5140:
5137:
5135:
5132:
5130:
5127:
5125:
5122:
5120:
5119:Horseshoe map
5117:
5115:
5112:
5110:
5107:
5105:
5102:
5100:
5097:
5093:
5090:
5089:
5088:
5085:
5083:
5080:
5078:
5075:
5073:
5070:
5068:
5065:
5063:
5060:
5058:
5055:
5054:
5052:
5046:
5043:
5040:
5033:
5027:
5024:
5022:
5019:
5017:
5016:Quantum chaos
5014:
5012:
5009:
5007:
5004:
5002:
4999:
4997:
4994:
4993:
4991:
4985:
4980:
4976:
4972:
4958:
4955:
4953:
4950:
4948:
4945:
4943:
4940:
4938:
4935:
4933:
4930:
4928:
4925:
4924:
4922:
4916:
4910:
4907:
4905:
4902:
4900:
4897:
4895:
4892:
4890:
4887:
4885:
4882:
4880:
4877:
4875:
4872:
4870:
4867:
4865:
4862:
4860:
4857:
4855:
4852:
4850:
4847:
4845:
4842:
4840:
4837:
4835:
4832:
4830:
4827:
4825:
4824:Arnold tongue
4822:
4820:
4817:
4816:
4813:
4807:
4804:
4802:
4799:
4797:
4794:
4792:
4789:
4787:
4784:
4782:
4779:
4777:
4774:
4772:
4769:
4768:
4766:
4760:
4757:
4753:
4749:
4742:
4737:
4735:
4730:
4728:
4723:
4722:
4719:
4706:
4702:
4698:
4697:Brian Hoskins
4695:
4692:
4688:
4684:
4681:
4678:
4674:
4673:Drew Weissman
4670:
4667:
4664:
4660:
4656:
4653:
4650:
4646:
4643:
4642:
4640:
4636:
4629:
4625:
4622:
4619:
4615:
4611:
4610:Akira Yoshino
4608:
4605:
4601:
4597:
4594:
4591:
4587:
4584:
4581:
4580:Alain Fischer
4577:
4573:
4570:
4567:
4563:
4560:
4557:
4553:
4550:
4547:
4546:Masato Sagawa
4543:
4539:
4535:
4532:
4529:
4528:Toshio Hirano
4525:
4521:
4517:
4514:
4511:
4507:
4504:
4503:
4501:
4497:
4490:
4489:David E. Kuhl
4486:
4483:
4480:
4476:
4472:
4469:
4466:
4462:
4458:
4455:
4452:
4448:
4447:John Houghton
4445:
4442:
4438:
4434:
4431:
4428:
4424:
4420:
4419:Kenichi Honda
4417:
4414:
4410:
4406:
4403:
4400:
4396:
4392:
4389:
4386:
4382:
4379:
4376:
4372:
4369:
4368:
4366:
4362:
4355:
4351:
4347:
4344:
4341:
4337:
4333:
4330:
4327:
4323:
4319:
4315:
4312:
4309:
4305:
4302:
4299:
4295:
4294:Nick Holonyak
4292:
4289:
4285:
4282:
4279:
4275:
4272:
4269:
4265:
4262:
4259:
4255:
4252:
4249:
4245:
4241:
4237:
4236:Marvin Minsky
4234:
4233:
4231:
4227:
4220:
4216:
4213:
4210:
4206:
4202:
4198:
4194:
4190:
4187:
4184:
4180:
4176:
4173:
4170:
4166:
4163:
4160:
4156:
4153:
4152:
4150:
4146:
4141:
4134:
4129:
4127:
4122:
4120:
4115:
4114:
4111:
4099:
4098:
4094:
4092:
4089:
4087:
4084:
4082:
4079:
4077:
4074:
4072:
4069:
4068:
4065:
4058:
4055:
4052:
4051:Ferenc Krausz
4048:
4044:
4041:
4038:
4035:
4032:
4028:
4024:
4021:
4020:
4018:
4014:
4007:
4003:
4000:
3997:
3996:Didier Queloz
3993:
3990:
3987:
3984:
3981:
3977:
3974:
3971:
3967:
3964:
3961:
3958:
3955:
3951:
3947:
3944:
3941:
3937:
3933:
3930:
3929:
3927:
3923:
3916:
3912:
3909:
3906:
3903:
3900:
3896:
3892:
3889:
3886:
3882:
3879:
3876:
3872:
3869:
3868:
3866:
3862:
3855:
3854:Dan Shechtman
3852:
3849:
3848:Michael Berry
3845:
3842:
3839:
3836:
3833:
3829:
3826:
3823:
3820:
3817:
3814:
3811:
3807:
3804:
3801:
3797:
3794:
3793:
3791:
3787:
3780:
3776:
3775:Roger Penrose
3773:
3770:
3766:
3762:
3759:
3756:
3752:
3749:
3746:
3742:
3739:
3736:
3732:
3728:
3725:
3722:
3718:
3715:
3712:
3708:
3704:
3703:Freeman Dyson
3701:
3698:
3694:
3690:
3687:
3686:
3684:
3680:
3673:
3669:
3666:
3663:
3660:
3659:
3657:
3653:
3649:
3641:
3636:
3634:
3629:
3627:
3622:
3621:
3618:
3612:
3609:
3606:
3602:
3598:
3595:
3593:
3589:
3586:
3584:
3580:
3575:
3572:
3568:
3563:
3560:
3557:
3554:
3550:
3549:Eugene Dynkin
3546:
3543:
3540:
3536:
3533:
3528:
3523:
3519:
3515:
3511:
3507:
3506:
3505:Physics Today
3501:
3496:
3493:
3490:
3487:
3484:
3481:
3477:
3474:
3471:
3469:
3466:
3464:
3460:
3457:
3456:
3446:
3440:
3436:
3431:
3430:
3419:
3418:The Economist
3415:
3411:
3408:
3403:
3387:
3384:(in French).
3383:
3382:
3377:
3371:
3355:
3351:
3350:
3345:
3339:
3323:
3319:
3315:
3309:
3294:
3288:
3273:
3267:
3251:
3247:
3243:
3237:
3221:
3217:
3211:
3195:
3191:
3187:
3181:
3162:
3158:
3151:
3135:
3131:
3127:
3121:
3105:
3101:
3099:
3095:
3087:
3071:
3067:
3063:
3057:
3050:
3046:
3043:
3038:
3030:
3029:New Scientist
3023:
3007:
3003:
2999:
2992:
2973:
2969:
2965:
2958:
2954:
2948:
2932:
2928:
2924:
2920:
2916:
2912:
2908:
2904:
2900:
2896:
2892:
2885:
2878:
2871:
2867:
2863:
2859:
2853:
2837:
2833:
2832:
2827:
2820:
2804:
2800:
2796:
2789:
2781:
2777:
2775:0-7167-1186-9
2771:
2767:
2766:
2758:
2750:
2746:
2745:
2738:
2736:
2727:
2723:
2722:
2717:
2710:
2704:
2703:0-7167-0473-0
2700:
2696:
2691:
2683:
2681:9781861977656
2677:
2673:
2666:
2658:
2652:
2648:
2641:
2632:
2627:
2623:
2616:
2608:
2604:
2600:
2596:
2592:
2585:
2570:
2566:
2559:
2551:
2547:
2543:
2536:
2530:
2527:
2517:
2512:
2511:
2503:
2495:
2493:9780470057568
2489:
2485:
2481:
2477:
2470:
2451:
2444:
2442:
2433:
2431:
2422:
2420:0-415-34495-6
2416:
2412:
2405:
2389:
2385:
2384:
2379:
2373:
2354:
2347:
2345:
2336:
2334:
2332:
2315:
2311:
2307:
2303:
2299:
2292:
2276:
2272:
2268:
2261:
2245:
2241:
2237:
2230:
2214:
2210:
2206:
2202:
2196:
2189:
2183:
2175:
2171:
2170:
2165:
2158:
2156:
2154:
2152:
2150:
2141:
2137:
2133:
2129:
2124:
2119:
2115:
2111:
2108:(7322): 378.
