1. Feigenbaum Mitchell Jay Feigenbaum. Born 19 Dec 1944 in Philadelphia, USA. Click thepicture above to see three larger pictures Show birthplace location. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Feigenbaum.html

Mitchell Jay Feigenbaum Born: 19 Dec 1944 in Philadelphia, USA Click the picture above to see three larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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's (or Mitch's as he is known) mother is Mildred Sugar whose parents emigrated to the United States from Kiev. Mitchell was the middle child of his parents three children, having an older brother Edward and a younger sister Glenda. Mitchell entered a public school for gifted children when he was five years old. Unlike Edward who displayed all the characteristics of a child prodigy, reading from a very young age, Mitchell could not read when he entered school and he needed tutoring from his mother to bring him up to the level of the other children. Moved to a different school, he became somewhat bored and had no friends among the other children. In fact up until the time he went to university Mitchell would not enjoy the company of his fellow pupils. 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. Perhaps the reason was that he tried reading articles in

2. Princíp Spätnej Väzby A Deterministický Chaos 12 feigenbaum mitchell QUANTITATIVE UNIVERSALITY FOR CLASS OF NONLINEARTRANSFORMATIONS. JOURNAL OF STATISTIC PHYSICS 19 (1978) STR.. http://www.geocities.com/kozmologia/clanok1.html

spä na hlavnú stránku anglicky webdesign: miki nko Princíp spätnej väzby a deterministický chaos MikulᚠAlexík Žilinská univerzita v Žiline, FRI-KTK, Ve¾ký diel, 01026 Žilina Abstrakt: V príspevku je poukázané, že vo viacerých oboroch èinnosti sú prejavy deterministického chaosu spojené s vlastnosami spätnej väzby v danej oblasti. V technických systémoch je známa syntéza obvodov s vlastnosami deterministického chaosu a bolo poukázané na jeho kladné vlastnosti. "Boh hrá s vesmírom kocky. Ale sú to kocky, v ktorých je zaliate olovo. A hlavným cie¾om fyziky dnes je zisti, pod¾a akých pravidiel tam bolo zaliate a ako by sme to mohli využi vo svoj prospech." Joseph Ford, technologický inštitút Georgia Organizátor prvej konferencie o chaose v r. 1977, Como, Italia Edmund Huserl v závere svojej práce Karteziánske meditácie cituje Augustina "Noli foras ire, in te redi, in inferiore homine habitat veritas" (Nechoï na námestia, v tebe hovorím, pravda sídli v ¾udskom vnútre). 1. Úvod

3. Mitchell Feigenbaum Lab Pioneered bifurcations in the mid 70s and for whom the feigenbaum tree is named.Category Science Math Chaos and Fractals Chaos People......Back to RU Home, Laboratory of Mathematical Physics mitchell feigenbaumToyota Professor. Nonlinear systems and chaotic dynamics. http://www.rockefeller.edu/labheads/feigenbaum/feigenbaum.html

Laboratory of Mathematical Physics Mitchell Feigenbaum Toyota Professor Nonlinear systems and "chaotic" dynamics. Our lab investigates the new field of nonlinear systems and "chaotic" dynamics. We create analytical methods of description and time evolution of complicated disordered phenomena. It is the main effort of this laboratory to extend the scope of the problems over which these methods hold sway, to extend the methods themselves developing appropriate mathematics and to improve the methods for extracting such information from actual experimental studies ranging from fluids to brains. Lab Web Page Lab Members E-mail Publications

4. ACM Guide: Author Index Translate this page EA Feigenbaum E. Feigenbaum Edward A. Feigenbaum Edward Feigenbaum J FeigenbaumJ. Feigenbaum Joan Feigenbaum Leslie feigenbaum mitchell J. Feigenbaum. http://portal.acm.org/authors.cfm?part=author&coll=portal&dl=ACM&row=F&idx=57&id

5. Www.tbtf.com/resource/macarthurites.txt Weiss Jay Michael 3/84 Woese Carl R. 3/84 Bernstein Shelly C. 11/84 Bickel PeterJ. 11/84 Drayton William 11/84 Drell Sidney 11/84 feigenbaum mitchell J. 11/84 http://www.tbtf.com/resource/macarthurites.txt

