❤️ Billion (disambiguation) 🏵️

"Billion is a name for a large number. It may refer specifically to: * 1,000,000,000 (, one thousand million), the short scale definition * 1,000,000,000,000 (, one million million), the long scale definition Billion may also refer to: * Billions (TV series), a Showtime series * Billions (film), a 1920 silent comedy * Billion (company), a Taiwanese modem manufacturer * Jack Billion (born 1939), 2006 Democratic Party candidate for governor of South Dakota * Mr. Billion, a 1977 film by Jonathan Kaplan * "Billions" (song), a song on Russell Dickerson's album Yours See also * Long and short scales * Names of large numbers * Billion laughs, an XML parser vulnerability * Golden billion, a Russian term for the wealthy people of the developed world * Billon (disambiguation) * BN (disambiguation) "

❤️ Boat 🏵️

"A recreational motorboat with an outboard motor A boat is a watercraft of a large range of types and sizes, but generally smaller than a ship, which is distinguished by its larger size, shape, cargo or passenger capacity, or its ability to carry boats. Small boats are typically found on inland waterways such as rivers and lakes, or in protected coastal areas. However, some boats, such as the whaleboat, were intended for use in an offshore environment. In modern naval terms, a boat is a vessel small enough to be carried aboard a ship. Anomalous definitions exist, as lake freighters long on the Great Lakes are called "boats". Boats vary in proportion and construction methods with their intended purpose, available materials, or local traditions. Canoes have been used since prehistoric times and remain in use throughout the world for transportation, fishing, and sport. Fishing boats vary widely in style partly to match local conditions. Pleasure craft used in recreational boating include ski boats, pontoon boats, and sailboats. House boats may be used for vacationing or long-term residence. Lighters are used to convey cargo to and from large ships unable to get close to shore. Lifeboats have rescue and safety functions. Boats can be propelled by manpower (e.g. rowboats and paddle boats), wind (e.g. sailboats), and motor (including gasoline, diesel, and electric). History Silver model of a boat, tomb PG 789, Royal Cemetery of Ur, 2600-2500 BCE. Boats have served as transportation since the earliest times. Circumstantial evidence, such as the early settlement of Australia over 40,000 years ago, findings in Crete dated 130,000 years ago, and in Flores dated to 900,000 years ago,First Mariners – Archaeology Magazine Archive. Archive.archaeology.org. Retrieved on 2013-11-16. suggest that boats have been used since prehistoric times. The earliest boats are thought to have been dugouts, and the oldest boats found by archaeological excavation date from around 7,000–10,000 years ago. The oldest recovered boat in the world, the Pesse canoe, found in the Netherlands, is a dugout made from the hollowed tree trunk of a Pinus sylvestris that was constructed somewhere between 8200 and 7600 BC. This canoe is exhibited in the Drents Museum in Assen, Netherlands. Other very old dugout boats have also been recovered. Rafts have operated for at least 8,000 years. A 7,000-year-old seagoing reed boat has been found in Kuwait. Boats were used between 4000 and 3000 BC in Sumer, ancient Egypt and in the Indian Ocean. Boats played an important role in the commerce between the Indus Valley Civilization and Mesopotamia. Evidence of varying models of boats has also been discovered at various Indus Valley archaeological sites. Uru craft originate in Beypore, a village in south Calicut, Kerala, in southwestern India. This type of mammoth wooden ship was constructed solely of teak, with a transport capacity of 400 tonnes. The ancient Arabs and Greeks used such boats as trading vessels. The historians Herodotus, Pliny the Elder and Strabo record the use of boats for commerce, travel, and military purposes. Types Boats with sails in Bangladesh Boats can be categorized into three main types: # Unpowered or human-powered. Unpowered craft include rafts meant for one-way downstream travel. Human-powered boats include canoes, kayaks, gondolas and boats propelled by poles like a punt. # Sailboats, propelled mainly by means of sails. # Motorboats, propelled by mechanical means, such as engines. Terminology The hull is the main, and in some cases only, structural component of a boat. It provides both capacity and buoyancy. The keel is a boat's "backbone", a lengthwise structural member to which the perpendicular frames are fixed. On most boats a deck covers the hull, in part or whole. While a ship often has several decks, a boat is unlikely to have more than one. Above the deck are often lifelines connected to stanchions, bulwarks perhaps topped by gunnels, or some combination of the two. A cabin may protrude above the deck forward, aft, along the centerline, or covering much of the length of the boat. Vertical structures dividing the internal spaces are known as bulkheads. The forward end of a boat is called the bow, the aft end