81. Fractal Geometry In the 1970s this cascade was studied (for a process equivalent to looking at theMandelbrot set for real numbers) by mitchell feigenbaum, and Pierre Coulette http://classes.yale.edu/math190a/Fractals/MandelSet/MandelScalings/MandelScaling

82. Feigenbaum-Diagramm(4) Translate this page Endzustandsdiagramm für alle möglichen a zwischen 1 und 4 haben, so entsteht dasnach dem amerikanischen Physiker mitchell J. feigenbaum benannte feigenbaum http://www.freiequelle.de/chaos/4_fei.html

Site Map freiequelle.de Chaos Feigenbaum-Diagramm(4) Feigenbaum-Diagramm Auf der x-Achse ist der Parameter a a zwischen und haben, so entsteht das nach dem amerikanischen Physiker Mitchell J. Feigenbaum benannte Feigenbaum - Diagramm Bild 12 : Endzustandsdiagramm der Funktionschar f(x)=ax(1-x) a=1...4 (Feigenbaum - Diagramm). ( Nehmen wir zum Beispiel a=2.8 . Iteriert man nun die Funktion f(x)=2.8x(1-x) (Funktionsgraphen siehe Bild 5 a=4 an so sehen wir das schon aus Bild 7 bekannte Chaos. Feigenbaum-Punkt Schaut man sich den Verlauf des Diagramms ab dem Wert a=3 an, so tritt genau im Punkt a=3 eine Bifurkation auf a=3.449490... auf . Die ersten sieben Bifurkationspunkte (Periodenverdoppelungspunkte) sind in der folgenden Tabelle dargestellt: Bifurkationpunkte Differenzen Feigenbaum - Punkt , welcher den Wert a=s_unendlich=3.5699456... hat. Alle a rechts im Koordinatensystem von diesem Punkt ( ) enden im Chaos. Feigenbaum-Konstante k delta ist. universal . Da delta Fraktal 11. Aug 2002 weiter: Fazit(5) Kennzeichen des Chaos(3) freiequelle.de Chaos Feigenbaum-Diagramm(4) Site Map

83. Fractal Links - Ulli's Fractal Home EMail. Ihre Lieblingsadresse..bitte mitteilen. mitchell feigenbaum,Fractal VIPs ..mitchell feigenbaum. Michael Barnsley, http://www.fraktalwelt.de/myhome/frlinks.htm

Ulli's Fractal Home [Links] Home Ring Introduction Liapunov Lindenmayer I Lindenmayer II IFS I Feigenbaum Lake Iterations IFS II Branches IFS III Hyperbolic IFS IV Fractal Gallery Essays Links awards Thanks for visiting my Fractal Home. I hope that you are one of the persons who are fascinated by fractals like me. If you don't did it before, here is your last chance to send an EMail . If you don't want to because it's your first contact with the subject 'fractal' or my offers are not what you've searched for, then take my fractal links to other sites perhaps to learn more about fractals. Good bye, surf in again a next time! EMail Kontakt aufnehmen. Ansonsten benutzen Sie doch meine Links, um vielleicht etwas Passenderes zu finden. Ulli Surf out to... Wachstumssimulationen FRACTINT Homepage Best universal fractal program (excellent Mandelbrot) Fractal Link Collection Mehr fraktale Links im Suchkatalog School! FAME Riesiges Fraktalmuseum mit Hintergrundinfos Your favorite fractal link Please tell me by EMail. Ihre Lieblingsadresse..bitte mitteilen. Fractal VIPs Mitchell Feigenbaum Fractal VIPs Michael Barnsley Fractal VIPs Benoit Mandelbrot This site won the following awards: back to the top

84. Unfolding Processes, Emergent Phenomena And Numbers' Structural Legacy - Mitchel Topic Structure Principles and Applications in the Sciences and Music. ProfessorMitchell feigenbaum (Theoretical Physics, Rockefeller University). http://www.connectedglobe.com/tbrf/webinteraction1/journal0101.html

