21. 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

22. Feigenbaum - Ulli's Fractal Home Translate this page Bifurkations-Diagramme - feigenbaum, mitchell feigenbaumdiagramme stellen das Verhalteneines dynamischen Systems (eine mathematische Formel) bei der Iteration http://www.fraktalwelt.de/myhome/figwin-g.htm

Ulli's Fractal Home [Feigenbaum-Seite] Home Ring Introduction Liapunov Lindenmayer I Lindenmayer II IFS I Feigenbaum Symmetry I Lake Iterations IFS II Branches IFS III Hyperbolic IFS IV Fractal Gallery Essays Links in english Bifurkations-Diagramme - Feigenbaum, Mitchell detaillierter Artikel Systemtheorie Die Screenshots zeigen Feigenbaum 3.1 Vorschaubilder anklicken:

23. Feigenbaum - Ulli's Fractal Home Bifurcation Diagrams feigenbaum, mitchell Iterating a formula,it is possible that the results walk to a fixed value. Raising http://www.fraktalwelt.de/myhome/figwin.htm

Ulli's Fractal Home [Feigenbaum-Page] Home Ring Introduction Liapunov Lindenmayer I Lindenmayer II IFS I Feigenbaum Symmetry I 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 4.3 (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!

24. 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

25. Editing Mitchell Feigenbaum - Edit - Wikipedia, The Free Encyclopedia mitchell J. (was Joan) feigenbauma topic from mathhistory-list mitchell J. (was Joan) feigenbaum.post a message on this topic post a message on a new topic 24 http://en.wikipedia.org/w/wiki.phtml?title=Mitchell_Feigenbaum&action=edit

26. Mitchell J. (was: Joan) Feigenbaum By Antreas P. Hatzipolakis fgnbaum/fgnbaum.html http//www.astro.virginia.edu/~eww6n/math/feigenbaumConstant.html2. feigenbaum of feigenbaum s constant = mitchell J. feigenbaum (1944 http://mathforum.org/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

27. Feigenbaum's Universal Constant It is said that mr. mitchell feigenbaum called home to his mother when he discoveredthis universality and said this was going to make him famous. 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=?

28. MathSeek.com - Site Profile For Mitchell Feigenbaum Pioneeredbifurcations in the mid 70s and for whom the feigenbaum tree is named....... mitchell feigenbaum Site Profile. Title mitchell feigenbaum. http://www.mathseek.com/profiles/6549.php

@import url(http://www.animationseek.com/style.css); Search Directory Forum Mitchell Feigenbaum Site Profile Title: Mitchell Feigenbaum Description: Pioneered bifurcations in the mid 70s and for whom the Feigenbaum tree is named. Url: http://www.rockefeller.edu/labheads/feigenbaum/feigenbaum.html Category: Science/Math/Chaos_and_Fractals/Chaos/People Add / Update Url Become an Editor Link to Us ... MathSeek.com - Math Search Engine - Seeking Sites about Math,Applications,Education,Recreations,Statistics,Algebra,Analysis,Chaos,Fractals,Combinatorics,Differential,Equations,Geometry,Logic,Foundations,Number,Theory,Numerical,Analysis,Operations,Research,Precalculus. PhysicsSeek.com SocialScienceSeek.com TechnologySeek.net BaseballSeek.com ... MartialArtsSeek.com

29. Books Written By Mitchell Feigenbaum - Textbook Land orders over $50 TextbookX.com Free shipping on orders over $75.More Coupons Details . Books Written By mitchell feigenbaum. http://www.textbookland.com/author/Mitchell Feigenbaum