the stern. Facing forward the right side is referred to as starboard and the left side as port. Building materials Traditional Toba Batak boat (circa 1870), photograph by Kristen Feilberg Fishing boats in Visakhapatnam, India Until the mid-19th century most boats were made of natural materials, primarily wood, although reed, bark and animal skins were also used. Early boats include the bound-reed style of boat seen in Ancient Egypt, the birch bark canoe, the animal hide-covered kayak and coracle and the dugout canoe made from a single log. By the mid-19th century, many boats had been built with iron or steel frames but still planked in wood. In 1855 ferro- cement boat construction was patented by the French, who coined the name "ferciment". This is a system by which a steel or iron wire framework is built in the shape of a boat's hull and covered over with cement. Reinforced with bulkheads and other internal structure it is strong but heavy, easily repaired, and, if sealed properly, will not leak or corrode. As the forests of Britain and Europe continued to be over-harvested to supply the keels of larger wooden boats, and the Bessemer process (patented in 1855) cheapened the cost of steel, steel ships and boats began to be more common. By the 1930s boats built entirely of steel from frames to plating were seen replacing wooden boats in many industrial uses and fishing fleets. Private recreational boats of steel remain uncommon. In 1895 WH Mullins produced steel boats of galvanized iron and by 1930 became the world's largest producer of pleasure boats. Mullins also offered boats in aluminum from 1895 through 1899 and once again in the 1920s,WH Mullins boat history, Salem Ohio but it wasn't until the mid-20th century that aluminium gained widespread popularity. Though much more expensive than steel, aluminum alloys exist that do not corrode in salt water, allowing a similar load carrying capacity to steel at much less weight. Around the mid-1960s, boats made of fiberglass (aka "glassfibre") became popular, especially for recreational boats. Fiberglass is also known as "GRP" (glass- reinforced plastic) in the UK, and "FRP" (for fiber-reinforced plastic) in the US. Fiberglass boats are strong, and do not rust, corrode, or rot. Instead, they are susceptible to structural degradation from sunlight and extremes in temperature over their lifespan. Fiberglass structures can be made stiffer with sandwich panels, where the fiberglass encloses a lightweight core such as balsa.. as in the Iroqois catamaran or foam. Cold moulding is a modern construction method, using wood as the structural component. In cold moulding very thin strips of wood are layered over a form. Each layer is coated with resin, followed by another directionally alternating layer laid on top. Subsequent layers may be stapled or otherwise mechanically fastened to the previous, or weighted or vacuum bagged to provide compression and stabilization until the resin sets. Propulsion The most common means of boat propulsion are as follows: * Engine ** Inboard motor ** Stern drive (Inboard/outboard) ** Outboard motor ** Paddle wheel ** Water jet (jetboat, personal water craft) ** Fan (hovercraft, air boat) * Man (rowing, paddling, setting pole etc.) * Wind (sailing) Buoyancy A boat displaces its weight in water, regardless whether it is made of wood, steel, fiberglass, or even concrete. If weight is added to the boat, the volume of the hull drawn below the waterline will increase to keep the balance above and below the surface equal. Boats have a natural or designed level of buoyancy. Exceeding it will cause the boat first to ride lower in the water, second to take on water more readily than when properly loaded, and ultimately, if overloaded by any combination of structure, cargo, and water, sink. As commercial vessels must be correctly loaded to be safe, and as the sea becomes less buoyant in brackish areas such as the Baltic, the Plimsoll line was introduced to prevent overloading. European Union classification Since 1998 all new leisure boats and barges built in Europe between 2.5m and 24m must comply with the EU's Recreational Craft Directive (RCD). The Directive establishes four categories that permit the allowable wind and wave conditions for vessels in each class:"The Barge Buyer's Handbook" - DBA publications *Class A - the boat may safely navigate any waters. *Class B - the boat is limited to offshore navigation. (Winds up to Force 8 & waves up to 4 metres) *Class C - the boat is limited to inshore (coastal) navigation. (Winds up to Force 6 & waves up to 2 metres) *Class D - the boat is limited to rivers, canals and small lakes. (Winds up to Force 4 & waves up to 0.5 metres) Gallery File:A boat in India.JPG|A boat on the Ganges River File:Babur crossing the river Son.jpg|Babur crossing river Son; folio from an illustrated manuscript of ‘Babur-Namah’, Mughal, Akbar Period, AD 1598 File:Tug Boat NY 1.jpg|A tugboat is used for towing or pushing another larger ship File:DerelictBoatFollyIs.jpg|A ship's derelict lifeboat, built of steel, rusting away in the wetlands