Patterns and Fractals © 2000
Lines in blue are "Links".
Lines in white are "quotes".
Lines beginning with a yellow (g) are news or updates.
Black lines are my text, You are allowed to copy from the text, providing the copyright is properly attributed to [© Ben Tamari ( www.ecometry.biz )].
Update 22-August-2008
Patterns Quotes
"Messages are themselves a form of pattern and organization." p. 21.
"Organism is opposed to chaos, to disintegration, to death, as message is to noise." p. 95.
"A pattern is a message, and may be transmitted as a message." p. 96.
"We are but whirlpools in a river of ever-flowing water. We are not stuff that abides, but patterns that perpetuate themselves." p. 96.
"It is the pattern maintained by this homeostasis, which is the touchstone of our personal identity." p. 96.
Norbert Wiener (1954) "The Human Use of Human Beings", Da Capo Press.
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"Our conscious representations are sometimes ordered (or arranged in a pattern) before they have became conscious to us." p. 308.
Carl G. Jung (1964) "Man and his Symbols", Aldus Books-Jupiter Books.
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"As in all matter organized into biological units, there is a pattern, an order, in human bodies."
Rolf I. P. (1989) "Rolfing", p. 15, Healing Art Press.
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"The human mind is a powerful pattern-recognition machine, more powerful than any computer yet built.
Sometimes it is too powerful; it detects patterns where they do not really exist."
Gleick J. and Porter E. (1990) "Nature's Chaos", p. 35, Little, Brown and Company.
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"A mathematician, like a painter or a poet, is a maker of patterns.
If his patterns are more permanent than theirs, it is because they are made with ideas."
Hardy G.H. (1992) "Mathematician's Apology", p. 84, Canto ed., Cambridge University Press.
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"Understanding of life begins with the understanding of patterns."
Capra F. (1996) "The Web of Life", p. 80, Anchor Books.
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"Fractals are to chaos what geometry is to algebra."
Sprott. J. C. (2003) "Chaos and Time-Series Analysis", p. 272, Oxford UP.
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"Patterns are the fool's gold of financial markets."
Mandelbrot B. B. and Hudson R. L. (2004) "The (mis) Behavior of Markets", p. 21, Basic Books.
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"Humans are pattern-seeking animals."
Graham B. (2006) "The Intelligent Investor", p. 220, Revised Edition, Updated with New Commentary by Jason Zweig, Collins.
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Fractalization of the Language (25-August-2002)
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A word is worth a thousand ...?...
As the old saying goes: "A picture is worth a thousand words"
[But sometimes: One (good) sentence is worth a thousand pictures. for example: "A picture is worth a thousand Words" (To follow suit Mobius Strip).] 5-April-2007.
A metaphor is worth a thousand pictures
An allegory is worth a thousand metaphors
A .....?..... is worth a thousand allegories
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Fractals relate to Attractors as Cobblestones in Roads. (2000)
Fractals in Nature:
Mesopotamia Ganges Siberian Traps Nasser Lake Wadi Hadramaw Eastern Greenland Norwegian Fjords
Georg Gerster thunderbolts.info NASA
Volcano Zeph Van Allen Springs dendrite David Lynch EPOD Jupiter - NASA
Splash and Flow:
Harold Edgerton Alexander Lillevik
Clouds:
Clouds Clouds in Guadalupe Clouds Cloudburst Rockywave
NASA NASA Vehrenberg K.G. Kenneth Ford Oytun Ka
MultiFractals:
Electricity:
Lightning Electric Spark Electric Spark Kirlian "lightning storm" Electric Spark Lichtenberg figure Subatomic Particles Static Electric Ball
Unknown Manfred Kage A. von Hippel E. Lane Ted Kinsman CERN
Diffractions:
Iridium Crystal
Erwin Moller
Water:
Sea:
Coccolithophore Larva Starfish Diatom Radiolaria
Emiliania Huxley William White Bisson brothers Maurice Burton
Plants:
Animals:
Human Body:
Fractal 5D-2L The Brain The Heart The Eye The Middle Ear DNA molecule The Kidney The Lung
Ben Tamari John Andre Aasen Joe McNally Roy McClenaghan Lennart Nilsson Kavenoff and Bowen Manfred Kage Julius Comroe
Blood in the Brain Blood in The Head The Nerves in Brain Vitamin
SPL/Photo Res. "Mind & Body" David Philips
Fractals in Arts:
Fractals in Architecture:
India Muqarnas Dome Tomb of Zubaida, Baghdad
Scala, "Islam Art and Architecture" p. 117
Religion: Archeology: Graphics: Sound:
Mandala Ancient Korinth - Roman Vila Hyperbolic Tiling Fractal Image Sound Waves
Time-Life "Ancient Wisdom and Secret Sects" p. 139 Postcard William T. Shaw Peitgen and Saupe Jung "Man and his Symbols" p. 305
Fractals in Computer 2 Dimensions. (figured with FractInt):
Mandelbroth Set KAM, Kolmogorov-Arnold-Moser Barnsley Circle Complex Newton
Dynamic Lyapunov Popcorn Spider Unit
Fractals in Computer 3 Dimensions:
Walrus uses 3D. hyperbolic geometry to display graphs under a fisheye-like distortion, it is being developed by Young Hyun at CAIDA,
based on research by Tamara Munzner. figured with Walrus - Graph Visualization Tool .
