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	Mitchell Feigenbaum - Biocrawler (Site not responding. Last check: 2007-10-17)
		Mitchell Jay Feigenbaum (born December 19 1944; Philadelphia, USA) is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constant.
		In 1975 Feigenbaum, using the HP-65 computer he was given, discovered that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4.6692.
		Feigenbaum's other contributions include important new fractal methods in cartography when he was hired by Hammond to develop techniques to allow computers to assist in drawing maps.
	www.biocrawler.com /encyclopedia/Mitchell_Feigenbaum (490 words)

	Mitchell Feigenbaum -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-17)
		The son of a (The property of being smooth and shiny) Polish and a (The Slavic language spoken in the Ukraine) Ukrainian immigrant, Feigenbaum's education was not a happy one.
		In 1975 Feigenbaum, using the (additional info and facts about HP-65) HP-65 computer he was given, discovered that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4.6692.
		Feigenbaum's other contributions include important new ((mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry) fractal methods in (The making of maps and charts) cartography when he was hired by Hammond to develop techniques to allow computers to assist in drawing maps.
	www.absoluteastronomy.com /encyclopedia/m/mi/mitchell_feigenbaum.htm (460 words)

	PlanetMath: Feigenbaum constant
		That is, the ratio of the intervals between the bifurcation points approaches Feigenbaum's constant.
		Feigenbaum discovered that this constant arose in any dynamical system that approaches chaotic behavior via period-doubling bifurcation, and has a single quadratic maximum.
		This is version 3 of Feigenbaum constant, born on 2002-04-07, modified 2005-02-28.
	planetmath.org /encyclopedia/FeigenbaumConstant.html (187 words)

	Mitchell Feigenbaum Summary
		The American physicist Mitchell Jay Feigenbaum (born 1944) laid the foundations for studying the world of complicated events in nature by recognizing patterns underlying the application of mathematical equations.
		Mitchell Jay Feigenbaum was born in Philadelphia, Pennsylvania, on December 19, 1944.
		The son of a Polish and a Ukrainian Jewish immigrants, Feigenbaum's education was not a happy one.
	www.bookrags.com /Mitchell_Feigenbaum (1722 words)

	Philosophical Reflections in Physics and Math (Site not responding. Last check: 2007-10-17)
		Mitchell Feigenbaum, a physicist, considered the foregoing case involving color perception to be a crucial example of how order and universality could emerge from apparent chaos and turbulence.
		In general, Feigenbaum found the behavior of the system was extremely sensitive to the value of 'r' which determined the steepness of the arch of the parabola.
		Feigenbaum's universal convergence ratio, however, seemed to provide a window through which to observe the coming into being of the spectrum of frequencies which heralded the transition from orderly to nonlinear behavior in a given system.
	amanesis.org /Physics/chaosd.htm (3258 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		In 1975, Dr. Feigenbaum, using the small HP-65 computer he had been issued, discovered that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4.6692...
		The Logistic map is a prominent example of the mappings that Feigenbaum studied in his noted 1978 article: Quantitative Universality for a Class of Nonlinear Transformations.
		Feigenbaum's other contributions include important new fractal methods in cartography, starting when he was hired by Hammond to develop techniques to allow computers to assist in drawing maps.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Mitchell_Feigenbaum (713 words)

	Feigenbaum (Site not responding. Last check: 2007-10-17)
		Mitchell Feigenbaum's father is Abraham Joseph Feigenbaum, an analytic chemist whose parents had emigrated from a town near Warsaw in Poland to the United States.
		Mitchell was the middle child of his parents three children, having an older brother Edward and a younger sister Glenda.
		Feigenbaum's mother taught him algebra when he was in the fifth form but reading continued to be something that he did not like much.
	www-gap.dcs.st-and.ac.uk /~history/Mathematicians/Feigenbaum.html (1940 words)