All MacArthur Foundation award winners, 1981 to 1999 Tab-delimited Ascii Source: http://www.macfdn.org/programs/fel/complete-list-6.htm Most recently updated 1999-10-16 Ammons A. R. 6/81 Brodsky Joseph 6/81 Chudnovsky Gregory V. 6/81 Coles Robert 6/81 Errington Shelly 6/81 Gates Henry Louis, Jr. 6/81 Ghiselin Michael 6/81 Gould Stephen Jay 6/81 Graham Ian 6/81 Imbrie John 6/81 Lewis Elma 6/81 McPherson James 6/81 Mottahedeh Roy P. 6/81 Osheroff Douglas D. 6/81 Root-Bernstein Robert 6/81 Rosen Lawrence 6/81 Schorske Carl E. 6/81 Silko Leslie Marmon 6/81 Walcott Derek 6/81 Warren Robert Penn 6/81 Wolfram Stephen 6/81 Cairns John 12/81 Cohen Joel E. 12/81 Critchfield Richard 12/81 Gardner Howard 12/81 Gaventa John P. 12/81 Hawkins David 12/81 Holdren John P. 12/81 Huxtable Ada Louise 12/81 Kates Robert W. 12/81 Lee Raphael Carl 12/81 McCarthy Cormac 12/81 McClintock Barbara 12/81 Mulligan Richard 12/81 Pagels Elaine H. 12/81 Pingree David 12/81 Richards Paul G. 12/81 Rorty Richard 12/81 Taylor Joseph H., Jr. 12/81 Woodford Michael 12/81 Zweig George 12/81 Ajami Fouad 8/82 Bigelow Charles A. 8/82 Brown Peter Robert Lamont 8/82 Darnton Robert 8/82 Diaconis Persi 8/82 Gaddis William 8/82 Mehta Ved 8/82 Moses Robert Parris 8/82 Muller Richard A. 8/82 Nancarrow Conlon 8/82 Ortiz Alfonso 8/82 Rochberg Francesca 8/82 Sabel Charles F. 8/82 Shapey Ralph 8/82 Silverstein Michael 8/82 Whitfield Randolph, Jr. 8/82 Wilczek Frank 8/82 Wiseman Frederick 8/82 Witten Edward 8/82 Berry R. Stephen 2/83 Curtin Philip D. 2/83 Durham William H. 2/83 Efron Bradley 2/83 Felten David L. 2/83 Goitein Shelomo D. 2/83 Gutierrez Ramon Arturo 2/83 Julesz Bela 2/83 Kennedy William 2/83 Kolakowski Leszek 2/83 Leithauser Brad 2/83 Levine Lawrence W. 2/83 Manheim Ralph 2/83 Peskin Charles S. 2/83 Robinson Julia 2/83 Sayles John 2/83 Sellars Peter 2/83 Wilson Adrian 2/83 Winter Irene J. 2/83 Wrighton Mark S. 2/83 Bialer Seweryn 8/83 Clark William C. 8/83 Forsberg Randall Caroline Watson 8/83 George Alexander 8/83 Greene Mott T. 8/83 Gunn James E. 8/83 Hopfield John J. 8/83 Law Sylvia A. 8/83 Merton Robert K. 8/83 Morris Walter F., Jr. 8/83 Ramanujan A. K. 8/83 Rivlin Alice M. 8/83 Schoen Richard M. 8/83 Uhlenbeck Karen K. 8/83 Archibald George W. 3/84 Cortes Ernesto J., Jr. 3/84 Hass Robert 3/84 Hehir J. Bryan 3/84 Irwin Robert W. 3/84 Jhabvala Ruth Prawer 3/84 Kristeller Paul Oskar 3/84 Lawrence-Lightfoot Sara 3/84 Lechtman Heather Nan 3/84 Lerner Michael 3/84 Lewis Andrew W. 3/84 Mandell Arnold J. 3/84 Meselson Matthew 3/84 Nelson David R. 3/84 Piore Michael J. 3/84 Shklar Judith N. 3/84 Simic Charles 3/84 Stuart David 3/84 Toews John E. 3/84 Turrell James 3/84 Weiss Jay Michael 3/84 Woese Carl R. 3/84 Bernstein Shelly C. 11/84 Bickel Peter J. 11/84 Drayton William 11/84 Drell Sidney 11/84 Feigenbaum Mitchell J. 11/84 Freedman Michael H. 11/84 Hames Curtis G. 11/84 Heath Shirley Brice 11/84 Howland Bette 11/84 Irwin Bill 11/84 John Fritz 11/84 Kinnell Galway 11/84 Kraus Henry 11/84 Mathews Peter 11/84 Newhall Beaumont 11/84 Payne Roger S. 11/84 Roberts Edward V. 11/84 Sperling Elliot 11/84 Sulloway Frank 11/84 Toomre Alar 11/84 Tversky Amos 11/84 Varnedoe J. Kirk T. 11/84 Wallach Bret 11/84 Winfree Arthur T. 11/84 Young Billie Jean 11/84 Abrahamson Joan 7/85 Ashbery John 7/85 Benton John F. 7/85 Bloom Harold 7/85 Chalidze Valery 7/85 Cronon William 7/85 Cunningham Merce 7/85 Diamond Jared M. 7/85 Edelman Marian Wright 7/85 Halperin Morton H. 7/85 Hayes Robert M. 7/85 Hutchins Edwin 7/85 Maloof Sam 7/85 McGuire Andrew 7/85 Noonan Patrick F. 7/85 Oster George F. 7/85 Palaima Thomas G. 7/85 Raven Peter H. 7/85 Richardson Jane 7/85 Schopen Gregory 7/85 Stahl Franklin W. 7/85 Steffy J. Richard 7/85 Stewart Ellen 7/85 Taylor Paul 7/85 Yau Shing-Tung 7/85 Adams Paul R. 8/86 Babbitt Milton 8/86 Beckwith Christopher I. 8/86 Benson Richard M. A. 8/86 Brown Lester R. 8/86 Bynum Caroline Walker 8/86 Christian William A., Jr. 8/86 Farriss Nancy Marguerite 8/86 Gross Benedict H. 8/86 Hine Daryl 8/86 Horner John Robert 8/86 Joe Thomas C. 