Benoît Mandelbrot was the first to use a computer to plot the Mandelbrot set.

Benoît B. Mandelbrot (born November 20, 1924) is a Polish-born French mathematician and leading proponent of fractal geometry. He is Sterling Professor of Mathematical Sciences, Emeritus at Yale University and IBM Fellow Emeritus at the Thomas J. Watson Research Center. Download high resolution version (1024x768, 189 KB)This is a file from the Wikimedia Commons, a repository of free content hosted by the Wikimedia Foundation. ... Download high resolution version (1024x768, 189 KB)This is a file from the Wikimedia Commons, a repository of free content hosted by the Wikimedia Foundation. ... A rendering of the Mandelbrot set: black points represent the stable points under the iterative map In mathematics, the Mandelbrot set is a fractal that is defined as the set of points c in the complex plane for which the iteratively defined sequence: does not tend to infinity. ... November 20 is the 324th day of the year (325th in leap years) in the Gregorian Calendar. ... 1924 was a leap year starting on Tuesday (link will take you to calendar). ... Mathematics is the study of quantity, structure, space and change. ... The Mandelbrot set, named after its discoverer, is a famous example of a fractal. ... Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Thales (circa 624-547 BC) dealing with spatial relationships. ... A Sterling Professorship is the highest academic rank at Yale University, awarded to a tenured faculty member considered one of the best in his field. ... This article is about the institution of higher learning in the United States. ... International Business Machines Corporation (IBM, or colloquially, Big Blue) (NYSE: IBM) (incorporated June 15, 1911, in operation since 1888) is headquartered in Armonk, New York, USA. The company manufactures and sells computer hardware, software, and services. ... The Thomas J. Watson Research Center is the headquarters for the IBM Research Division. ...

Early years

Born in Warsaw, Mandelbrot lived in France from the age of 12 to the end of his college studies. He was born into a family with a strong academic tradition - his mother was a medical doctor and his uncle, Szolem Mandelbrojt, was a famous Parisian mathematician. His father, however, made his living trading clothing. His family left Poland for Paris in 1936. There, Benoît was introduced to mathematics by his two uncles. Warsaw (Polish: Warszawa, see also other names, in full The Capital City of Warsaw, Polish: Miasto Stołeczne Warszawa) is the capital of Poland and its largest city. ... Szolem Mandelbrojt (1899 – 1983) was a French mathematician, from a Polish-Lithuanian Jewish background. ... 1936 was a leap year starting on Wednesday (link will take you to calendar). ...

Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle. In 1944 he returned to Paris to attend the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. He graduated from the École Polytechnique in 1947, and spent two years at the California Institute of Technology where he studied aeronautics. Back in France, he studied for a Ph.D. in Mathematical Sciences at the University of Paris, graduating in 1952. Mushroom cloud from the nuclear explosion over Nagasaki rising 18 km (over 11 miles) into the air. ... Tulle is a netting, which is often starched, made of various fibers, including silk, nylon, and rayon, that is often used for veils or gowns. ... 1944 was a leap year starting on Saturday (link will take you to calendar). ... The cadets of Polytechnique rushed to the defense of Paris against the foreign armies in 1814. ... Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. ... Paul Pierre Lévy (September 15, 1886 - December 15, 1971) was a French mathematician who was active especially in probability theory, introduced martingales and Lévy flights. ... 1947 was a common year starting on Wednesday (link will take you to calendar). ... The California Institute of Technology (commonly known as Caltech) is a private, coeducational university located in Pasadena, California, in the United States. ... The Sorbonne, Paris, in a 17th century engraving The historic University of Paris (French: Université de Paris) first appeared in the second half of the 12th century, but was in 1970 reorganized as 13 autonomous universities (University of Paris I–XIII). ... 1952 was a leap year starting on Tuesday (link will take you to calendar). ...

From 1949 to 1957 Mandelbrot was a staff member at the Centre National de la Recherche Scientifique. During this time he spent a year at the Institute for Advanced Study in Princeton where he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva. 1949 is a common year starting on Saturday. ... 1957 was a common year starting on Tuesday of the Gregorian calendar. ... The Centre National de la Recherche Scientifique (CNRS) is one of the most prominent scientific research institutions in France. ... Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, designed to foster pure cutting-edge research by scientists in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship. ... See also: the Borough of Princeton, New Jersey Princeton Township highlighted in Mercer County. ... John von Neumann in the 1940s. ... 1955 is a common year starting on Saturday of the Gregorian calendar. ... Geneva: the Mont Blanc bridge over the Rhône River and St Peters Cathedral Geneva (French: Genève) is the second-most populous city in Switzerland located where Lake Geneva (French: Lac Léman, but the Genevois are fond of calling it Lac de Genève) empties into the...

In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. He remained at IBM for the rest of his working life, becoming an IBM Fellow, and later Fellow Emeritus. 1958 was a common year starting on Wednesday of the Gregorian calendar. ... International Business Machines Corporation (IBM, or colloquially, Big Blue) (NYSE: IBM) (incorporated June 15, 1911, in operation since 1888) is headquartered in Armonk, New York, USA. The company manufactures and sells computer hardware, software, and services. ... The Thomas J. Watson Research Center is the headquarters for the IBM Research Division. ... Yorktown Heights is an unincorporated hamlet and census-designated place (CDP) located in the town of Yorktown in Westchester County, New York. ... State nickname: Empire State Other U.S. States Capital Albany Largest city New York Governor George Pataki Official languages None Area 141,205 km² (27th)  - Land 122,409 km²  - Water 18,795 km² (13. ... An IBM Fellow is an appointed position at IBM made by IBM’s CEO. Typically only 4 or 5 IBM Fellows are appointed each year, at the annual Corporate Technical Recognition Event (CTRE) event in June. ...