	Springer Science+Business Media : Press Releases
		Among the prizewinners is Springer author Mitchell Feigenbaum, Professor and Laboratory Head at Rockefeller University.
		Mitchell Feigenbaum, one of two awardees in the category Physical Sciences and Mathematics, has published articles in Springer’s Journal of Statistical Physics.
		Feigenbaum is well known for his pioneering studies in chaos theory.
	www.springer-sbm.com /index.php?id=291&backPID=132&L=0&tx_tnc_news=2361 (268 words)

	Maps that shape the world
		Feigenbaum therefore designed a computer program that takes data about the boundary around an area to be mapped and calculates what the "optimal conformal projection" (the projection that minimises inaccuracies) will be.
		Feigenbaum's maps of regular shapes such as Australia have a very small distortion, while Africa and North America may be distorted by 3 per cent.
		Feigenbaum treats the space around a point as a continuum, and takes into account the space available in the whole of the mapped area.
	www.fortunecity.com /emachines/e11/86/maps.html (1890 words)

	The Feigenbaum Scenario in a Unified Science of Life and Mind
		The surprising answer demonstrated by Mitchell Feigenbaum in 1975, while he was still a graduate student in physics, is that both order and chaos are generated in the pattern of answers that come from this simple process of iteration.
		The essential dynamics of a Feigenbaum bifurcation diagram is illustrated by a branching tree in figure two where each branch represents an answer or "choice" in the series of solutions to an equation obtained by a process of feedback or iteration.
		The Feigenbaum scenario is presented as a mathematical model of the creative cosmos that could express the common dynamics unifying the sciences of matter, life and mind.
	www.ernestrossi.com /feigenbaumUnifiedLifeMind.htm (5029 words)

	MITCHELL FEIGENBAUM (Site not responding. Last check: 2007-10-17)
		Mitchell Feigenbaum, einer der größten Naturwissenschaftler des letzten Jahrhunderts, formuliert ein Konzentrat seines Denkens, welches ihn zur Entdeckung der Zahlen alpha = 2, 50290 und delta = 4,69920 geführt hat, die ihm zu Ehren Feigenbaumzahlen genannt werden.
		Die filmische Zeigweise nutzt chaotische Prozesse in der Filmchemie, um über die Entwicklungsvorgänge des Filmmaterials den Inhalt der Gedanken von Mitchell Feigenbaum in Analogie zu visualisieren.
		Mitchell Feigenbaum, one of the most important scientist of the last century, formulates a condensed extract of his process of reasoning, which led him to the discovery of the numbers alpha = 2,50290 and delta = 4,69920, which are called Feigenbaumnumbers so as to honour him.
	www.wernernekes.de /vhs012.html (214 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		Feigenbaum's inspiration was to wonder whether other phenomena considered to be chaotic might also be pseudo-random, obeying deterministic programs just as pseud-random numbers do.
		The startling aspect of Feigenbaum's work was his discovery that despite the different operations performed by different nonlinear functions--despite the different dance steps they used- -their iterated paths approached chaos at the same rate and showed the same characteristic patterns of period doubling.
		Feigenbaum works with the exact definitions of mathematical formulae; Derrida is concerned with language, which is notoriously resistant to formalization.
	xroads.virginia.edu /~DRBR/hayles.txt (6980 words)

	Chaos-Making a New Science by James Gleick
		Clouds represented a side of nature that the mainstream of physics had passed by, a side that was at once fuzzy and detailed, structured and unpredictable.
		In 1974, though few of his colleagues knew it, Feigenbaum was working on a problem that was deep: chaos.
		For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the turbulent sea, in the fluctuations of wildlife populations, in the oscillations of the heart and the brain.
	www.around.com /chaos.html (1460 words)