8/86 Keightley David N. 8/86 Libchaber Albert J. 8/86 Page David C. 8/86 Perle George 8/86 Randi James 8/86 Rudovsky David 8/86 Shapley Robert 8/86 Steinberg Leo 8/86 Turco Richard P. 8/86 Whiteside Thomas 8/86 Wilson Allan C. 8/86 Wright Jay 8/86 Wuorinen Charles 8/86 Abish Walter 7/87 Axelrod Robert 7/87 Coleman Robert F. 7/87 Crase Douglas 7/87 Friedan Daniel H. 7/87 Gross David 7/87 Herskowitz Ira 7/87 Howe Irving 7/87 Jacobs Wesley Charles, Jr. 7/87 Jeffery Peter 7/87 Judson Horace Freeland 7/87 Kauffman Stuart Alan 7/87 Kenney Richard 7/87 Lander Eric Steven 7/87 Malin Michael C. 7/87 Meier Deborah W. 7/87 Momigliano Arnaldo Dante 7/87 Mumford David 7/87 Rosenberg Tina 7/87 Rumelhart David 7/87 Sapolsky Robert Morris 7/87 Schapiro Meyer 7/87 Schwarz John H. 7/87 Seger Jon 7/87 Shenker Stephen 7/87 Shulman David 7/87 Snowden Muriel Sutherland 7/87 Strand Mark 7/87 Swenson May 7/87 Thong Huynh Sanh 7/87 Wilson William Julius 7/87 Wrangham Richard Walter 7/87 Archambeau Charles B. 8/88 Baxandall Michael David Kighley 8/88 Behar Ruth 8/88 Blake Ran 8/88 Burnett Charles 8/88 DeVries Philip James 8/88 Dubus Andre 8/88 Edwards Helen T. 8/88 Else Jon H. 8/88 Fleagle John G. 8/88 Fleischer Cornell H. 8/88 Haile Getatchew 8/88 Jeanloz Raymond 8/88 Kahl Marvin Philip 8/88 Pierce Naomi 8/88 Pynchon Thomas 8/88 Pyne Stephen J. 8/88 Roach Max 8/88 Roldan Hipolito (Paul) 8/88 Roosevelt Anna Curtenius 8/88 Rosenberg David Alan 8/88 Rotroff Susan Irene 8/88 Schwartz Bruce 8/88 Shaw Robert S. 8/88 Spence Jonathan Dermot 8/88 Swerdlow Noel M. 8/88 Tomlinson Gary Alfred 8/88 Walker Alan 8/88 Williams Eddie 8/88 Wright Rita P. 8/88 Youngberg I. Garth 8/88 Amsterdam Anthony G. 8/89 Avery Byllye 8/89 Bronstein Alvin J. 8/89 Buss Leo William 8/89 Cantor Jay 8/89 Davis George D. 8/89 Grossman Allen 8/89 Harbison John 8/89 Hefner W. Keith 8/89 Hotchkiss Ralf David 8/89 Irwin John Rice 8/89 Janzen Daniel H. 8/89 Lansky Aaron 8/89 Moody Jennifer Alice 8/89 Morris Errol 8/89 Paley Vivian Gussin 8/89 Powers Richard 8/89 Proffer Ellendea Catherine 8/89 Puryear Martin 8/89 Reagon Bernice Johnson 8/89 Rosengarten Theodore 8/89 Rossiter Margaret W. 8/89 Russell George 8/89 Solo Pam 8/89 Van Vliet Claire 8/89 Velasquez Baldemar 8/89 Viola Bill 8/89 Wigginton Eliot 8/89 Wright Patricia Chapple 8/89 Bailar John Christian, III 8/90 Clarke Martha 8/90 d'Amboise Jacques 8/90 Davenport Guy 8/90 Delpit Lisa 8/90 Eaton John C. 8/90 Ehrlich Paul R. 8/90 Erickson Charlotte J. 8/90 Friedlander Lee 8/90 Geller Margaret Joan 8/90 Graham Jorie 8/90 Hampl Patricia 8/90 Hollander John 8/90 Holt Thomas Cleveland 8/90 Kazhdan David 8/90 King Calvin R. 8/90 Koehl M. A. R. 8/90 Kopell Nancy 8/90 Moschen Michael 8/90 Nabhan Gary Paul 8/90 Ortner Sherry B. 8/90 Pitts Otis, Jr. 8/90 Rainer Yvonne 8/90 Schudson Michael S. 8/90 Scott Rebecca J. 8/90 Shell Marc 8/90 Sontag Susan 8/90 Stallman Richard 8/90 Tudor Guy 8/90 Varela Maria 8/90 Vlastos Gregory 8/90 Whealy Kent 8/90 Wolf Eric 8/90 Wolfe Sidney M. 8/90 Woodson Robert L. 8/90 Zalaquett Jose D. 8/90 Barton Jacqueline K. 7/91 Berman Paul 7/91 Blinn James F. 7/91 Branch Taylor 7/91 Brown Trisha 7/91 Buhle Mari Jo 7/91 Churchland Patricia Smith 7/91 Donoho David 7/91 Feld Steven 7/91 Fulton Alice 7/91 Gomez-Pena Guillermo 7/91 Grotowski Jerzy 7/91 Hammons David 7/91 Harris Sophia Bracy 7/91 Hyde W. Lewis 7/91 Khan Ali Akbar 7/91 Klainerman Sergiu 7/91 Kreitman Martin E. 7/91 Lane Harlan 7/91 Linder William J. 7/91 Locke Patricia 7/91 Morris Mark 7/91 Ophuls Marcel 7/91 Rampersad Arnold 7/91 Schuller Gunther 7/91 Schwartz Joel 7/91 Taylor Cecil 7/91 Taymor Julie 7/91 Werner David 7/91 Westphal James A. 7/91 Wilner Eleanor 7/91 Benshoof Janet 7/92 Blackburn Robert H. 7/92 Blackwell Unita 7/92 Bourg Lorna 7/92 Cavell Stanley 7/92 Clampitt Amy 7/92 Daubechies Ingrid 7/92 Ewald Wendy 7/92 Feldman Irving 7/92 Fields Barbara J. 7/92 Hall Robert H. 7/92 Hanson Ann Ellis 7/92 Holland John H. 7/92 Jackson Wes 7/92 Keller Evelyn Fox 7/92 Lacy Steve 7/92 Lebsock Suzanne 7/92 Long Sharon R. 7/92 Manea