Purposes History Symposia Journal Trustees Membership Tureck Email Bookshop INTERACTION, Volume I Date of publication: 15th April, 1997 Proceedings of the First International Symposium, Oxford, December 1995 Topic: Structure: Principles and Applications in the Sciences and Music Professor Mitchell Feigenbaum (Theoretical Physics, Rockefeller University) Unfolding Processes, Emergent Phenomena and Numbers' Structural Legacy "It is a pleasure to be here. As I was walking outside and smoking, I noticed that there is a motto on the building. The motto says "Get knowledge, get riches but with all thy gettings get understanding". Basically that is what I will try to talk about. The subject of physics concerns itself with things that are characterized by order, regularity and invariance. These are almost the same words, and I will try to address as I go along different aspects of that. do with nature. You probably know that Pythagoreans took that relation very seriously and regarded nature as coequal to number. Moreover, nature was regarded as a discretion, in the sense that it was discrete, built out of pieces, so to speak numbers. It is hard to know what these things mean, one has lost too many references over the millennia. You probably know that in general we don't believe that anymore, that is, we don't believe in general that the world is discrete. That doesn't mean we can't entertain the possibility that it is. The notion (of convention) of a continuum makes sense when one thinks of Zeno's paradoxes, which are paradoxes against the idea of the world being discrete, but rather needing a continuum for its description.

85. Exploring The Feigenbaum Fractal What is the logistic equation? The logistic equation is the formula MitchellFeigenbaum mainly worked upon developing the theory behind these fractals. http://www.stud.ntnu.no/~berland/math/feigenbaumold/explore.html

Exploring the Feigenbaum fractal This page is not finished yet, but will contain the following topics. What is the logistic equation? Why does x stop converging at 0.75? What do the windows do in the image? What is the Feigenbaumattractor? ... Could the Feigenbaum formula be used to generate random numbers? What is the logistic equation? The logistic equation is the formula Mitchell Feigenbaum mainly worked upon developing the theory behind these fractals. The formula is meant to describe population. f(x) = a * x * (1 - x) A simple model of population over time is a proportional relationship to the last year. Say we had x animals last year. This year we should have a*x animals. But this does not apply to the real nature. A better description would be to include a factor dependant on how much room there is left, and let x express the ratio of fullness in the area (from to 1). Then the 1-x factor is added, so that if the area is almost full, the population will not increase beneath the upper limit. Expanding the logistic equation, we get:

86. Biografisk Register Translate this page 365-300 f.Kr.) Euler, Leonhard (1707-83) Faltings, Gerd (1954-) feigenbaum, MitchellJ. (1943-) Feit, Walter Fermat, Pierre de (1601-65) Ferrari, Ludovico (1522 http://www.geocities.com/CapeCanaveral/Hangar/3736/biografi.htm

Biografisk register Matematikerne er ordnet alfabetisk på bakgrunn av etternavn. Linker angir at personen har en egen artikkel her. Fødsels- og dødsår oppgis der dette har vært tilgjengelig. Abel, Niels Henrik Abu Kamil (ca. 850-930) Ackermann, Wilhelm (1896-1962) Adelard fra Bath (1075-1160) Agnesi, Maria G. (1718-99) al-Karaji (rundt 1000) al-Khwarizmi, Abu Abd-Allah Ibn Musa (ca. 790-850) Anaximander (610-547 f.Kr.) Apollonis fra Perga (ca. 262-190 f.Kr.) Appel, Kenneth Archytas fra Taras (ca. 428-350 f.Kr.) Argand, Jean Robert (1768-1822) Aristoteles (384-322 f.Kr.) Arkimedes (287-212 f.Kr.) Arnauld, Antoine (1612-94) Aryabhata (476-550) Aschbacher, Michael Babbage, Charles (1792-1871) Bachmann, Paul Gustav (1837-1920) Bacon, Francis (1561-1626) Baker, Alan (1939-) Ball, Walter W. R. (1892-1945) Banach, Stéfan (1892-1945) Banneker, Benjamin Berkeley, George (1658-1753) Bernoulli, Jacques (1654-1705) Bernoulli, Jean (1667-1748) Bernstein, Felix (1878-1956) Bertrand, Joseph Louis Francois (1822-1900) Bharati Krsna Tirthaji, Sri (1884-1960)

87. Feigenbaum ͼ The summary for this Chinese (Simplified) page contains characters that cannot be correctly displayed in this language/character set. http://iai.edu123.com/math/math_05/misc/html/chaosb.htm