	Falling all the way: Cascade diagrams
		The ratios of the gaps in the fourth column of Table 8 was discovered by Feigenbaum to have a limit value 4.6692....
		The story goes that Feigenbaum was so excited by the universality of his number that he immediately called his mom and related how this number would make him famous.
		The proof of one version of the universality of Feigenbaum's number was given in [CE80].
	www.math.okstate.edu /mathdept/dynamics/lecnotes/node54.html (757 words)

	Los Alamos: Blinded by profits? - Opinion
		Mitchell Feigenbaum represents one of the most eccentric and brilliant minds to inhabit the Theoretical Division of Los Alamos National Laboratory in the 1970s.
		An atmospheric scientist who experimented with a 26-hour work day, Feigenbaum was one of the founders of chaos theory and embodies the non-nuclear side of LANL - perhaps the only side that Einstein would still be proud of.
		The hotbed of creativity of Mitchell Feigenbaum's Los Alamos may be a thing of the past, as business interests portend to strangle science at an already reeling facility.
	www.dailytexanonline.com /news/2004/07/07/Opinion/Los-Alamos.Blinded.By.Profits-691803.shtml (845 words)

	math lessons - Mitchell Feigenbaum
		Mitchell Jay Feigenbaum (born December 19 1944; Philadelphia, USA) is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constant.
		The Logistic map is a well known example of the mappings that Feigenbaum studied in his famous 1978 article: Quantitative Universality for a Class of Nonlinear Transfomations.
		"Using fractal geometry to describe natural forms such as coastlines, mathematical physicist Mitchell Feigenbaum developed software capable reconfiguring coastlines, borders, and mountain ranges to fit a multitude of map scales and projections.
	www.mathdaily.com /lessons/Mitchell_Feigenbaum (498 words)

	An Experiment with Mathematics
		The higher periods have another remarkable property which was analysed by Mitchell Feigenbaum in the 1970s when he was at Los Alamos in the US.
		Feigenbaum found that the same numbers and the same structure appear for all sufficiently smooth functions f(x), whose graph has only one maximum.
		Period doubling and Feigenbaum numbers appear not only on the mathematician's computer screen but also in many kinds of natural chaos including the dripping tap and the beating heart.
	www.fortunecity.com /emachines/e11/86/expmaths.html (2917 words)

	Nov 28, Question 2 (Site not responding. Last check: 2007-10-17)
		Instead, I think that Ruelle was trying to tell us that Mitchell Feigenbaum’s experimental result stands out in the theory of chaos.
		This leads me to believe that Feigenbaum's findings were so groud breaking that it took an editor who understood the subject to publish it.
		I also feel that Ruelle did NOT consider Feigenbaum's theory to be mistaken, as mentioned, Ruelle states "in hydrodynamics was a particularly convincing proof that modes had to give way to chaos" (p.69).
	www.yorku.ca /bwall/math3500/responses/nov28q2.htm (1656 words)

	[No title]
		One of the first persons to study chaotic behavior in simple mathematical systems was Mitchell Feigenbaum.
		Feigenbaum wanted to create a mathematical feed-back system based on a quadratic equation.
		Feigenbaum wanted to study a simple quadratic where the orbit of a starting point would not "blow-up" to infinity.
	archive.ncsa.uiuc.edu /Classes/MATH198/whubbard/GRUMC/geometryExplorer/help/examples/cobwebChaos.html (910 words)

	References for Feigenbaum (Site not responding. Last check: 2007-10-17)
		M J Feigenbaum, Using nonlinear dynamics to make a new world atlas, in Towards the harnessing of chaos (Amsterdam, 1994), 1-9.
		M J Feigenbaum, Scaling function dynamics, in Chaos, order, and patterns, Lake Como, 1990 (New York, 1991), 1-23.
		M J Feigenbaum, Low-dimensional dynamics and the period doubling scenario, in Dynamical systems and chaos, Sitges/Barcelona, 1982 (Berlin, 1983), 131-148.
	www-history.mcs.st-and.ac.uk /References/Feigenbaum.html (112 words)