Monday, May 31st 2004 Click Here To Bookmark Us! Textbook Price Comparison Compares prices on new and used textbooks in seconds. Bookstore Information Tax, shipping, and contact info for each bookstore we search. Instant Order Tracking You can instantly track your orders shipping status here. Trouble Finding A Book? If you're having trouble finding any textbooks go here for help. About Us Contact Us :: Amazon.com Free shipping on orders over 25$ :: BarnesAndNoble.com :: Powells.com Free shipping on orders over $50 :: TextbookX.com Free shipping on orders over $75 Books Written By: Mitchell Feigenbaum Chaos: The New Science (Nobel Conference XXVI) John Holte James Gleick Ilya Prigogine ... Benoit Mandelbrot 19 March, 1993 ISBN: 0819189340 Page 1 of 1 COMPARE TEXTBOOK PRICES BOOKSTORE INFO NEED HELP? WEBMASTERS ... CONTACT US ©2000-2003 TextbookLand.com

30. APPENDIX B: Colloquially, the control systems and filters employed by the Iscog. feigenbaum,mitchell (prop. n) American physicist-laureate of the Late Modern era. http://www.wilmccarthy.com/apdxb.htm

APPENDIX B: GLOSSARY A.U. - (n) Astronomical Unit; the mean distance from the center of Sol to the center of Earth. Equal to 149,604,970 kilometers, or 49.9028 light-seconds. ANTIAUTOMATA - (adj.) Describes any weapon intended for use against robots. ARC DE FIN - (n) A hypothetical device for diverting photons from the fourth-dimensional extremum of spacetime. Attributed to Bruno de Towaji. ARCHIMEDES - (prop. n) Greek physicist from the Classical era. AUTRONIC - (adj.) Capable of self-directed activity. Commonly used to differentiate "robots" from teleoperated or "waldo" devices. BLITTERSTAFF - (n) An antiautomata weapon employing a library of rapidly shifting wellstone compositions. Attributed to Bruno de Towaji. BONDRIL BUNKERLITE CASIMIR EFFECT - (n) The exclusion of vacuum wavelengths by closely spaced, uncharged, conducting plates, causing the plates to be pressed together. Earliest evidence of the Zero Point Field. CASIMIR, HENDRICK - (prop. n) Dutch physicist of the Old Modern era. CATALONIA - (prop. n) Former Mediterranean nation at the northeast of the Iberian penninsula, historically a part of Spain.

31. Das Feigenbaum-Diagramm Translate this page Der amerikanische Physiker mitchell feigenbaum beschäftigte sich mit der Frage,welche Aussage sich über die Entwicklung einer Population über viele http://www.lenne-schule.de/fachb/inf/feige.htm

3. Das Feigenbaum-Diagramm Der amerikanische Physiker Mitchell Feigenbaum beschäftigte sich mit der Frage, welche Aussage sich über die Entwicklung einer Population über viele Zeiträume für steigende Wachstumsfaktoren machen läßt. Dabei ist er von der üblichen Wachstumsgleichung unter der Normierungsbedingung ausgegangen. Dabei ergab sich folgendes Bild: In der Vertikalen wird die Populationsgröße abgetragen. In der Horizontalen - sinnvollerweise erst beginnend bei einem Wachstumsfaktor von 1 (sonst stribt die Population zwingend aus) - wird der Wachstumsfaktor bis kurz unter 4.0 abgetragen. Darüber hinaus ist keine Berechnung möglich. Bis zu einem Wachstumsfaktor von 3.0 ist ein Zustand genau voraussagbar. Dann gibt es plötzlich zwei Mögliche Zustände. An diesem Punkt, einem Bifurkationspunkt, kam es zu einer Periodenverdoppelung. Hier die ersten Bifurkationspunkte: b b b b b b b Setzt man die Abstände benachbarter Bifurkationspunkte nun ins Verhältnis, läßt sich vermuten, daß dieser Quotient einer Konstanten zustrebt, d.h. daß die Folge der Quotienten einen Grenzwert hat. Tatsächlich ergab sich folgender Wert: zurück