Feigenbaum ͼ µü´ú¶þ´Î·½³Ìf(x)=ax(1-x) ÊÇ»ìÂÒµÄÒ»¸öÖøûÀý×Ó. ÏÂæµÄС³ÌÐò»­³öÁËÕâ¿Îº¯Êý µÄËùÓÐatractors.ÍêȫͼÊǸù¾ÝÎïÀíѧ¼ÒMitchell Feigenbaum (USA)üûµÄ. "µü´ú f(x)=ax(1-x)" IAIÖÐÐÄ edu123.com °æȨËùÓÐ

88. Randy Braith's Home Page J Am Coll Cardiol 1999;3411701175. feigenbaum M, Welsch M, MitchellM, Vincent K, Pepine C, Pollock M, Braith RW. Contracted plasma http://www.hhp.ufl.edu/ess/faculty/rbraith/rbraith.htm

RANDY W. BRAITH, Associate Professor Department of Exercise and Sport Sciences, and the Department of Medicine (Division of Cardiology) and Physiology EDUCATIONAL BACKGROUND BS: Bemidji State University, Mn., 1973 MS: St. Cloud State University, Mn., 1984 PhD: University of Florida, 1991 Post-Doc: University of Florida, 1993 RESEARCH INTERESTS glucocorticoids as part of their immunosuppression regimen. All pharmacological interventions have failed to prevent osteoporosis in patients receiving long-term glucocorticoids. However, we have clearly demonstrated that resistance exercise is osteogenic and effective in preventing glucocorticoid-induced osteoporosis. We are currently examining the efficacy of combining the anti-resorptive effects of bisphosphonate agents with the osteogenic effects of progressive resistance training in an attempt to devise the optimal anti-osteoporosis therapy for organ transplant recipients. We are concurrently investigating the catabolic effects of glucocorticoids on skeletal muscle in organ transplant recipients. Through muscle biopsy techniques and gel electrophoresis we are determining the efficacy of resistance exercise training in reversing skeletal muscle myopathy in both heart failure and heart transplant recipients.

89. RECENT RESEARCH PUBLICATIONS Rehabilitation of Heart Transplant Recipients. Circulation 2000, (in press). FeigenbaumM, Welsch M, mitchell M, Vincent K, Pepine C, Pollock M, Braith RW. http://www.hhp.ufl.edu/ess/clinphys/BPUBLICATION.htm

RECENT RESEARCH PUBLICATIONS Braith RW , R.M. Mills, C.S. Wilcox, G.L. Davis, and C.E. Wood. Breakdown of Blood Pressure and Fluid Volume Homeostasis in Heart Transplant Recipients. J Am Coll Cardiol Braith RW , R.M. Mills, V.A. Convertino, C.S. Wilcox, G.L. Davis, and C.E. Wood. Fluid Homeostasis After Heart Transplantation: The Role of Cardiac Denervation. J Heart Lung Transplant Braith RW , R.M. Mills, M.A. Welsch, M.H. Pollock, J. Keller. Resistance Training Reverses Steroid-Induced Osteoporosis After Heart Transplantation. J Amer Coll Cardiol Baylis C, Braith RW , B Santmyire, K. Engles. Renal Nerve Activity Does not Mediate Vasoconstrictor Responses to Acute Nitric Oxide Synthesis Inhibition in Conscious Rats. J Amer Soc Nephr Braith RW and M.A. Welsch. Exercise Training in Heart Failure. In: Practical Approaches to the Treatment of Heart Failure Eds. R.M. Mills and J. Young. Williams and Wilkins, 1998:125-147. Braith RW , M.A. Welsch, R.M. Mills, J.W. Keller, M.L. Pollock. Resistance Exercise Prevents Glucocorticoid-Induced Myopathy in Heart Transplant Recipients. Med Sci Sports Exerc Braith RW and M.J. Mitchell.