	MLA 31500 (Site not responding. Last check: 2007-10-17)
		This chapter centers on a famous contribution to nonlinear dynamics and the theory of chaotic behavior made by Mitchell Feigenbaum while he worked at the Los Alamos National Laboratory.
		FeigenbaumÕs scientific and professional background had both conventional and unconventional aspects.
		In GleickÕs book, we read of Robert MayÕs investigations of the logistic map, Mitchell FeigenbaumÕs discovery of scaling and universality, and Albert LibchaberÕs experiment on thermal convection in liquid helium.
	astro.uchicago.edu /~voort/mla315notes5 (610 words)

	Symposia presnted by the Tureck Bach Research Foundation (Site not responding. Last check: 2007-10-17)
		After a buffet lunch the afternoon session was chaired by Dr. Robin Stinchcombe, Physics, and consisted of lectures by Professor Sir Roger Penrose, Rouse Ball Professor of Mathematics, and Professor Richard Dawkins, Biology.
		The morning of December 17 was occupied by a Round Table Discussion of ideas that emerged from the lectures with Rosalyn Tureck, Mitchell Feigenbaum, Roger Penrose and Dr Richard Dawkins.
		Lectures from this First Annual Symposium are contained in the first issue of the Tureck Bach Research Foundation journal, INTERACTION, published 2 April 1997 containing the lectures by Rosalyn Tureck, Mitchell Feigenbaum and Roger Penrose.
	www.connectedglobe.com /tbrf/symposium1.html (296 words)

	Logistic Map
		In 1976, Robert May and Mitchell Feigenbaum discovered an equation that shocked the scientific community.
		To make this equation easier to study, May and Feigenbaum created one graph that shows the results for many different values of g.
		The logistic map (below) is a graph for all values of g from 0 to 4 that shows the end result(s) of the equation.
	www.geocities.com /CapeCanaveral/Hangar/7959/logisticmap.html (453 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		During World War II, because of the long range aircraft and their dependence on the weather Feigenbaum believed weather forecasting could be reduced to a combination of equations.
		Feigenbaum began CIA funded weather studies at Los Alamos and began looking for chaos everywhere.
		In the 1960s the very earliest powerful analog computers were used to model the weather, and added some clues to the complexity of the problem while chaos (the mathematics) was begun and the term the “butterfly effect” was introduced.
	www.polyvin.com /Chaosltr.html (2040 words)

	Tea at the Ford (Site not responding. Last check: 2007-10-17)
		Mitchell Feigenbaum is a physicist who's done major work in chaos theory.
		Mitchell Feigenbaum is apparently the author of the chaos theory.
		Feigenbaum made several significant contributions to the logistic map which models chaotic behavior.
	www.teaattheford.net /conversation.php?id=908 (19009 words)

	A Beginner's Guide to Chaos: Feigenbaum's Bifurcation Diagram (Site not responding. Last check: 2007-10-17)
		The bifurcation diagram was not created by Mitchell Feigenbaum, but he found a way to understand it that no one had thought of.
		Feigenbaum discovered that the bifurcations were occurring at a ratio that approached an irrational number that is approximately 4.669 in the bifurcation diagram.
		4.669 is a universal constant in much the same way 3.14 is. Feigenbaum's bifurcation diagram is often called the fig tree because Feigenbaum means fig tree in German (also the bifurcation diagram looks somewhat like a sideways tree).
	www.yiin.ca /chaos/fig.htm (158 words)

	Definition of Mitchell Feigenbaum
		Mitchell Jay Feigenbaum (born December 19 1944; Philadelphia, USA) is a mathematician whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constant.
		"Using fractal geometry to describe natural forms such as coastlines, mathematical physicist Mitchell Feigenbaum developed software capable reconfiguring coastlines, borders, and mountain ranges to fit a multitide of map scales and projections.
		The list of authors can be found here.
	www.wordiq.com /definition/Mitchell_Feigenbaum (539 words)

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