2107:
2103:
2099:
2095:
2089:
2087:
2078:
2072:
2068:
2061:
2059:
2057:
2055:
2053:
2051:
2049:
2047:
2039:
2034:
2026:
2022:
2018:
2011:
1995:
1991:
1985:
1978:
1977:
1970:
1962:
1956:
1952:
1948:
1942:
1934:
1926:
1922:
1921:
1915:
1908:
1892:
1888:
1887:
1882:
1875:
1873:
1856:
1852:
1848:
1841:
1839:
1837:
1832:
1819:
1814:
1813:
1804:
1765:
1764:
1755:
1714:
1707:
1703:
1699:
1695:
1691:
1685:
1683:
1678:
1667:
1664:
1661:
1660:Skewness risk
1658:
1655:
1652:
1649:
1646:
1643:
1640:
1637:
1634:
1631:
1628:
1626:
1625:List of Poles
1623:
1620:
1617:
1614:
1613:Kurtosis risk
1611:
1608:
1605:
1599:
1596:
1593:
1590:
1587:
1584:
1581:
1578:
1577:
1567:
1566:
1561:
1558:
1546:
1542:
1541:
1536:
1531:
1528:
1524:
1520:
1519:0-7167-2213-5
1516:
1512:
1508:
1507:Dietmar Saupe
1504:
1500:
1497:
1493:
1487:
1482:
1481:
1474:
1471:
1468:
1466:
1462:
1458:
1457:Vintage Books
1454:
1453:
1448:
1445:
1442:
1439:
1436:
1433:
1429:
1426:
1423:
1419:
1415:
1411:
1407:
1403:
1399:
1398:
1392:
1389:
1386:
1383:
1380:
1377:
1373:
1370:
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1320:
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1306:
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1294:The Economist
1290:
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1168:
1165:
1162:
1160:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1134:Barnard Medal
1133:
1130:
1127:
1126:
1124:
1121:
1119:
1115:
1111:
1107:
1102:
1100:
1096:
1093:in 2000, the
1092:
1089:Prize of the
1088:
1084:
1074:
1072:
1068:
1064:
1060:
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1051:
1049:
1039:
1034:
1033:
1025:
1023:
1019:
1013:
1008:
1005:
1004:
997:
995:
991:
987:
983:
982:
977:
971:
969:
963:
961:
957:
953:
952:blood vessels
949:
945:
935:
933:
929:
924:
922:
918:
917:
910:
908:
902:
900:
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890:
885:
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874:
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868:
861:
856:
854:
850:
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836:
832:
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824:
823:
814:
810:
805:
801:
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795:
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787:
786:complex plane
783:
779:
775:
765:
763:
759:
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751:
747:
743:
740:
737:, but rather
736:
732:
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655:
653:
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633:
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628:Lycée du Parc
623:
621:
620:Zina Morhange
615:
613:
609:
606:
602:
598:
594:
589:
587:
583:
579:
578:rote learning
575:
571:
567:
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531:
523:
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517:
513:
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505:
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482:
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430:
429:geomorphology
426:
422:
418:
413:
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406:
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394:
390:
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383:
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375:
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364:
360:
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347:mathematician
344:
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332:
326:
323:
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318:
316:
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308:
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269:
267:
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254:
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249:
248:
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242:
239:
235:
232:
231:Barnard Medal
227:
222:
217:
212:
204:
200:
196:
190:
189:
184:
180:
172:Aliette Kagan
170:
166:
160:
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150:
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132:
127:
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95:
90:
80:
76:
72:
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55:
51:
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35:
28:
25:
22:
6146:Chaos theory
6141:Kaleidoscope
6132:
6124:
6116:
6061:
6042:Gaston Julia
6022:Georg Cantor
5847:Escape-time
5779:Gosper curve
5727:LĂ©vy C curve
5712:Dragon curve
5591:Box-counting
5467:Mary Tsingou
5432:David Ruelle
5427:Otto Rössler
5396:
5372:Michel HĂ©non
5342:Leon O. Chua
5299:Tilt-A-Whirl
5269:FPUT problem
5154:Standard map
5149:Logistic map
4974:
4748:Chaos theory
4649:Svante PÀÀbo
4586:Hideo Hosono
4556:Jean Fréchet
4538:Brian Druker
4534:Janet Rowley
4516:Ken Thompson
4433:Makoto Nagao
4404:
4395:Anne McLaren
4336:Jozef Schell
4264:Gerhard Ertl
4258:John J. Wild
4244:Dan McKenzie
4209:Robert Gallo
4201:Frank Fenner
4179:Gurdev Khush
4095:
3992:Michel Mayor
3966:Peter Zoller
3936:Alain Aspect
3891:Robert Brout
3838:John Wheeler
3821:
3731:Peter Hirsch
3693:Leo Kadanoff
3547:held by the
3509:
3503:
3434:
3417:
3402:
3390:. Retrieved
3379:
3370:
3358:. Retrieved
3354:the original
3347:
3338:
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3317:
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3287:
3275:. Retrieved
3266:
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3236:
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3224:. Retrieved
3210:
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3194:the original
3189:
3180:
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3161:the original
3150:
3138:. Retrieved
3129:
3120:
3108:. Retrieved
3097:
3093:
3086:
3074:. Retrieved
3065:
3056:
3037:
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3001:
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2979:. Retrieved
2972:the original
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2894:
2890:
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2869:
2866:the original
2861:
2852:
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2831:The Atlantic
2829:
2819:
2807:. Retrieved
2788:
2780:the original
2764:
2757:
2749:the original
2743:
2726:the original
2719:
2709:
2694:
2690:
2671:
2665:
2649:. Springer.
