Patterns, Fractals and  Attractors

 

Published 2000,  Update 07-January-2014

 

 

 

 

Patterns Quotes

Norbert Wiener (1954) "The Human Use of Human Beings", Da Capo Press. p. 21, 95, 96 respectively.

"Messages are themselves a form of pattern and organization."

"Organism is opposed to chaos, to disintegration, to death, as message is to noise."

"A pattern is a message, and may be transmitted as a message."

"We are but whirlpools in a river of ever-flowing water."

"We are not stuff that abides, but patterns that perpetuate themselves."

"It is the pattern maintained by this homeostasis, which is the touchstone of our personal identity."

 

Carl G. Jung (1964) "Man and his Symbols", Aldus Books-Jupiter Books. p. 308.

"Our conscious representations are sometimes ordered (or arranged in a pattern) before they have became conscious to us."

 

Ni Hua-Ching (1983) "The Book of Changes and the Unchanging Truth", Seven Star Communications, Santa Monica. p. 23.

ying yang "All Movement, all change, is a pattern of the interaction of yin and yang."

 

Rucker R. (1987) "MIND TOOLS: The Five Levels of Mathematical Reality", Houghton Mifflin Company, Boston. p. 3.

"Mathematics is the study of pure pattern, and everything in the cosmos is a kind of pattern."

 

Rolf I. P.  (1989) "Rolfing",  Healing Art Press. p. 15.

"As in all matter organized into biological units, there is a pattern, an order, in human bodies."

 

Gleick J. and Porter E. (1990) "Nature's Chaos", Little, Brown and Company.  p. 35.

"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.
"

 

Hardy G.H. (1992) "Mathematician's Apology", Canto ed., Cambridge University Press.  p. 84.

"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."

 

Casti L. J. (1992) "Reality Rules: I Picturing the World in Mathematics - The Fundamentals", John Willey. p. 229.

"We can think of the evolution of a cellular automaton as a pattern-recognition process, in which all initial configurations in the basin of attraction of a particular attractor are thought of as instances of some pattern with the attractor being the "archetype" of this pattern. Thus, the evolution of the different state trajectories toward this attractor constitutes recognition of the pattern."

 

Stewart (1995) "NATUR'S NUMBERS: Discovering Order and Pattern in the Universe", Phoenix. p. 1, 1, 3, 16, 21, 142, 168, respectably.

"We live in a universe of patterns."

"Nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes."

"Patterns possess utility as well as beauty."

"Each of nature's patterns is a puzzle, nearly always a deep one."

"Mathematics is the science of patterns, and nature exploits just about every pattern that there is."

"Even when the consequence of natural laws seem to be patternless, the laws are still there and so are the patterns."

"Nature's patterns are "emergent phenomena, They emerged from an ocean of complexity ..."

 

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

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

 

Devlin K. (1998) "The Language Of Mathematics: Making the Invisible Visible", Freeman / Owl books. p. 3.

"...mathematics is the science of patterns."

 

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

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

 

Mandelbrot  B. B. and Hudson R. L. (2004) "The (mis) Behavior of Markets", Basic Books. p. 21.

Patterns are the fool's gold of financial markets.

 

Pickover, C. A.  ed. (2005) "PATTERN BOOK: Fractals, Art and Nature", World Scientific. p. 403

Yuzo Nakano: "I did my research as an artist, not as a scientist: ... the reality of nature is the shape of patterns formed by the continual oscillation and transformation of energy."

 

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

"Humans are pattern-seeking animals."

 

Wolfram S. (2009) "Cellular Automata as Models of Complexity" (1984).

"Natural systems from snowflakes to mollusc shells show a great diversity of complex patterns. The origins of such complexity can be investigated through mathematical models termed `cellular automata'."

 

 

stoper

 

 

Fragments

Fractalization of the Language I  (29-April 2002)

A word is worth a thousand ...?... .

A picture is worth a thousand words, as the old saying goes.

But sometimes: One good sentence is worth a thousand pictures.
for example: A picture is worth a thousand words. (following Mobius strip). (added: 5-April-2007).

A metaphor is worth a thousand pictures.

An allegory is worth a thousand metaphors.

A .....?..... is worth a thousand allegories.

Fractalization of the Language II (15 November-2009)

Between any two 'points' in a set of: points, numbers, words, sentences, paragraphs, thoughts, etc.,
we can put another 'point', and if the set is not big enough, we can add another 'point'.