Norman 7/92 Marshall Paule 7/92 Massing Michael 7/92 McCabe Robert H. 7/92 Meiselas Susan 7/92 Mesa-Bains Amalia 7/92 Schneider Stephen H. 7/92 Scott Joanna 7/92 Scott John T. 7/92 Terborgh John W. 7/92 Tharp Twyla 7/92 Treisman Philip Uri 7/92 Ulrich Laurel Thatcher 7/92 Vermeij Geerat J. 7/92 Wagner Gunter P. 7/92 Cartwright Nancy D. 7/93 Christodoulou Demetrios 7/93 Crawford Maria Luisa 7/93 Crouch Stanley 7/93 England Nora C. 7/93 Farmer Paul E. 7/93 Foe Victoria E. 7/93 Gaines Ernest J. 7/93 Greer Pedro Jose, Jr. 7/93 Gunn Thom 7/93 Hamilton Ann 7/93 Karanja Sokoni T. 7/93 Lauterbach Ann 7/93 Lee Stephen 7/93 Levine Carol 7/93 Lovins Amory B. 7/93 Lubchenco Jane 7/93 Lubic Ruth Watson 7/93 Powell Jim 7/93 Profet Margie 7/93 Scanlon Thomas M., Jr. 7/93 Shirley Aaron 7/93 Siemering William H. 7/93 Silbergeld Ellen Kovner 7/93 van der Kuijp Leonard W. J. 7/93 von Hippel Frank 7/93 Wideman John Edgar 7/93 Williams Heather 7/93 Williams Marion 7/93 Williams Robert H. 7/93 Wright Henry T. 7/93 Adams Robert 7/94 Blunden Jeraldyne 7/94 Braxton Anthony 7/94 Brubaker Rogers 7/94 Coleman Ornette 7/94 Gelfand Israel M. 7/94 Ginsburg Faye D. 7/94 Hartmann Heidi I. 7/94 Jones Bill T. 7/94 Kenmore Peter E. 7/94 Marshall Joseph E., Jr. 7/94 McKecuen Carolyn 7/94 Meadows Donella H. 7/94 Mitchell Arthur 7/94 Morales Hugo 7/94 Pease-Pretty on Top Janine 7/94 Reale Willie 7/94 Rich Adrienne 7/94 Sam Sam-Ang 7/94 Wisdom Jack 7/94 Anders Allison 7/95 Buchwald Jed Z. 7/95 Butler Octavia 7/95 Cisneros Sandra 7/95 Close Sandy 7/95 Cuny Frederick C. 7/95 Emerson Sharon B. 7/95 Foreman Richard 7/95 Guillermoprieto Alma 7/95 Hamilton Virginia 7/95 Hopkins Donald 7/95 Kieffer Susan Werner 7/95 LeCompte Elizabeth 7/95 Limerick Patricia Nelson 7/95 Marletta Michael A. 7/95 Matson Pamela A. 7/95 McClary Susan 7/95 Monk Meredith 7/95 Petchesky Rosalind Pollack 7/95 Rogers Joel 7/95 Sherman Cindy 7/95 Stevenson Bryan 7/95 Strausfeld Nicholas 7/95 White Richard 7/95 Angel James Roger Prior 7/96 Avila Joaquin G. 7/96 Berube Allan 7/96 Block Barbara 7/96 Connelly Joan Breton 7/96 Daniel Thomas L. 7/96 Eakes Martin Daniel 7/96 Goldstein Rebecca 7/96 Greenstein Robert 7/96 Howard Richard 7/96 Jesurun John 7/96 Lenski Richard E. 7/96 Massiah Louis 7/96 McLoyd Vonnie C. 7/96 Moss Thylias 7/96 Otake Eiko and Koma 7/96 Seiberg Nathan 7/96 Smith Anna Deavere 7/96 Stoneman Dorothy 7/96 Strickland William E., Jr. 7/96 Alfaro Luis 7/97 Breuer Lee 7/97 Celmins Vija 7/97 Charnov Eric L 7/97 Cobell Elouise C. 7/97 Galison Peter 7/97 Harrington Mark 7/97 Harris Eva 7/97 Kremer Michael 7/97 Lande Russell S. 7/97 Marshall Kerry James 7/97 Moran Nancy A. 7/97 Ong Han 7/97 Ross Kathleen A. 7/97 Samuelson Pamela 7/97 Stewart Susan 7/97 Streb Elizabeth 7/97 Trimpin 7/97 Wacquant Loic J. D. 7/97 Walker Kara E. 7/97 Wallace David Foster 7/97 Wiles Andrew 7/97 Williams Brackette F. 7/97 Antoni Janine 7/98 Applebroog Ida 7/98 Barry Ellen 7/98 Berners-Lee Tim 7/98 Bierds Linda 7/98 Brooten Bernadette 7/98 Carlstrom John 7/98 Davis Mike 7/98 Folbre Nancy 7/98 Greif Avner 7/98 Guan Kun-Liang 7/98 Hill Gary 7/98 Hirsch Edward 7/98 Jalal Ayesha 7/98 Johnson Charles 7/98 Krubitzer Leah 7/98 Kwoh Stewart 7/98 Lewis Charles 7/98 McDonald William 7/98 Miller Peter 7/98 Mitchell Don 7/98 Nelson Rebecca 7/98 Ochs Elinor 7/98 Reed Ishmael 7/98 Santer Benjamin 7/98 Sims Karl 7/98 Thomas Dorothy 7/98 Zeskind Leonard 7/98 Zimmerman Mary 7/98 Banfield Jillian 7/99 Bertozzi Carolyn 7/99 Blair Bruce 7/99 Bonifaz John 7/99 Carlson Shawn 7/99 Danner Mark 7/99 Diller Elizabeth 7/99 Forges Alison des 7/99 Friedlander Saul 7/99 Gordon Jennifer 7/99 Hillis David 7/99 Horowitz Sara 7/99 Jones Jacqueline 7/99 Kiessling Laura 7/99 Kurke Leslie 7/99 Lewis David 7/99 Maldacena Juan 7/99 McDougall Gay J. 7/99 McGrath Campbell 7/99 Moore Dennis A. 7/99 Murry Elizabeth 7/99 Osorio Pepon 7/99 Scofidio Ricardo 7/99 Shor Peter 7/99 Silberstein Eva 7/99 Subra Wilma 7/99 Vandermark Ken 7/99 Wallace Naomi 7/99 Weeks Jeffrey 7/99 Wilson Fred 7/99 Bing Xu 7/99 Zepeda Ofelia 7/99