2646:
2640:
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2568:
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2529:
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2469:
2457:. Retrieved
2440:
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2372:
2360:. Retrieved
2343:
2318:. Retrieved
2301:
2291:
2279:. Retrieved
2274:
2270:
2260:
2248:. Retrieved
2229:
2217:. Retrieved
2208:
2201:Olson, Steve
2195:
2182:
2174:the original
2167:
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2101:
2066:
2033:
2025:the original
2020:
2010:
1998:. Retrieved
1984:
1975:
1969:
1950:
1941:
1918:
1914:"Mandelbrot"
1907:
1895:. Retrieved
1886:The Guardian
1884:
1859:. Retrieved
1850:
1713:
1706:The Guardian
1705:
1701:
1563:
1549:. Retrieved
1545:the original
1538:
1510:
1479:
1469:
1451:
1443:
1437:
1431:
1424:
1401:
1395:
1387:
1381:
1375:
1368:
1338:
1327:
1324:, 1977, 2020
1321:
1311:Bibliography
1304:
1298:
1293:
1275:
1256:
1215:Nevada Prize
1175:Harvey Prize
1141:Casimir Funk
1122:
1103:
1080:
1052:
1047:
1044:
1031:
1027:
1018:stock market
1015:
1010:
1001:
998:
993:
986:self-similar
980:
973:
965:
948:river basins
941:
925:
914:
912:
904:
898:
892:
887:
883:
863:
858:
845:
840:
830:
826:
820:
818:
794:Pierre Fatou
790:Gaston Julia
771:
761:
757:
749:
723:
707:
661:
640:Gaston Julia
625:
617:
597:World War II
590:
582:World War II
563:
519:
493:
481:econophysics
477:chaos theory
409:
374:World War II
367:
342:
339:
338:
320:Ken Musgrave
310:L. E. Calvet
265:Institutions
256:Aerodynamics
237:
221:Harvey Prize
202:
198:
194:
186:
149:Chaos theory
83:(2010-10-14)
24:
6257:IBM Fellows
6172:2010 deaths
6167:1924 births
6137:(1987 book)
6129:(1986 book)
6121:(1982 book)
6107:Fractal art
6027:Bill Gosper
5991:LĂ©vy flight
5737:Peano curve
5732:Moore curve
5618:Topological
5603:Correlation
5452:Nina Snaith
5442:Yakov Sinai
5327:Rufus Bowen
5077:Duffing map
5062:Baker's map
4987:Theoretical
4899:SRB measure
4806:Phase space
4776:Bifurcation
4457:Albert Fert
4413:Seiji Ogawa
4274:Frank Press
4140:Japan Prize
4086:Mathematics
4071:Agriculture
4057:Martin Rees
4047:Paul Corkum
3986:Yoseph Imry
3950:Harald Rose
3911:Albert Fert
3899:Peter Higgs
3765:Bruno Rossi
3349:The Gazette
3170:15 December
2320:20 November
2281:25 December
1717:Pronounced
1378:, Springer.
1180:Honda Prize
1095:Japan Prize
1067:Cantor dust
860:Mandelbrot.