of Folly Island, South Carolina, United States File:EgyptTombOarboat.jpg|A boat in an Egyptian tomb, painted around 1450 BC File:Historic Center of Quito - World Heritage Site by UNESCO - Photo 437.jpg|Dugout boats in the courtyard of the Old Military Hospital in the Historic Center of Quito File:Jiajing Emperor on his state barge.jpg|Ming Dynasty Chinese painting of the Wanli Emperor enjoying a boat ride on a river with an entourage of guards and courtiers File:Kambojika Putta Khemara Tarei (front).jpg|Worlds longest dragon boat on display in Phnom Penh, Cambodia File:lifeboat.17-31.underway.arp.jpg|At 17 metres long, the Severn-class lifeboats are the largest operational lifeboats in the UK File:Oldboats.JPG|Aluminum flat-bottomed boats ashore for storage File:Sauce Bottle - geograph.org.uk - 13422.jpg|A boat shaped like a sauce bottle that was sailed across the Atlantic Ocean by Tom McClean File:Yacht and Sails.JPG|Anchored boats in Portovenere, Italy File:Groep in een boot, Stadsbuitengracht Utrecht, 2019 - 2.jpg|A boat in Utrecht, Netherlands See also * Abora * Barge * Cabin cruiser * Canoe * Car float * Coracle * Dinghy * Dory * Fishing vessel * Flatboat * Halkett boat * Inflatable boat * Kayak * Launch (boat) * Lifeboat * Lighter * Log canoe * Narrowboat * Naval architecture * Panga (boat) * Pirogue * Poveiro * Rescue craft * Riverboat * Rowing * Sailboat * Sampan * Ship * Ship's boat * Skiff * Tour boat * Traditional fishing boats * Tûranor PlanetSolar * Watercraft * Yacht References External links * University of Washington Libraries Digital Collections – Freshwater and Marine Image Bank, (enter search term "vessels" for images of boats and vessels.) Category:Watercraft Category:Fishing equipment "

❤️ Benoit Mandelbrot 🏵️

"Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life".https://www.insidescience.org/news/remembering-father-fractalsBenoit Mandelbrot: Fractals and the art of roughness. ted.com (February 2010)Hudson & Mandelbrot, Prelude, page xviii He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature. In 1936, while he was a child, Mandelbrot's family emigrated to France from Warsaw, Poland. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM, where he became an IBM Fellow, and periodically took leaves of absence to teach at Harvard University. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences. 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 Mandelbrot set 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", like clouds or shorelines, actually had a "degree of order". His math and geometry-centered research career included contributions to such fields as statistical physics, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, economics, geology, medicine, physical cosmology, engineering, chaos theory, econophysics, metallurgy and the social sciences.list includes specific sciences mentioned in Hudson & Mandelbrot, the Prelude, p. xvi, and p. 26 Toward the end of his career, he was Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012. Early years Mandelbrot was born in a Jewish family, in Warsaw during the Second Polish Republic. 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 rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me." Later, the family's move to France, the war, and his acquaintance with his father's brother, the mathematician Szolem Mandelbrojt who had moved to Paris around 1920, further prevented a standard education. The family emigrated from Poland to France in 1936, when he was 11. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle, France. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies.Hemenway P. (2005) Divine proportion: Phi in art, nature and science. Psychology Press. Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period: In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc in Lyon, and in 1945 to 1947 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. 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 PhD degree in Mathematical Sciences at the University of Paris in 1952. Research career From 1949 to 1958, 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, New Jersey, where he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva, Switzerland (to collaborate with Jean Piaget at the International Centre for Genetic Epistemology) and later to the Université Lille Nord de France. 