90. CHAPITRE 4 : LA CONSTANTE DE FEIGENBAUM Translate this page La découverte de cette constante est due entièrement au mathématicien MitchellJ. feigenbaum, qui l'a calculée à l'aide d'une simple calculette vers 1975. http://josephv.test.free.fr/fractal/feigenbaum/FEIGENBAUM.html

CHAPITRE 4 : LA CONSTANTE UNIVERSELLE DE FEIGENBAUM FICHIER MAPLE CORRESPONDANT : FEIGENBAUM.MWS A ] Les bifurcations de Feigenbaum Comme on l'a vu dans le chapitre 1 , l'itérateur quadratique possède un attracteur qui dépend de . Pour tenter de visualiser les variations de cet attracteur en fonction du paramètre , on peut utiliser la procédure feigenbaum , qui admet trois arguments : début et fin sont les bornes respectivement inférieure et supérieure de l'intervalle des paramètres que l'on veut visualiser. pas est la distance que l'on prend entre deux points consécutifs de l'intervalle considéré. Plus l'intervalle est étroit, plus on a intérêt à choisir pas petit, mais il faut naturellement tenir compte de la vitesse et surtout de la mémoire de la machine. On pourra aussi modifier le test d'arrêt de compteurs de boucle k au sein de la procédure. Dans un premier temps, feigenbaum(1,4,pas) , où pas est à définir (par exemple 0.01), permet de visualiser les variations générales. On obtient ce qu'on appelle le diagramme de Feigenbaum Comme on l'a vu dans le chapitre 1 , l'attracteur est d'abord formé d'un unique point, qui est le point fixe attractif de l'itérateur. Puis apparaissent successivement les cycles de longueur 2, 4, 8, ..., pour des valeurs successives des paramètres qu'une utilisation patiente et minutieuse de la procédure

91. Stanford Computer Forum - Faculty Profile - John Mitchell http://forum.stanford.edu/profile/mitchell.html

Home Search About the Forum Video Page ... Faculty Profile Faculty Member... Mary Baker Serafim Batzoglou Tom Binford Dan Boneh David Cheriton William J. Dally Giovanni De Micheli David Dill Dawson Engler Ron Fedkiw Edward Feigenbaum Richard Fikes Mike Flynn Armando Fox Hector Garcia-Molina Mike Genesereth Bernd Girod Gene H. Golub Leonidas J. Guibas Patrick Hanrahan John Hennessy Mark Horowitz Oussama Khatib Don Knuth Daphne Koller Christos Kozyrakis Monica Lam Jean-Claude Latombe Marc Levoy David Luckham Zohar Manna Chris Manning Teresa Meng John McCarthy Edward McCluskey Nick McKeown John Mitchell Rajeev Motwani Andrew Ng Nils Nilsson Joseph Oliger Kunle Olukotun Serge Plotkin Balaji Prabhakar Vaughan Pratt Eric Roberts Mendel Rosenblum Kenneth Salisbury Russ Shackelford Yoav Shoham Fouad Tobagi Jeff Ullman Jennifer Widom Gio Wiederhold Terry Winograd Mihalis Yannakakis Research Areas Select Area... Information Systems Systems/Ubiquitous Computing Computation Architecture Interaction Infrastructure Representation Computation Speech Game Theoretic Methods Compilers Physical Modeling Computing Operating Systems /Dependability John Mitchell Professor of Computer Science Gates Bldg. 476

92. Advent...or Waiting I was reading recently about the work of the mathematician MitchellFeigenbaum. He wanted to understand how it could be that patterns http://unitytemple.org/sermons/Archive/wait98.htm

T h e U n i t y T e m p l e P u l p i t A sermon by F. Jay Deacon Delivered at Unity Temple Unitarian Universalist Congregation Oak Park, Illinois December 6, 1998 couple of weeks ago I spoke of Harvest, the time when things are ripe and it is time to harvest it. Many of the moments of our lives are times for some small harvest and a few moments are ripe for some major gathering in of the fruit of long periods of planting and laboring and waiting. But most of the moments of our lives are planting times, watering times, waiting times, nothing quite ripe. I will not ask, have you ever waited. Everyone has waited, and wondered, felt sometimes the stagnancy and sometimes the dread of waiting. If your religious background is Christian, you will recognize this season as Advent, and Advent is about that, really. It comes from biblical stories composed by Jewish people living under a cruel Roman occupation. They placed their hope in a Messiah. The Galilean teacher Jesus began to teach a different vision of what this Kingdom was that they were supposed to be waiting for. It is hard to wait, and there is something in us that feels itself to be waiting because it is stirred by hope as well as fear, something in us that wants to know how to wait, how to be with this time. But we wait. In a hopeful discontent in our private lives, and beyond that, we may feel the advent of some great spiritual renaissance that is slowly emerging from the ruins of our civilization.

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