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The Beauty Of Fractals
''The Beauty of Fractals'' is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success. The book includes a total of 184 illustrations, including 88 full-colour pictures of Julia sets. Although the format suggests a coffee table book, the discussion of the background of the presented images addresses some sophisticated mathematics which would not be found in popular science books. In 1987 the book won an Award for distinguished technical communication. Summary The books starts with a general introduction to Complex Dynamics, Chaos and fractals. In particular the Feigenbaum scenario and the relation to Julia sets and the Mandelbrot set is discussed. The following special sections provide in depth detail for the shown images: Verhulst Dynamics, Julia Sets and Their Computergraphical Generation, Sullivan's Classifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heinz-Otto Peitgen
Heinz-Otto Peitgen (born April 30, 1945 in Bruch, Nümbrecht near Cologne) is a German mathematician and was President of Jacobs University from January 1, 2013 to December 31, 2013. Peitgen contributed to the study of fractals, chaos theory, and medical image computing, as well as helping to introduce fractals to the broader public. Life Peitgen studied mathematics, physics and economics from 1965 until 1971 in Bonn, where he received his PhD in 1973. His doctoral dissertation was entitled “Asymptotische Fixpunktsätze und Stabilität” (English: “Asymptotic Fixed-point Theorems and Stability”). After receiving his habilitation in 1977, he was awarded a professorship in mathematics at the University of Bremen, where he served until 2012. There, he was involved in establishing and developing the Institute for Dynamical Systems, where in 1982 he set up a computer graphics laboratory for mathematical experiments. Since 1992, Peitgen has served as the director of the Cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia Set
In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values. Thus the behavior of the function on the Fatou set is "regular", while on the Julia set its behavior is "chaotic". The Julia set of a function is commonly denoted \operatorname(f), and the Fatou set is denoted \operatorname(f). These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century. Formal definition Let f(z) be a non-constant holomorphic function from the Riemann sphere on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science Books
A science book is a work of nonfiction, usually written by a scientist, researcher, or professor like Stephen Hawking (''A Brief History of Time''), or sometimes by a non-scientist such as Bill Bryson ('' A Short History of Nearly Everything''). Usually these books are written for a wide audience presumed to have a general education rather than a specifically scientific training, as opposed to the very narrow audience that a scientific paper would have, and are therefore referred to as popular science. As such, they require considerable talent on the part of the author to sufficiently explain difficult topics to people who are totally new to the subject, and a good blend of storytelling and technical writing. In the UK, the Royal Society Prizes for Science Books are considered to be the most prestigious awards for science writing. In the US, the National Book Awards briefly had a category for science writing in the 1960s, but now they just have the broad categories of fiction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1986 Non-fiction Books
The year 1986 was designated as the International Year of Peace by the United Nations. Events January * January 1 ** Aruba gains increased autonomy from the Netherlands by separating from the Netherlands Antilles. **Spain and Portugal enter the European Community, which becomes the European Union in 1993. *January 11 – The Gateway Bridge in Brisbane, Australia, at this time the world's longest prestressed concrete free-cantilever bridge, is opened. * January 13– 24 – South Yemen Civil War. * January 20 – The United Kingdom and France announce plans to construct the Channel Tunnel. *January 24 – The Voyager 2 space probe makes its first encounter with Uranus. * January 25 – Yoweri Museveni's National Resistance Army Rebel group takes over Uganda after leading a five-year guerrilla war in which up to half a million people are believed to have been killed. They will later use January 26 as the official date to avoid a coincidence of dates with Dictator Idi Amin's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frontiers Of Chaos
Frontiers may refer to: * Frontier, areas near or beyond a boundary Arts and entertainment Music * ''Frontiers'' (Journey album), 1983 * ''Frontiers'' (Jermaine Jackson album), 1978 * ''Frontiers'' (Jesse Cook album), 2007 * ''Frontiers'' (Psycho le Cemu album), 2003 * "Frontiers", a song by Symphony X from ''The Odyssey'' * Frontiers Records, an Italian record label Other uses in arts and entertainment * ''Frontier(s)'', a 2007 horror film * ''Frontiers'' (magazine), a LGBT magazine * ''Frontiers'' (1989 TV series), a 1989 British documentary series that aired on the BBC * ''Frontiers'' (1996 TV series), a 1996 British crime drama that aired on ITV Science and academia ''Frontiers in...'' series of journals * Frontiers Media, publisher of the ''Frontiers in...'' series of 59 journals * ''Frontiers in Endocrinology'' * ''Frontiers in Plant Science'' * ''Frontiers in Psychology'' * ''Frontiers in Physics'' * ''Frontiers for Young Minds'', not part of the series proper P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert W