Wislawa Szymborska (2005) "COLON" "The nightmare of the poet" (translate Deena Land, 15-July-201)

"An allocated number of words. Never a needless one
Meaning - no poetry
And no philosophy and no religion.
"

Fractals relate to attractors as cobblestones in roads. (added 1.1.2000)

Fractals and chaos is like sewing and cooking. (added: 28-March-2009)

 

stoper

 

Patterns in Nature:
Siberian TrapsWadi HadramawLake ErepecuNamibiaUtah Manantah Reservoir, Mali Jeff AluGreenland2012
Siberian Trap               Wadi Hadramaw            Lake Erepecu               Namibia                        Utah             Manantah Reservoir, Mali  Jeff Alu    Greenland 2012

/volcanofiji IslandsThe Zagros Mountains - IranThe poleHector GarridoNature Fractal Christchurch, New Zealand
Volcano                           Fiji Islands                                      The Zagros Mountains, Iran           The pole                         Héctor Garrido      hristchurch, New Zealand  


Zeph Van AllenspringsSand PatternsPele FingerprintsAlluvial FanIn Southern IranHimalayaPuma
Zeph Van Allen              Springs                 Macaskill-Sand Patterns  Hanson-Pele Fingerprints    Alluvial Fan In Iran             Himalaya               Bill Burton - Puma        


NapoleoniteBeijing OncolitesPatternSand FractalDolomitPattern
Denovich-Napoleonite        Beijing Oncolites - Shanan  


Dendrites:
dendritedendritedendritedendritedendritedendritedendrite
Diffusion Limited Aggregation (DLA)


Rivers and Deltas:
Delta MesopotamiaDelta GangesDelta Delta the Selenga RiverDelta Nasser LakeDelta Greenlanddelta MissuriYukon delta
Mesopotamia   Ganges              Aerial Snaking Delta    Selenga River           Nasser Lake               Greenland dela                Missouri          Yukon delta - NASA


Cracked: glass, mud, metal, rocks and wood respectively:
Harold Edgerton Crack GlassCrack Glass Crack Glass Crack Glass Crack GlassCrack Glass
crack mudcrack mudcrack mudcrack mudcrack mudcrack snow
crack metalcrack metalcrack lavacrack rockscrack rockscrack asphalt
crack woodcrack woodcrack woodcrack woodcrack woodcrack woodcrack wood


Drops, Splashes and Bubbles:
Harold EdgertonRaffaele De MatolaIrene MullerHarold EdgertonsplashBubbleBubble
Harold Edgerton  


Flow, Whirlpools, Swirls, Vortices and Symmetry:
water patternsflawwater flawwater flawwater flawwater flawmargarinClark LittleflamsmokesmokefireVorticeVortice Ying Yangwhirlpool
whirlpoolJupiterVorticeswhirlpoolVorticewhirlpoolsymmetry
NASA                                                                                                                                                                                Alexander Lillevik                  Symmetry


Short Movies of Water Patterns:  video: Ben Tamari, music: Mordechai Cohen
SwirlWater LightWater FlawWater Gold lineswater ringWater StarsWater Flaw
Double Swirl                         Water Moon Light           Water Flaw    Water Gold lines             Water Patterns                   Water stars                 Water Interference


Clouds:
CloudsCloudsCloudsCloudsCloudsCloudsCloudsAsh CloudAsh CloudAtom BombSuper cell Thunder stormVolcano
NASA                              NASA Mount C leveland           J. Warren                                           Atom bomb                            
Sarychev Peak Volcano


Multi Fractals:
Multi FractalsMulti Fractals
Multi FractalsMulti Fractals
Multi fractalMulti FractalsMulti Fractals
Multi FractalsMult iFractals  James Van Gundy
Multi FractalsmultifractalMulti Fractals/Multi Fractal



Electricity:
ElectricityElectricityElectricityElectricityElectricityElectricityElectricityElectricity
Lightning        Kirlian "lightning storm"   Static Electric Ball       Lichtenberg figure           Electric spark             Electric spark             Positive discharge


Diffractions and Interferences:
DiffractionsDiffractionsDiffractionsDiffractionsDiffractionsDiffractions
interefernce
interferenceInterferencesInterferencesInterferences
QuasicrystalsInterferencesinterferenceInterferences


Vibrations:
                                                                                    Cymatics:
VibrationsVibrationsVibrationsVibrationsAtoms in an enzyme Molecule
VibrationsSound VibrationChladni Vibrationssound waves
SubAtomic Particles   Atom                                           Berenice Abbott      Peter Cadogan           
Cymatics                                          Chladni                        Sound waves


Self Organization, Emergence and Complexity:
Self OrganizationSelf OrganizationSelf OrganizationSelf OrganizationSelf OrganizationSelf Organization Jerry MatchettSelf OrganizationSelf OrganizationSelf Organization
Space: The finel frontier               Gardhaia, Algeria       Robert B. Haas                                         Jerry Matchett


Astronomy,
Astronomyspiral starsun eclypsesun
Saturn                             
     spiral star                                      Sun


Microscopic fungus, Diffusion, Cellular Automata, Nano Technology:

Sordaria Fimicola AndersoncellCellular Automata Jonathan McCabeCellular Automata Jonathan McCabenano technologynano technology
Sordaria fimicola       Cell                               Jonathan McCabe                                        Nanotechnology 1          Nanotechnology 2