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 35 years, becoming an IBM Fellow, and later Fellow Emeritus. From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics. Randomness in financial markets Mandelbrot saw financial markets 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 financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α 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 scale parameter. Developing "fractal geometry" and the Mandelbrot set As a visiting professor 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 Gaston Julia and Pierre Fatou, Mandelbrot used 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 1979. In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.The Fractal Geometry of Nature, by Benoît Mandelbrot; W H Freeman & Co, 1982; This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts". Mandelbrot speaking about the Mandelbrot set, during his acceptance speech for the Légion d'honneur in 2006 In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, Fractals: Form, Chance and Dimension.Fractals: Form, Chance and Dimension, by Benoît Mandelbrot; W H Freeman and Co, 1977; According to computer scientist and physicist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before".Wolfram, Stephen. "The Father of Fractals", Wall Street Journal, 22 November 2012 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": Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesco broccoli are two examples from nature." He points out an unexpected conclusion: 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 graphic computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s psychedelic art with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist Johannes Kepler, who calculated and described the orbits of the planets.Ivry, Benjamin. "Benoit Mandelbrot Influenced Art and Mathematics", Forward, 17 November 2012 A Mandelbrot set Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke: According to Clarke, "the Mandelbrot set 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 infinite complexity?" Clarke also notes an "odd coincidence > the name Mandelbrot, and the word "mandala"—for a religious symbol—which I'm > sure is a pure coincidence, but indeed the Mandelbrot set does seem to > contain an enormous number of mandalas. 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 Yale, and obtained his first tenured post in 1999, at the age of 75. At the time of his retirement in 2005, he was Sterling 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 of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies. 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: In his paper titled How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension published in Science in 1967 Mandelbrot discusses self-similar curves that have Hausdorff dimension that are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals."Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?": Benoit Mandelbrot (1967). "Benoît Mandelbrot, Novel Mathematician, Dies at 85", The New York Times. 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 The Fractal Geometry of Nature 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 extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new: Fractals are also found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry: > Clouds are not spheres, mountains are not cones, coastlines are not circles, > and bark is not smooth, nor does lightning travel in a straight line. > —Mandelbrot, in his introduction to The Fractal Geometry of Nature Section of a Mandelbrot set 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 The Fractal Geometry of Nature accessible to non- specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics. Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang 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.Galaxy Map Hints at Fractal Universe, by Amanda Gefter; New Scientist; 25 June 2008 Awards and honors Mandelbrot's awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003,Laureates of the Japan Prize. japanprize.jp and the Einstein Lectureship of the American Mathematical Society in 2006. The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Chevalier in France's Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006. An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises. A partial list of awards received by Mandelbrot: Retrieved from Internet Archive 15 December 2013. * 2004 Best Business Book of the Year Award * AMS Einstein Lectureship * Barnard Medal * Caltech Service * Casimir Funk Natural Sciences Award * Charles Proteus Steinmetz Medal * Fellow, American Geophysical Union * Fellow of the American Statistical AssociationView/Search Fellows of the ASA, accessed 20 August 2016. * Fellow of the American Physical Society (1987) * Franklin Medal * Harvey Prize (1989) * Honda Prize * Humboldt Preis * IBM Fellowship * Japan Prize (2003) * John Scott Award * Légion d'honneur (Legion of Honour) * Lewis Fry Richardson Medal * Medaglia della Presidenza della Repubblica Italiana * Médaille de Vermeil de la Ville de Paris * Nevada Prize * Member of the Norwegian Academy of Science and Letters. * Science for Art * Sven Berggren-Priset * Władysław Orlicz Prize * Wolf Foundation Prize for Physics (1993) Legacy Mandelbrot died from pancreatic cancer at the age of 85 in a hospice in Cambridge, Massachusetts on 14 October 2010. Reacting to news 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 the most important figures of the last fifty years." Chris Anderson, TED conference curator, described Mandelbrot as "an icon who changed how we see the world". Nicolas Sarkozy, President of France at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".Benoît Mandelbrot's obituary. The Economist (21 October 2010) 