6. Mitchell Feigenbaum Lab Back to RU Home, Laboratory of Mathematical Physics mitchell FeigenbaumToyota Professor. Attempts at the analytical description of http://www.rockefeller.edu/labheads/feigenbaum/feigenbaum-lab.html

Laboratory of Mathematical Physics Mitchell Feigenbaum Toyota Professor Attempts at the analytical description of nature regularly encounter strong nonlinearities. The majority of existing methods treat only weak nonlinearities and consist of corrections to behaviors that are simple distortions of linear behavior. The methods in the strong case, on the other hand, are largely recent developments and pertain to behaviors qualitatively distinct from linear ones. One of the most striking such behaviors is the appearance of highly erratic spatial configurations and/or highly erratic temporal evolution, a phenomenon called "chaos." The hallmark of chaotic motion is a lack of predictability despite the total absence of any random ingredients. Even if one should want to determine just statistical properties of these motions, the methods of statistics cannot be applied in any straightforward manner. This impediment is a consequence of the fact that the motion, rather than exploring all possibilities allowed to it by the constraints of finite energy, finite resources, etc., instead lies in a highly complicated subspace a so-called strange set or strange attractor. Thus an a priori calculated average over "everything" will generally produce erroneous results.

7. Feigenbaum - Ulli's Fractal Home mitchell feigenbaum i uniwersalno. "Dla kadego z przygotowaniem matematycznym, http://home.wtal.de/schwebin/myhome/figwin.htm

