Patterns and Fractals
© 2000
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-May-2008
Patterns Quotes
"Understanding of life begins with the understanding of patterns."
Capra F. (1996) "The Web of Life", p. 80, Anchor Books.
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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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"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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"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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"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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"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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"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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Fractalization of the Language (25-August-2002)
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•
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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 Volcano
Nasser Lake
Wadi Hadramaw
Alaska
Jupiter
Georg Gerster
Robert Harding
NASA
NASA
NASA
NASA
Zeph
Van Allen
Time-Life - "The Poles"
Springs
dendrite
Mud
Flow:
Clouds:
Clouds
Clouds in Guadalupe
Clouds
Cloudburst
Rockywave
NASA
NASA
Vehrenberg K.G.
Kenneth
Ford
Oytun
Ka
Electricity:
Lightning
Electric
Spark
Electric Spark
Kirlian "lightning storm"
Lichtenberg figure
Subatomic Particles
Iridium Crystal
Unknown
Manfred Kage
A. von Hippel
E.
Lane
Ted
Kinsman
CERN
Erwin Moller
Diffraction:
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
Ben Tamari
John Andre Aasen
Joe McNally
Roy McClenaghan
Lennart Nilsson
Kavenoff and Bowen
Manfred Kage
Blood in the Brain
Blood in The Head
The
Lung
The Nerves in Brain
Vitamin
SPL/Photo
Res.
"Mind & Body"
Julius
Comroe
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:
Mandala Ancient Korinth - Roman Vila
Fractal Image
Time-Life
"Ancient Wisdom and Secret Sects" p. 139 Postcard Peitgen
and Saupe
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 .
●
Attractors in Nature:
An X Class Flare Region on the Sun
A Mysterious Hexagonal Cloud System on Saturn
The Cat's Eye Nebula
TRACE
Project
NASA NASA
NASA
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 )
BooksAdam 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.
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.
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
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