32. The Feigenbaum Constant And Universality mitchell feigenbaum noticed that succesive differences appear to converge geometrically(see Fig.(3.9)) and that the ratio of successive separations tends to a http://staff.science.nus.edu.sg/~parwani/c1/node34.html

Next: Experimental Tests Up: A Discrete Model of Previous: Bifurcation Diagrams Contents The Feigenbaum Constant and Universality Let us denote the critical value of at which the logistic map bifurcates into a period- orbit as , so that for the map has a stable period orbit. Look at the bifurcation diagram in Fig.(3.7) and Fig.(3.9). Notice how the distance, , between period doublings decreases as the control parameter is increased. The first few values of are Mitchell Feigenbaum noticed that succesive differences appear to converge geometrically (see Fig.(3.9)) and that the ratio of successive separations tends to a constant as k goes to infinity, Although the discussion so far has been strictly limited to the logistic map, the constant is the same for other smooth one-dimensional maps with a single hump . This is an example of universality , a concept which we will encounter more of when studying phase transitions in the next chapter. In general systems fall into different universality classes, so that systems within each class have the same behaviour. For the present discussion, one says that all 'unimodal' (smooth, concave downwards, with a single hump) maps belong to the same universality class, that is bifurcate at a rate leading to the universal Feigenbaum constant . The actual proof of this statement is quite involved, but briefly stated, it uses the concept of the renormalisation group that was developed to deal with critical phenomena in statistical mechanics. Although Eq.(

33. FEIGENBAUM Translate this page Dieses Diagramm heißt übrigens nicht feigenbaum, weil es so aussieht, sondernwurde benannt nach dem Physiker mitchell feigenbaum (1945-), der sich in den http://www.beepworld.de/members19/baum-horoskop/feigenbaum.htm

FEIGENBAUM Zurück Feigenbaum 14. 6. - 23. 6. Die Empfindsamkeit bitte beachten sie die LINK Hinweise von mir bitte geben sie Ihre Stimme ab Zauberblume - Danke für den Klick und die Bewertung Feigenbaum Danke für die Veröffentlichung Ficus carica Der Feigenbaum ist mit unseren Zimmergummibäumen verwandt. Im Gegensatz zu ihnen wirft er aber sein Laub im Herbst ab und muß deshalb nicht unbedingt hell überwintert werden – ein Vorteil für Kübelpflanzenfreunde mit Platzproblemen. Der Reiz dieses attraktiven Strauches wird durch seine Früchte noch erhöht. Allerdings sollte man nicht auf eine reiche Ernte spekulieren, denn von den sich im Herbst bildenden kleinen Feigen übersteht nur ein Teil die Überwinterung und reift im kommenden Sommer tatsächlich aus. Die Feige ist eine uralte Kulturpflanze. Bereits im Altertum nutzte man ihre Früchte. Ihre unprüngliche Heimat liegt vermutlich im Mittelmeerraum und Vorderasien, genau läßt sich das nicht mehr zurückverfolgen. Heute findet man sie aber auch in nahezu allen wärmeren Regionen der Erde. Wilde und verwilderte Bäume kann man häufiger in Italien oder Griechenland entdecken. Erde: Sie sollte durchlässig und nicht zu torfhaltig sein, z. B. Einheitserde zu einem Drittel mit feinem Kies vermischt.

34. References 5 feigenbaum, mitchell, ``Quantatitive Universality for a Class of NonlinearTransformations , Journal of Statistical Physics, 19, (1978), 2552. http://users.viawest.net/~keirsey/node5.html