Later years

From 1955 onwards Mandelbrot worked on problems and published papers in fields as diverse as information theory, economics and fluid dynamics. He became convinced that a common theme of self-similar structures ran through all of these real-world problems. In 1975 Mandelbrot coined the term fractal to describe these structures, and published his ideas in Les objets fractals, forme, hasard et dimension (translated into English as Fractals: form, chance and dimension in 1977). Information theory is a branch of the mathematical theory of probability and mathematical statistics that quantifies the concept of information. ... Economics (deriving from the Greek words οίκω [okos], house, and νέμω [nemo], rules hence household management) is the social science that studies the allocation of scarce resources to satisfy unlimited wants. ... This article or section should be merged with Fluid mechanics Fluid dynamics is the study of fluids (liquids and gases) in motion, and the effect of the fluid motion on fluid boundaries, such as solid containers or other fluids. ... A self-similar object is exactly or approximately similar to a part of itself. ... 1975 was a common year starting on Wednesday (the link is to a full 1975 calendar). ... The Mandelbrot set, named after its discoverer, is a famous example of a fractal. ... 1977 was a common year starting on Saturday (the link is to a full 1977 calendar). ...

In 1979, while on secondment as Visiting Professor of Mathematics at Harvard University, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Julia and by Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets of the equation z² - c. While investigating how the topology of these Julia sets depended on the complex parameter c, he discovered the Mandelbrot set fractal that is now named after him. 1979 is a common year starting on Monday. ... Harvard University is a private university in Cambridge, Massachusetts, USA, and a member of the Ivy League. ... Julia sets, described by Gaston Julia, are fractal shapes defined on the complex number plane. ... The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. ... Pierre Fatou was the first to define the Mandelbrot set. ... A rendering of the Mandelbrot set: black points represent the stable points under the iterative map In mathematics, the Mandelbrot set is a fractal that is defined as the set of points c in the complex plane for which the iteratively defined sequence: does not tend to infinity. ...

In 1982 Mandelbrot published an expanded and updated version of his ideas in The Fractal Geometry of Nature. This hugely influential work brought fractals into the mainstream of both professional and popular mathematics. 1982 is a common year starting on Friday of the Gregorian calendar. ...

On his retirement from IBM in 1987, Mandelbrot joined the faculty of Yale as Sterling Professor of Mathematical Sciences. Mandelbrot was awarded the prestigious Japan Prize in 2003. The asteroid 27500 Mandelbrot was named in his honour. 1987 is a common year starting on Thursday of the Gregorian calendar. ... This article is about the institution of higher learning in the United States. ... The Japan Prize is awarded to people from all parts of the world whose original and outstanding achievements in science and technology are recognized as having advanced the frontiers of knowledge and served the cause of peace and prosperity for mankind. ... An asteroid is a small, solid object in our Solar System, orbiting the Sun. ...

Mandelbrot and fractals

Although Mandelbrot invented the word fractal, many of the objects featured in The Fractal Geometry of Nature had been previously described by other mathematicians (the Mandelbrot set being a notable exception). However, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and highlighted their common properties, such as self-similarity (sometimes partial or statistical), scale invariance and (usually) non-integer Hausdorff dimension. In physics, scale invariance is the feature of physical objects of laws that do not change if the space is magnified, i. ... In mathematics, the Hausdorff dimension is an extended non-negative real number, that is in the closed infinite interval [0, ∞], associated to any metric space . ...

He also emphasised the use of fractals as realistic and useful models of many natural phenomena, including the shape of coastlines and river basins; the structure of plants, blood vessels and lungs; the clustering of galaxies; Brownian motion; and stock market prices. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry. As he says in the Introduction to The Fractal Geometry of Nature: The arterial system The blood vessels are part of the circulatory system and function to transport blood throughout the body. ... The heart with relation to the lungs (from an older edition of Grays Anatomy) This x-ray of the human chest shows the lungs as dark regions The lung is an organ belonging to the respiratory system and interfacing to the circulatory system of air-breathing vertebrates. ... This article is about a celestial body. ... An example of 1000 simulated steps of Brownian motion in two dimensions. ... A stock market is a market for the trading of publicly held company stock and associated financial instruments (including stock options, convertibles and stock index futures). ... In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ...

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

Mandelbrot's informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. It sparked a widespread popular interest in fractals as well as contributing to new fields of science such as chaos theory. Chaos theory, in mathematics and physics, deals with the behavior of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions (see butterfly effect). ...

Pronunciation

In English, "Mandelbrot" is pronounced man-dull-bro. In Yiddish and German it is pronounced as mand'lbrot and the name means "almond bread". The English language is a West Germanic language that originates in England. ... Yiddish (Yid. ... This article refers to the plant. ...

See also

• How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension is a paper by mathematician Benoît Mandelbrot, first published in Science in 1967. ...

External links

• Mandelbrot's page at Yale (http://www.math.yale.edu/mandelbrot/)
• Interview of the École Polytechnique site (http://www.polytechnique.edu/interview.php?id=12)
• Biography of Mandelbrot (http://www.bookrags.com/biography/benoit-b-mandelbrot/)
• Video stream of Mandelbrot lecturing at MIT (http://mitworld.mit.edu/play/52/)

Wikipedia does not have an article with this exact name. ... Wikiquote is a sister project of Wikipedia, using the same MediaWiki software. ...

Suggested reading

• The Fractal Geometry of Nature, by Benoît Mandelbrot; W H Freeman & Co, 1982; ISBN 0716711869
• The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, by Benoit Mandelbrot and Richard L. Hudson; Basic Books, 2004; ISBN 0-465-04355-0