Tuesday, November 18, 2008

Patterns and Fractals

                           Patterns  and  Fractals © 2000             

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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.

"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.

"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.

 "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.

"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.

"Understanding  of life begins with the understanding of patterns."

Capra F. (1996) "The Web of Life",   p. 80, Anchor Books.

"Fractals are to chaos what geometry is to algebra."

Sprott. J. C. (2003) "Chaos and Time-Series Analysis", p. 272, Oxford UP.

"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.

"Humans are pattern-seeking animals."

Graham B. (2006) "The Intelligent Investor", p. 220, Revised Edition, Updated with New Commentary by Jason Zweig, Collins.


Fractalization of the Language   (25-August-2002)

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

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 in Guadalupe       Clouds                    Cloudburst                                       Rockywave                                
NASA                                               NASA                         Vehrenberg K.G.     Kenneth Ford                                 Oytun Ka



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                      


Iridium Crystal 
Erwin Moller     



Coccolithophore Larva                      Starfish                 Diatom                           Radiolaria                                                                                                                     
Emiliania Huxley          William White  Bisson brothers   Maurice Burton                                                                                                                                            




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           
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 .


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




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.



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    Science


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