849:Fern leaves
684:Jean Piaget
572:during the
568:family, in
526:Early years
473:engineering
445:linguistics
421:meteorology
378:aeronautics
325:Murad Taqqu
315:Eugene Fama
251:Mathematics
229:1985
224:1986
219:1989
214:1993
211:Japan Prize
209:2003
97:Nationality
6161:Categories
5945:Orbit trap
5940:Buddhabrot
5933:techniques
5921:Mandelbulb
5722:Koch curve
5655:Cantor set
5510:Complexity
5407:Edward Ott
5254:Convection
5179:Continuous
4854:Ergodicity
4628:Rattan Lal
4604:Adi Shamir
4451:Akira Endo
4371:Ian McHarg
4318:Bruce Ames
4197:Isao Arita
4142:recipients
3954:Knut Urban
3727:Erwin Hahn
3488:(lecture).
3392:17 October
3360:16 October
3328:17 October
3298:21 January
3190:amstat.org
3140:17 October
3110:17 October
3076:17 October
2937:11 January
2842:16 October
2809:17 October
2569:Medium.com
2522:17 October
2394:17 October
2383:BBC Online
2250:19 October
2094:Gomory, R.
1935:required.)
1897:17 October
1889:. London.
1861:16 October
1828:References
1812:-dÉl-broht
1690:circumflex
1619:Lacunarity
1551:17 October
1455:New York:
1316:In English
1083:Wolf Prize
944:coastlines
780:that were
778:Julia sets
648:PhD degree
487:, and the
485:metallurgy
401:IBM Fellow
343:Mandelbrot
216:Wolf Prize
197:1990
59:1924-11-20
19:See also:
6052:Paul LĂ©vy
5931:Rendering
5916:Mandelbox
5862:Julia set
5774:Hexaflake
5705:Minkowski
5625:Recursion
5608:Hausdorff
5422:Mary Rees
5382:Bryna Kra
5315:theorists
5124:Ikeda map
5114:HĂ©non map
5104:Gauss map
4786:Limit set
4771:Attractor
4471:Vint Cerf
4332:Leo Esaki
4308:Masao Ito
4081:Chemistry
3917:(2006â07)
3887:(2002â03)
3840:(1996â97)
3834:(1994â95)
3747:(1984â85)
3737:(1983â84)
3512:(6): 63.
3381:Le Figaro
3256:7 October
3200:20 August
3012:20 August
2981:5 January
2626:CiteSeerX
2310:0362-4331
2000:8 January
1763:-dÉl-brot
1580:1/f noise
1404:(2): 70.
1101:in 2006.
782:invariant
654:in 1952.
644:Paul LĂ©vy
457:economics
441:neurology
425:hydrology
380:from the
355:roughness
340:Benoit B.
297:Paul LĂ©vy
195:Chevalier
168:Spouse(s)
5962:fractals
5849:fractals
5817:L-system
5759:T-square
5567:Fractals
5498:articles
5240:Physical
5159:Tent map
5049:Discrete
4989:branches
4919:Theorems
4755:Concepts
4091:Medicine
3476:Archived
3410:Archived
3386:Archived
3322:Archived
3250:Archived
3220:Archived
3134:Archived
3104:Archived
3098:officier
3070:Archived
3045:Archived
3006:Archived
2955:(2004).
2931:Archived
2927:15662830
2919:17837158
2836:Archived
2803:Archived
2574:19 March
2516:Archived
2450:Archived
2388:Archived
2362:23 April
2353:Archived
2314:Archived
2244:Archived
2213:Archived
2132:21085164
2096:(2010).
1994:Archived
1949:(2008).
1891:Archived
1855:Archived
1573:See also
1071:Big Bang
994:fractals
968:geometry
960:galaxies
899:infinite
746:variance
703:Emeritus
465:medicine
437:taxonomy
393:American
351:polymath
203:Officier
154:Fractals
106:American
5911:Tricorn
5764:n-flake
5613:Packing
5596:Higuchi
5586:Assouad
5496:Related
5304:Weather
5242:systems
5035:Chaotic
4781:Fractal
4097:Physics
3583:YouTube
3571:YouTube
3514:Bibcode
3461:at the
3427:Sources
3277:14 June
3218:. APS.
3066:pnl.gov
3004:. PBS.