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". Bibliography in English *Fractals: Form, Chance and Dimension, 1977, 2020 * The Fractal Geometry of Nature, 1982 * Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E, 1997 by Benoit B. Mandelbrot and R.E. Gomory * Fractales, hasard et finance, 1959-1997, 1 November 1998 * Multifractals and 1/ƒ Noise: Wild Self- Affinity in Physics (1963–1976) (Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot * Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot) 14 December 2001 by Benoit Mandelbrot and F.J. Damerau * Fractals and Chaos: The Mandelbrot Set and Beyond, 9 January 2004 * The Misbehavior of Markets: A Fractal View of Financial Turbulence, 2006 by Benoit Mandelbrot and Richard L. Hudson * The Fractalist: Memoir of a Scientific Maverick, 2014 In French * La forme d'une vie. Mémoires (1924-2010) by Benoît Mandelbrot (Author), Johan-Frédérik Hel Guedj (Translator) References in popular culture * In 2004, the American singer-songwriter Jonathan Coulton wrote "Mandelbrot Set". Formerly, it contained the lines "Mandelbrot's in heaven / at least he will be when he's dead / right now he's still alive and teaching math at Yale". Live performances after Mandelbrot's passing in 2010 feature only the first line and a brief rock instrumental. * In 2007, the author Laura Ruby published "The Chaos King," which includes a character named Mandelbrot and discussion of chaos theory. * In 2017, Zach Weinersmith' webcomic, Saturday Morning Breakfast Cereal, portrayed Mandelbrot. * In 2017, Liz Ziemska published a novella, Mandelbrot The Magnificent, a fictional account of how Mandelbrot saved his family during WWII See also {- style="vertical-align:top" style="padding-right:2em"* "How Long is the Coast of Britain?" * Louis Bachelier * Zipf–Mandelbrot law * Seven states of randomness * Skewness risk * Kurtosis risk * Fractal dimension * Lacunarity * Self-similarity * Self- affinity * Hurst exponent * Fractional Brownian motion * Multifractal system * 1/f noise * Mandelbrot Competition |} Notes References Bibliography * Further reading * Mandelbrot, Benoit B. (2010). The Fractalist, Memoir of a Scientific Maverick. New York: Vintage Books, Division of Random House. Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe and Cornelia Zahlten: Fractals: An Animated Discussion (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. (re-published by Films for the Humanities & Sciences, ) * Mandelbrot, Benoit B. (1997) Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, Springer. Mandelbrot, Benoit B., Gaussian Self-Affinity and Fractals, Springer: 2002. "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature", NOVA, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008. 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, 613–615. * Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79–106. * Mandelbrot, B. (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517–543. * Mandelbrot, B. (1964) Random walks, fire damage amount and other Paretian risk phenomena. Operations Research, 12, 582–585. External links Mandelbrot's page at Yale * "Benoît Mandelbrot: Fractals and the art of roughness" (TED address). * Fractals in Science, Engineering and Finance (lecture). * FT.com interview on the subject of the financial markets which includes his critique of the "efficient market" hypothesis. Mandelbrot relates his life story (Web of Stories). * Interview (1 January 1981, Ithaca, NY) held by the Eugene Dynkin Collection of Mathematics Interviews, Cornell University Library. * Video animation of Mandelbrot set, zoom factor 10342. * , a three-dimensional Mandelbrot-set projection. * Category:1924 births Category:2010 deaths Category:20th-century American mathematicians Category:21st-century French mathematicians Category:20th- century American economists Category:21st-century American economists Category:Alexander von Humboldt Fellows Category:California Institute of Technology alumni Category:Chaos theorists Category:Deaths from cancer in Massachusetts Category:Deaths from pancreatic cancer Category:École Polytechnique alumni Category:Fellows of the American Geophysical Union Category:Fellows of the American Statistical Association Category:Fellows of the Econometric Society Category:Fellows of the American Physical Society Category:French emigrants to the United States Category:French scientists Category:Harvard University people Category:IBM employees Category:IBM Fellows Category:IBM Research computer scientists Category:Institute for Advanced Study visiting scholars Category:Jewish French scientists Category:Members of the Norwegian Academy of Science and Letters Category:Members of the United States National Academy of Sciences Category:Officiers of the Légion d'honneur Category:Polish emigrants to France Category:Polish emigrants to the United States Category:Polish Jews Category:University of Paris alumni Category:Wolf Prize in Physics laureates Category:Yale University faculty Category:Yale Sterling Professors Category:20th-century French mathematicians Category:21st- century American mathematicians "