Herbert may refer to: People Individuals * Herbert (musician), a pseudonym of Matthew Herbert Name * Herbert (given name) * Herbert (surname) Places Antarctica * Herbert Mountains, Coats Land * Herbert Sound, Graham Land Australia * Herbert, Northern Territory, a rural locality * Herbert, South Australia. former government town * Division of Herbert, an electoral district in Queensland * Herbert River, a river in Queensland * County of Herbert, a cadastral unit in South Australia Canada * Herbert, Saskatchewan, Canada, a town * Herbert Road, St. Albert, Canada New Zealand * Herbert, New Zealand, a town * Mount Herbert (New Zealand) United States * Herbert, Illinois, an unincorporated community * Herbert, Michigan, a former settlement * Herbert Creek, a stream in South Dakota * Herbert Island, Alaska Arts, entertainment, and media Fictional entities * Herbert (Disney character) * Herbert Pocket (''Great Expectations'' character), Pip's close friend and roommate in the Cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adrien Douady
Adrien Douady (; 25 September 1935 – 2 November 2006) was a French mathematician. Douady was a student of Henri Cartan at the École normale supérieure, and initially worked in homological algebra. His thesis concerned deformations of complex analytic spaces. Subsequently, he became more interested in the work of Pierre Fatou and Gaston Julia and made significant contributions to the fields of analytic geometry and dynamical systems. Together with his former student John H. Hubbard, he launched a new subject, and a new school, studying properties of iterated quadratic complex mappings. They made important mathematical contributions in this field of complex dynamics, including a study of the Mandelbrot set. One of their most fundamental results is that the Mandelbrot set is connected; perhaps most important is their theory of renormalization of (polynomial-like) maps. The Douady rabbit, a quadratic filled Julia set, is named after him. Douady taught at the University of Nice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benoît Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-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". 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, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandelbrot Set
The Mandelbrot set () is the set of complex numbers c for which the function f_c(z)=z^2+c does not diverge to infinity when iterated from z=0, i.e., for which the sequence f_c(0), f_c(f_c(0)), etc., remains bounded in absolute value. This set was first defined and drawn by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian groups. Afterwards, in 1980, Benoit Mandelbrot obtained high-quality visualizations of the set while working at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York. Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications; mathematically, one would say that the boundary of the Mandelbrot set is a ''fractal curve''. The "style" of this recursive detail depends on the region of the set boundary being examined. Mandelbrot set images may be created by sampling the complex numbers and testing, for each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mitchell Feigenbaum
Mitchell Jay Feigenbaum (December 19, 1944 – June 30, 2019) was an American mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants. Early life Feigenbaum was born in Philadelphia, Pennsylvania, to Jewish emigrants from Poland and Ukraine. He attended Samuel J. Tilden High School, in Brooklyn, New York, and the City College of New York. In 1964, he began his graduate studies at the Massachusetts Institute of Technology (MIT). Enrolling for graduate study in electrical engineering, he changed his area of study to physics. He completed his doctorate in 1970 for a thesis on dispersion relations, under the supervision of Professor Francis E. Low. Career After short positions at Cornell University (1970–1972) and the Virginia Polytechnic Institute and State University (1972–1974), he was offered a longer-term post at the Los Alamos National Laboratory in New Mexico to study turbulence in fluids. Although a complete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Richter
Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a surname (including a list of people with the name) Culture * Peter (actor) (born 1952), stage name Shinnosuke Ikehata, Japanese dancer and actor * ''Peter'' (album), a 1993 EP by Canadian band Eric's Trip * ''Peter'' (1934 film), a 1934 film directed by Henry Koster * ''Peter'' (2021 film), Marathi language film * "Peter" (''Fringe'' episode), an episode of the television series ''Fringe'' * ''Peter'' (novel), a 1908 book by Francis Hopkinson Smith * "Peter" (short story), an 1892 short story by Willa Cather Animals * Peter, the Lord's cat, cat at Lord's Cricket Ground in London * Peter (chief mouser), Chief Mouser between 1929 and 1946 * Peter II (cat), Chief Mouser between 1946 and 1947 * Peter III (cat), Chief Mouser between 1947 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