Ulli's Fractal Home [Feigenbaum-Page] 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 auf deutsch Bifurcation Diagrams - Feigenbaum, Mitchell Iterating a formula, it is possible that the results walk to a fixed value. Raising a parameter the behavior changes to two periodically repeating values. With a more raised parameter you can see another bifurcation into four different values, that change to the next at every new iteration. A little bit later, there is one more bifurcation, etc. Beginning with a critical parameter-value no more order can be seen; the output values are chaotical and the next iteration result depends on minimal variations behind the decimal point in the input. My program Feigenbaum 4.1 (for Win) explores formulas in the described way and also allows time-diagrams, graphical iteration, phase diagramms in 2 or 3 dimensions and even Liapunov-Pictures. You can order the program only by EMail (please send me an aquivalent: ideas, pictures, programs, education-concepts, etc. with your mail). You are allowed to use the programs for your own, but not to distribute it to others!

8. Feigenbaum's Universal Constant It is said that mr. mitchell feigenbaum called home to his mother when he discovered this universality and said this was http://www.stud.ntnu.no/~berland/math/feigenbaum/feigconstant.html

F EIGENBAUM'S UNIVERSAL CONSTANT Back to main page Back to homepage Send comment The short answer: However, noone should be satisfied by that. In fact, this number is perhaps the most fantastic aspect of this fractal. There are many many formulas that produce the same tree, but the number is always the same. It is said that mr. Mitchell Feigenbaum called home to his mother when he discovered this universality and said this was going to make him famous. The famous value, comes when you compare the length of one part of the tree, that is a parts between the line divisions/bifurcations. See illustration at right. The first part is from -0.25 to 0.75, and has a length of 1.00. The next part is from 0.75 to 1.25, and has a length of 0.50. The relationship between the two lengths is 1.00/0.50=2.00. Now that is far from the Feigenbaumvalue, but the exact value springs up when you compare two parts as far right as possible, as long as x follows a periodic orbit. I have graphically found the values for the first 6 bifurcations: Bifurc no. Divides at Length This length/next length -0.25 - - 1 0.75 L1=1.0 L1/L2=2.0 2 1.25 L2=0.5 L2/L3=4.25 3 1.3677 L3=0.1147 L3/L4=4.492 4 1.3939 L4=0.0262 L4/L5=4.6208 5 1.39957 L5=0.00567 L5/L6=4.536 6 1.40082 L6=0.00125 L6/L7=?