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Attractors in Nature:
An X Class Flare Region on the Sun A Mysterious Hexagonal Cloud System on Saturn The Cat's Eye Nebula A Smoke Angel from Airplane Flares
TRACE Project NASA NASA NASA Russell E. Cooley IV
Attractors in Brain and Music:
The trajectory of a solution set of a dynamic model of the olfactory brain that simulates epileptic-activity Fractal Music
Walter J. Freeman Rolf Wallin
Attractors in Computer 3 Dimensions: figured with software attractors Eco1 (to download Eco0)
Lorenz Attractor Rossler Attractor Ikeda Attractor Tamari Attractor (The Nest )
Books
Adam J. A. (2003) "Mathematics In Nature: modeling patterns in the natural world", Princeton UP.
Anishchenko, Astakhow, Neiman, Vadivasova, Schimansky-Geier (2002) "NonLinear Dynamics of Chaotic and Stochastic Systems", Springer.
Auyang T. S. (1998) "Foundations of Complex-System Theories In Economics, Evolutionary Biology, and Statistical Physics", Cambridge UP.
Bak P., "How Nature Works: the science of self-organized criticality", 1997, p. 31, Cambridge University Press.
Banks J., Dragan V., Jones A., (2003) "Chaos: A Mathematical Introduction", Cambridge UP
Barnsley M. F. (1993) "Fractals EveryWhere", 2ed. Academic Press.
Barnsley M. F. (2006) "SuperFractals: Patterns of Nature", Cambridge UP.
Briggs J. (1992) "Fractals: The Patterns of Chaos", Simon & Schuster.
Brock, Hsieh and LeBaron (1991) "Nonlinear Dynamics, Chaos, and Instability, Statistical Theory and Economic Evidence", The MIT Press.
Burger E. B. & Starbird M. (2005) "Coincidences, Chaos, and All That Math Jazz", W.W. Norton & company, NY.
Chapman R. and Sprott J. C. (2005) "Images of a Complex World", include CD, World Scientific.
Capra F. (1996) "The Web of Life", Anchor Books.
Ching-Yao Hsieh and Meng-Hua Ye (1991) "Economics, Philosophy and Physics", ME Sharpe, N.Y.
Crilly A. J., Earnshaw R. A., Jones H. (Editors) (1991) "Fractals and Chaos", Springer-Verlag.
Cvitanovic' P. (editor) (1989) "Universality in Chaos", 2ed, Institute of Physics Publishing, Bristol and Philadelphia.
GyÖrgy D. (2007) "Symmetry", Birkhäuser.
Edwin A. A. (1884) "Flatland", Princeton UP 1991.
Feder J. (1988) "Fractals", Plenum Press.
Field M. and Golubitsky M. (1992) "Symmetry In Chaos: A Search for Pattern in Mathematics, Art and Nature", Oxford UP.
Frame and Mandelbrot, editors, (2002) "Fractals, Graphics, and Mathematics Education", The Mathematical Association of America.
Gleick J. (1987) "CHAOS - Making a New Science", New York: Viking.
Gleick and Porter (1990) "Nature's Chaos", Little, Brown and Company.
Hall N. (editor) (1991), "Exploring CHAOS", W.W. Norton & Company, N.Y..
Hilborn R. C. (1994) "Chaos and Nonlinear Dynamics", Oxford UP.
Holden A.V. (editor) (1986) "Chaos", Princeton UP.
Kauffman S.A. (1993) "The Origins Of Order", Oxford University Press.
Lesmoir-Gordon N. (2004) "The Colours of Infinity: The Beauty, The Power and the Sense of Fractals", include CD, Clear Books.
Lorenz H. W. (1993) "Nonlinear Dynamical Economics and Chaotic Motion", Springer-Verlag.
McCouley J. L. (1993) "Chaos, Dynamics, and Fractals", Cambridge.
Mandelbrot B. B. (1983) "The Fractal Geometry of Nature", Freeman.
Mandelbrot, B. B. (2004) "Fractals and Chaos", Springer.
Mandelbrot and Hudson, (2004) "The (Mis)Behavior Of Markets", Basic Books.