Next: About this document ... Up: Toward the Physics of Previous: Involution and Levels of References B ALDWIN , J.M. ``A new factor in evolution'', American Naturalist B USS , Leo W., The Evolution of Individually , Princeton University Press, (1987). C RUTCHFIELD , James P. and Karl Y OUNG , ``Computation at the Onset of Chaos'', In Complexity, Entropy, and the Physics of Information, SFI Studies in the Sciences of Complexity , Vol VIII, Ed. W.H. Z UREK , Addison-Wesley, (1990). C RUTCHFIELD , James, ``The Calculi of Emergence: Computation, Dynamics, and Induction'', Physica D F EIGENBAUM , Mitchell, ``Quantatitive Universality for a Class of Nonlinear Transformations'', Journal of Statistical Physics, G OODWIN , Brian, How the Leopard Changed its Spots , Touchstone Books, (1994). F ONTANA , Walter and Leo W. B USS . ``What would be conserved if `the tape were played twice'?'' Proc. Natl. Acad. Sci. USA, (1994), 757-761. K AUFFMAN , Stuart, The Origins of Order , Oxford University Press, (1993). K AUFFMAN , Stuart, At Home in the Universe , Oxford University Press, (1995).

35. Dave's Articles feigenbaum, mitchell, ``Quantatitive Universality for a Class of NonlinearTransformations , Journal of Statistical Physics, 19, (1978), 2552. http://users.viawest.net/~keirsey/articles.html

Articles Ackley, D.H., and Littman, M.L. "Altruism in the evolution of communication," In R.A. Brooks and P. Maes (eds.) Artificial Life IV (Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems), Cambridge, MA: The MIT Press (1994), pp. 40-48. Baez, John Octonions , http://math.ucr.edu/home/baez/Octonions/ B ALDWIN , J.M. ``A new factor in evolution'', American Naturalist Cahill, Reginald T, "Process Physics: Inertia, Gravity and the Quantum," arXiv:gr-qc/0110117, 3rd Australasian Conference on General Relativity and Gravitation, Perth, Australia, July 2001. Crutchfield, James. P, David P. Feldman, "Regular Unseen, Randomness Observed: Levels of Entropy Convergence," Sante Fe Institute Working Paper 01-020012. C RUTCHFIELD , James P. and Karl Y OUNG , ``Computation at the Onset of Chaos'', In Complexity, Entropy, and the Physics of Information, SFI Studies in the Sciences of Complexity , Vol VIII, Ed. W.H. Z UREK , Addison-Wesley, (1990). C RUTCHFIELD , James, ``The Calculi of Emergence: Computation, Dynamics, and Induction'', Physica D F EIGENBAUM , Mitchell, ``Quantatitive Universality for a Class of Nonlinear Transformations'', Journal of Statistical Physics

36. F-Fli and cybernetics, 862 in growth of bones, 1010 in visual system, 1075 Feedback shiftregisters, 974 see also Shift registers feigenbaum, mitchell J. (USA, 1944 http://www.wolframscience.com/nksonline/index/f-fli.html

INDEX A B C D ... E F G H I J ... Z F-Fli Flo-Fz F-Fli Fabric wrinkling of, Face-centered cubic (fcc) lattice, sphere packing, Voronoi diagram, Faces (geometrical) in deformable packings, and discrete spaces, in planar networks, Faces (human) development of bones in, parametrization of, random variations in, recognition of, Faceted crystal growth Factor (polynomial factorization) analog for Boolean formulas, and cycles in shift rules, and quadratic congruential generators, randomized algorithm for, and shift register periods, Factorial (n!) encoded as integer equation, and examples of universality, and hypersphere volume, leading digits in, and number of reversible block cellular automata, number with digits at, and QED perturbation series, as recursive sequence, and transcendental numbers, see also Gamma Factorial2 (double factorial) and isotropic tensors, Factories and self-reproducing systems, FactorInteger (integer factorization) and arithmetic system encoding

37. INDEX OF NAMES Fano, Robert M. (USA, 1917 ) and data compression, 1069 Fedorov, Evgraf S. (Russia,1853-1919) and shapes of 3D domains, 929 feigenbaum, mitchell J. (USA, 1944 http://www.wolframscience.com/nksonline/index/names/f-j.html?SearchIndex=f-j