9. Mitchell Feigenbaum feigenbaum, mitchell (1945 ) feigenbaum, mitchell (1945- ) Mathematician, born in Philadelphia, PA. http://userwww.sfsu.edu/~rsauzier/Feigenbaum.html

Feigenbaum, Mitchell (1945- ) Feigenbaum, Mitchell (1945- ) Mathematician, born in Philadelphia, PA. He is one of a small group of scientists who in the 1970s were growing more concerned about the inability of science to explain irregular occurrences in everyday life, such as the shape of clouds, the irregular flow from a dripping tap, and many other events that could be described as chaotic. He developed the mathematics of what is now called Chaos Theory, used in fields such as meteorology, aerodynamics, and ecology. You can check out his home page at Rockefeller University. See also Edward Lorenz Robert May and Benoit Mandelbrot Also, check ou this really hip chaos and fractals page. Return to the biography index . Back to my homepage , the school , the Journalism department , or the Underground student pipeline

10. References For Feigenbaum References for mitchell feigenbaum. Articles MJ feigenbaum, Computer generatedphysics, in Twentieth Century Physics (New York, 1995), 18231853. http://www-gap.dcs.st-and.ac.uk/~history/References/Feigenbaum.html

References for Mitchell Feigenbaum Articles: M J Feigenbaum, Computer generated physics, in Twentieth Century Physics (New York, 1995), 1823-1853. 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, Universal behavior in nonlinear systems, in Order in chaos, Los Alamos, N.M., 1982, Phys. D M J Feigenbaum, Low-dimensional dynamics and the period doubling scenario, in Dynamical systems and chaos, Sitges/Barcelona, 1982 (Berlin, 1983), 131-148. Hammond Atlas of the World (Maplewood, NJ, 1992), 9. A Pais, Mitchell Jay Feigenbaum, in The genius of science (Oxford, 2000), 84-104. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR May 2001 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Feigenbaum.html

11. Mitchell J. (was: Joan) Feigenbaum Biography of mitchell feigenbaum (19440BC) mitchell feigenbaum's father is Abraham Joseph feigenbaum, an analytic chemist whose parents had emigrated from a town http://mathforum.com/epigone/math-history-list/dorboigrum

a topic from math-history-list Mitchell J. (was: Joan) Feigenbaum post a message on this topic post a message on a new topic 24 Aug 1998 Mitchell J. (was: Joan) Feigenbaum , by Antreas P. Hatzipolakis 24 Aug 1998 Re: Mitchell J. (was: Joan) Feigenbaum , by Samuel S. Kutler 25 Aug 1998 Re: Mitchell J. (was: Joan) Feigenbaum , by Antreas P. Hatzipolakis The Math Forum

12. The Ernest Orlando Lawrence Award - Mitchell J. Feigenbaum, 1982 1980's Laureates mitchell J. feigenbaum, 1982 Physics For his discovery of the perioddoublingroute-to-chaos, which has furthered the understanding of a wide http://www.sc.doe.gov/sc-5/lawrence/html/Laureates/mitchellj.htm

1980's Laureates Mitchell J. Feigenbaum, 1982 Physics: For his discovery of the period-doubling route-to-chaos, which has furthered the understanding of a wide variety of nonlinear physical phenomena in fields as diverse as turbulence, solid state physics, plasma physics, chemical kinetics, and population biology. Go Back About the Award Award Laureates The Life of Ernest Orlando Lawrence ... Comments

13. Environmental Portraits - Mitchell Feigenbaum William Coupon Photography Environmental Portraits. mitchell feigenbaum© 2002 William Coupon; all rights reserved. Back to Portraits 2. http://www.williamcoupon.com/PLACES/mitchell.html

William Coupon Photography Environmental Portraits Mitchell Feigenbaum Back to Portraits 2 Photography Home How to Purchase

14. Mitchell J. (was: Joan) Feigenbaum By Antreas P. Hatzipolakis mitchell J. (was Joan) feigenbaum by Antreas P. Hatzipolakis Subject mitchell J. (was Joan) feigenbaum Author Antreas P. Hatzipolakis xpolakis@hol.gr Date Tue, 25 Aug 1998 025247 +0200 1. http://mathforum.com/epigone/math-history-list/dorboigrum/v01540B00B207B0B8E22A@