2899:Bibcode
2891:Science
2459:25 June
2219:22 July
2140:4393964
2110:Bibcode
2021:TED.com
1406:Bibcode
1263:hospice
1229:(2004)
1166:(1987)
981:Science
932:tenured
907:mandala
822:fractal
815:in 2006
461:geology
433:anatomy
47:in 2010
6010:People
5960:Random
5867:Filled
5835:H tree
5754:String
5642:system
5402:Hee Oh
5037:maps (
4884:Mixing
4707:(2024)
4693:(2023)
4679:(2022)
4665:(2021)
4651:(2020)
4630:(2019)
4620:(2018)
4606:(2017)
4592:(2016)
4582:(2015)
4568:(2014)
4548:(2012)
4530:(2011)
4512:(2010)
4491:(2009)
4481:(2008)
4467:(2007)
4453:(2006)
4443:(2005)
4429:(2004)
4415:(2003)
4401:(2002)
4387:(2001)
4377:(2000)
4356:(1999)
4342:(1998)
4328:(1997)
4310:(1996)
4300:(1995)
4296:Jr. /
4290:(1994)
4280:(1993)
4270:(1992)
4260:(1991)
4250:(1990)
4221:(1989)
4211:(1988)
4185:(1987)
4171:(1986)
4161:(1985)
4059:(2024)
4053:(2022)
4039:(2021)
4033:(2020)
4008:(2018)
3998:(2017)
3988:(2016)
3982:(2015)
3972:(2013)
3962:(2012)
3956:(2011)
3942:(2010)
3907:(2005)
3901:(2004)
3877:(2000)
3856:(1999)
3850:(1998)
3824:(1993)
3818:(1992)
3812:(1991)
3802:(1990)
3781:(1988)
3771:(1987)
3757:(1986)
3723:(1982)
3713:(1981)
3699:(1980)
3674:(1979)
3664:(1978)
3441:
2925:
2917:
2772:
2701:
2678:
2653:
2628:
2490:
2417:
2308:
2138:
2130:
2102:Nature
2073:
1957:
1700:. His
1525:
1517:
1488:
1472:, 2014
1463:
1346:
1332:, 1982
1177:(1989)
570:Warsaw
389:French
370:Warsaw
244:Fields
199:·
182:Awards
109:Polish
103:French
91:, U.S.
71:Poland
67:Warsaw
6086:Other
5313:Chaos
5092:outer
4796:Orbit
4638:2020s
4499:2010s
4364:2000s
4229:1990s
4148:1980s
4016:2020s
3925:2010s
3864:2000s
3789:1990s
3682:1980s
3655:1970s
2975:(PDF)
2960:(PDF)
2923:S2CID
2887:(PDF)
2453:(PDF)
2446:(PDF)
2356:(PDF)
2349:(PDF)
2271:Foton
2136:S2CID
1929:
1674:Notes
1149:Medal
1063:stars
956:lungs
605:Rabbi
601:Tulle
205:2006)
201:
5039:list
4763:Core
4076:Arts
3592:IMDb
3439:ISBN
3394:2010
3362:2010
3330:2010
3300:2023
3279:2021
3258:2010
3228:2020
3202:2016
3172:2013
3142:2010
3112:2010
3078:2010
3014:2009
2983:2007
2939:2016
2915:PMID
2844:2010
2811:2010
2770:ISBN
2699:ISBN
2676:ISBN
2651:ISBN
2576:2021
2524:2010
2488:ISBN
2461:2013
2415:ISBN
2396:2010
2364:2012
2322:2020
2306:ISSN
2283:2021
2252:2010
2221:2014
2128:PMID
2071:ISBN
2002:2018
1955:ISBN
1899:2010
1863:2010
1565:NOVA
1553:2010
1523:ISBN
1515:ISBN
1486:ISBN
1461:ISBN
1344:ISBN
966:Can
954:and
946:and
928:Yale
851:and
792:and
760:and
739:LĂ©vy
642:and
632:Lyon
514:and
391:and
386:dual
349:and
78:Died
53:Born
3601:TED
3599:at
3590:at
3581:on
3569:on
3522:doi
2907:doi
2895:156
2603:doi
2480:doi
2275:112
2118:doi
2106:468
1810:MAN
1766:or
1761:MAN
1414:doi
1402:280
1265:in
923:".
697:in
692:IBM
670:in
630:in
397:IBM
277:IBM
6163::
6096:"
4703:/
4699:/
4689:/
4675:/
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4661:/
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