38. AllRefer Encyclopedia - Chaos Theory (Mathematics) - Encyclopedia Some of the early investigators of chaos were the American physicist mitchell feigenbaum;the Polishborn mathematician and inventor of fractals (see fractal http://reference.allrefer.com/encyclopedia/C/chaosthe.html

AllRefer Channels :: Health Yellow Pages Reference Weather SEARCH : in Reference May 31, 2004 You are here : AllRefer.com Reference Encyclopedia Mathematics ... chaos theory By Alphabet : Encyclopedia A-Z C chaos theory, Mathematics Related Category: Mathematics chaos theory, in mathematics, physics, and other fields, a set of ideas that attempts to reveal structure in aperiodic, unpredictable dynamic systems such as cloud formation or the fluctuation of biological populations. Although chaotic systems obey certain rules that can be described by mathematical equations, chaos theory shows the difficulty of predicting their long-range behavior. In the last half of the 20th cent., theorists in various scientific disciplines began to believe that the type of linear analysis used in classical applied mathematics presumes an orderly periodicity that rarely occurs in nature; in the quest to discover regularities, disorder had been ignored. Thus, chaos theorists have set about constructing deterministic, nonlinear dynamic models that elucidate irregular, unpredictable behavior (see nonlinear dynamics ). Some of the early investigators of chaos were the American physicist Mitchell Feigenbaum; the Polish-born mathematician and inventor of fractals (see

39. A Beginner's Guide To Chaos: Feigenbaum's Bifurcation Diagram The bifurcation diagram was not created by mitchell feigenbaum, buthe found a way to understand it that no one had thought of. http://www.yiin.ca/chaos/fig.htm

Feigenbaum's Bifurcation Diagram The bifurcation diagram was not created by Mitchell Feigenbaum, but he found a way to understand it that no one had thought of. Among other things, the bifurcation diagram represents an idealized version of how a system can become chaotic. As you can see from the diagram below, the diagram splits into two after a certain point (a bifurcation) and into four at a later point. The bifurcations come faster and faster until the system becomes chaotic. Feigenbaum discovered that the bifurcations were occurring at a ratio that approached an irrational number that is approximately 4.669 in the bifurcation diagram. This was found to be true by experiment in real life examples. 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). Back to Index

40. Bibliography feigenbaum, mitchell J. (1978), Quantitative Universality For a Class of NonlinearTransformations, Journal of Statistical Physics, vol 19., No. http://inetsrv.lettersfromthecosmos.com/cosmos_ref.htm

Arbib, Michael A. (1964), Brains, Machines, and Mathematics, McGraw-Hill. Ashby, W. Ross (1964), Cybernetics, Methuen. Bertalanffy, Ludwig von (1968), General Systems Theory: Foundations, Development, Applications, New York, George Braziller. Baruss, Imants (1987), "Metanalysis of Definitions of Consciousness," Imagination, Cognition and Personality, vol 6(4), 1986-87, pp 321 - 329. Brook, Andrew (2000), "Unity of Consciousness: What It Is and Where It Is Found," Proceedings of the 22nd Annual Conference of the Cognitive Science Society, New York: LEA pp 102-108. Brown, Keith Wayne (1997), "The I/Not-I Discourse: The World of Existence and the World of Existenz", Epsitemology & Jaspers Seminar, http://www.unt.edu/heidegger/pdfs/kb1.pdf Clancey, W.J. (1989) The Frame of Reference Problem in Cognitive Modeling. Proceedings of 11th Annual Conference of the Cognitive Science Society. Ann Arbor. Erlbaum Associates, 107-114. Also see, http://cogprints.ecs.soton.ac.uk/archive/00000296/00/102.htm Crosson, F. J. and Sayre, K. M., editors (1967), Philosophy and Cybernetics, Simon and Schuster. Day, Richard H. (1982), "Irregular Growth Cycles," American Economic Review, June 1982, Vol. 72, No. 3, pp 406 – 444.

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