Mitchell J. (was: Joan) Feigenbaum by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Mitchell J. (was: Joan) Feigenbaum Author: xpolakis@hol.gr Date: http://www.mi.aau.dk/~abuch/feigenbaum.html http://www.mathsoft.com/asolve/constant/fgnbaum/fgnbaum.html http://www.astro.virginia.edu/~eww6n/math/FeigenbaumConstant.html 2. Feigenbaum of "Feigenbaum's constant" = Mitchell J. Feigenbaum (1944 - ) (The 'chaotic', as has called him Ed Wall) Web Page (cv): http://mmm.wwa.com/tbrf/feigenb.html PS: Joan Feigenbaum's Web Page: http://www.research.att.com/~jf/ APH The Math Forum

15. U.S. Particle Physicists feigenbaum, mitchell Title Tenured Faculty or Staff Phd Year 1970 FieldTheory Affil Rockefeller University Address Rockefeller Univ. http://susy.lbl.gov/server-java/HEPPerson?3830

16. U.S. Particle Physicists Braun, Dieter Catto, Sultan Cecchi, Guillermo Chialvo, Dante Cohen, EGD Convery,Mary Demortier, Luc Dubertret, Benoit feigenbaum, mitchell Gallinaro, Michele http://susy.lbl.gov/server-java/UniPerson?110

17. MITCHELL FEIGENBAUM In 1975, the eccentric scientist mitchell feigenbaum was probing the possibilitythat there was a point at which periodic equations turned chaotic. http://www.bath.ac.uk/~ma1ejm/feigenbaum.html

In 1975, the eccentric scientist Mitchell Feigenbaum was probing the possibility that there was a point at which periodic equations turned chaotic. With his calculator he began to use a combination of analytic algebra and numerical exploration to piece together an understanding of the quadratic map, concentrating on the boundary region between order and chaos. He noticed that it took increasingly more time to work out his answers, and as he waited for his output of data, it dawned on him that the numbers were converging geometrically. This suggested that an unexpected regularity was embedded in the system and that some part of it was repeating itself on different scales. Feigenbaum calculated this ' ratio of convergence ' as 4.669 to 3 decimal places. Unsure what the significance of this value really was, Feigenbaum started to analyse other functions that went through a sequence of bifurcations on the way to disorder. He found that each one produced the same ratio of convergence. In terms of chaos, this value is equal to the scale at which the bifurcation diagram is self-similar - i.e. make the diagram 4.669 times smaller and it will look like the next region of bifurcations. This universality was a revolutionary discovery as it gave scientists the first tools to analyse a chaotic system. BACK TO CHAOS THEORY EDWARD LORENZ BENOIT MANDELBROT HELGE VON KOCH

18. Tureck Bach Research Foundation Tureck Bach Research Foundation mitchell J. feigenbaum Biography. The RockefellerUniversity Box 75 1230 York Avenue New York, NY 10021-6399. EDUCATION. http://www.connectedglobe.com/tbrf/feigenb.html

Purposes History Symposia Journal Trustees Membership Tureck Email Links to Mitchell Feigenbaum Bookshop Mitchell J. Feigenbaum - Biography The Rockefeller University Box 75 1230 York Avenue New York, N.Y. 10021-6399 EDUCATION M.I.T. February, 1965 - June, 1970, Ph.D., Department of Physics Ph.D., Thesis, "The Relationship of Feynmann Parametrization and Double Dispersion Relations of Scattering Amplitudes for Higher Spin Particles" under supervision of F.E. Low M.I.T. September, 1964 - January, 1965, Department of Electrical Engineering Elected to membership in Sigma Xi C.C.N.Y. February, 1961 - August, 1964, B.E.E., Department of Electrical Engineering Elected to Honor Societies: Tau Beta Pi, Etta Kappa Nu Ranked first in class in School of Engineering PROFESSIONAL HONORS Member, The National Academy of Sciences, 1988 Dickson Prize, Carnegie-Mellon University, 1987 Member, The American Academy of Arts and Sciences, 1987 Wolf Foundation Prize in Physics, 1986 Fellow of the American Physical Society, 1985 MacArthur Foundation Award, October 1984

19. ID Feigenbaum-M-1987b Title Some Characterizations Of Strange Cited, null. Keywords, null. Authors, mitchell J. feigenbaum. First Authors, feigenbaum,mitchell J. Last Authors, feigenbaum, mitchell J. Status, Y. Year, 1987. Comments, http://leos.bu.edu/~cclo/detailed.php?person_id=23

20. ID Feigenbaum-M-1986a Title Time Ordering And The Thermodynaics Keywords, null. Authors, mitchell J. feigenbaum, Mogens H. Jensen, Itamar Procaccia.First Authors, feigenbaum, mitchell J. Last Authors, Procaccia, Itamar. Status, Y. http://leos.bu.edu/~cclo/detailed.php?person_id=12

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