Marks-Tarlow Terry (2008) "Psyche's Veil: Psychotherapy, fractals and complexity", Routledge.
Medio in Collaboration with Gallo (1992) "Chaotic Dynamics - Theory and Applications to Economics", Cambridge University Press.
Mira C. (1987) "Chaotic Dynamics", World Scientific.
Mirowski P. (1989) "More Heat Than Light: Economics as Social Physics, Physics as Nature's Economics", Cambridge University.
Moon F. C. (1987) "Chaotic Vibrations", John Wiley & Sons, N.Y..
Ott E. (1993) "Chaos in Dynamical Systems", Cambridge.
Peitgen H. O., and Saupe D. Editors (1988) "The Science of Fractal Images", Springer-Verlag.
Peitgen H. O., Jurgens H. and Saupe D. (1992) "Chaos and Fractals, New Frontiers Of Science", Springer-Verlag.
Peters E. E. (1991) "Chaos and Order in the Capital Markets", John Wiley & Sons, Inc.
Pickover C. A. (1990) "Computers, Pattern, Chaos and Beauty", St. Martin's Press, N.Y..
Pickover C.A. (1999) "Surfing Through Hyperspace", Oxford UP.
Prigogine I. (1980) "From Being To Becoming", W. H. Freeman And Company.
Puu T. (1991) "Nonlinear Economic Dynamics", 2ed., Springer-Verlag.
Ravi B. (1985) "The Great Depression Of 1990", Simon and Schuster, NY.
Reichl L.E. (1992) "The Transition to Chaos", Springer-Verlag.
Rosser J. B. (1991) "From Catastrophe to Chaos: A General Theory of Economics Discontinuities", Kluwer Academic Publishers.
Rucker R. v. B. (1977) "Geometry, Relativity and the Fourth Dimension", Dover.
Sardar Z. and Abrams I., (1998) "Introducing Chaos", Icon Books UK.
Schroeder M. (1991) "Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise", W. H. Freeman and Com. N.Y..
Seydel R. (1988) "From Equilibrium To Chaos", Elsevier.
Shaw W. T. (2006) "Complex Analysis with MATHEMATICA®" Cambridge UP.
Sprott J. C. (1993) "Strange Attractors: Creating Patterns in Chaos", M&T Books, NY.
Thom R. (1975) "Structural Stability and Morphogenesis", The Benjamin Pub.
Thompson D.W. (1942) "On Growth And Form", Dover Pub. New York 1992.
Ward M. (2001) "Universality, The Underlying Theory behind Life, the Universality and Everything", MacMillan.
Weeks J.R. (2002) 2ed. "The Shape of Space", 2002, Marcel Dekker, Inc. New York.
Wegner T. and Tyler B. (1993) "Fractal Creations", 2ed, Waite Group Press.
Wiener N. (1954) "The Human Use of Human Beings", Da Capo Press.
Zaslavsky G.M. (1985) "Chaos in Dynamic Systems", translated from Russian by Kisin V.I., Harwood AP.
Links
www.ams.org/mathimagery Art
www.fractalus.com Art
http://directory.google.com/Top/Science/Math/Chaos_and_Fractals/ Index
http://dmoz.org/Science/Math/Chaos_and_Fractals/ Index
http://mathres.kevius.com/art.html Index
http://mathforum.org/library/view/62158.html Index
http://spanky.triumf.ca/www/whats-new.html Index
www.student.math.uwaterloo.ca/~pmat370/FractalRefs.html Index
http://classes.yale.edu/fractals/ Learning
http://en.wikipedia.org/wiki/Fractals Learning
www.fractalfoundation.org/index.html Learning
http://local.wasp.uwa.edu.au/~pbourke/fractals/ Learning
http://math.bu.edu/DYSYS/dysys.html Learning
http://math.rice.edu/~lanius/frac/ Learning
www.3dfractals.com Math.
http://hypertextbook.com/chaos/ Math.
http://klein.math.okstate.edu/IndrasPearls/ Math.
www.around.com/chaos.html (Gleick) Science
http://www.chaos.umd.edu/ Science
http://chaos.aip.org/ Science
www.elumenati.com/id/street_science Science
http://www.gutenberg.org/files/20417/20417-h/20417-h.htm Science
www.math.uwaterloo.ca/~wgilbert/FractalGallery/FractalGallery.html Science
http://mathworld.wolfram.com/Chaos.html (Wolfram) Science
http://nlds.sdsu.edu/index.html#restoration Science
www.pha.jhu.edu/~ldb/seminar/index.html Science
www.pickover.com (Pickover) Science
http://star.tau.ac.il/~eshel/Bio_complexity/2.Dynamical%20Systems/intro_to_chaos.ppt#257,2 Science
http://139.78.112.6/IndrasPearls/Wonders/ Science
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