Sea Creatures:
diatomssea creaturesea creaturesea creatureLarvasea creature
Diatoms                                      Jellyfish 1                          Jellyfish 2                             Tina Carvalho    William White

sea creatureRadiolarianRadiolariandiatom
sea creaturebacteria
Emiliania Huxley                  Radiolarian                                                Maurice Burton


Shells:
ShellshellShellshellShellShellShell


Trees:
Quiver treeTree    baobabtreeTree  Dracaenatreetreestrees
leavestreeTreeTreeTreeTreetreeTreeTree


Leaves:
leavesleafleaf
leafleafleafleafleaf
leafleafleafleafleafleafleafleafleafleaf
Antonio Franchi          


Plants:
Cauliflower Romanescocactuscactusleafthornthornthornthornthornthornthorndandelionthornsunflowerthornthornthornthorncactuscactuscactuscactusthornthorn


Animals:
skinskinsnake skingirapha skinzebra skinmetalagama tailfractalmuthbirdfractalpeacocksnail


Human Body:
brain Andre AasenbrainhearteyeearkidneyCyst Of Kidney
he Brain                             The Brain Scan          The Heart, McNally   The Eye, McClenaghan   The Ear, Nilsson   The Kidney, Kage      Cyst


Fractal 5D-2Llungblood in brainBlood in The HeadThe Nerves in BrainDNA moleculeVitamin
Fractal 5D-2L   Comroe            Blood in The Brain                   Blood in The Head                             The Nerves in Brain             DNA molecule            Vitamin


Architecture:
seashell-houseMonastery Of Saint Anthony EgyptAnabela Sequeira LaosAustralia Sydney Opera HouseBelgrade Sreten PantelicIndiaMyanmarMoroccofractal
The Nautilus             Egept                                   Laos           Australia, Sydney Opera House   Belgrade     India       Myanmar           Morocco             France


indiaMuqarnas Dome BaghdadIran VilaRoman VilaMIQELfractalchandelier fractal
India                        Muqarnas Dome, Baghdad   Iran Vila                      Italy, floor mosaic  Roman Vila             MIQEL                                                  Chandelier


Arts:
Mandelbroth Esher LikeHokusai fractal LikeHiroshige fractal likepersian art fractal likealvador Dali  visage of warAfrican fractalPoul Klee Fugue in Red
Mandelbroth set    Hokusai                                                                Hiroshige          Iran art           Salvador Dali - visage of war African fractal   Klee-Fugue in Red


Graphics:
EscherHyperbolic Tiling William ShawPeitgen and Saupe Yuzo NakanoFelipe Arte Mandalaeltic circle fractalTom ShanonJos Leys fractal
Escher                        William T. Shaw          Peitgen and Saupe       Yuzo Nakano          Felipe Arte        Celtic circle fractal       Tom Shannon            Jos Leys


Religion:
Yin Yang FractalMandalaMandalaMandalaMandalaHamsa Mira Krispel Ethiopian Cross
Yin and Yang             Mandala:                                                                                                                             Hamsa Mira Krispel
N EthiopianCross


Fractals in Computer 2 Dimensions (figured with FractInt).
KAM Kolmogorov Arnold MoserDynamicsBransleycircleComplex Newton
KAM, Kolmogorov-Arnold-Moser     Dynamic                            Barnsley                                    Circle                                       Complex Newton

Mandelbrot SetLyapunovpopcornspiderunity
Mandelbrot set                      Lyapunov                                    Popcorn                                    Spider                                          Unit
 

Fractals in Computer 3 Dimensions:
caidacaidacaidacaidacaida
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 Walru s - Graph Visualization Tool .



Cobwebs
Cobweb Robert Donovancubweb Moonjazzcubweb Kieran
Cobwebcubwebcubweb


Almost Mathematical Creatures in Nature:
Mandelbrot Set
Almost Mandelbrot, Dendi Caldera EthiopiaAlmost Mandelbrot Paul CheslAlmost Mandelbrot Set John MumawAlmost Mandelbrot SetAlmost Mandelbrot Se Campello Boris Ice ThingAlmost Mandelbrot Set - Antarctica IceAlmost Mandelbrot Set Ben TamariAlmost Mandelbrot Set Ben Tamari
Dendi Caldera, Ethiopia   Paul Chesley, Yellowstone   North pole of Saturn         John  Mumaw       Campello Boris - Ice Thing
    Antartica's Moving Ice  


Mobius Strip                                 Sierpinski fractal                
Almost Mobius StripMount Sierpinski
Drew Patrick                            Martin Richard                             


Natural Fractals:
similaritySimilarityLightninng FractalFungsNaturalFractalNaturalFractal
Pickover                                              Designin Nature


Natural Attractors
Sun Attractor NASASaturnCats Eye NebulaCats Eye NebulaCats Eye Nebulamoon's gravity
An X Class Flare Region on the Sun  A  Mysterious Hexagonal Cloud System on Saturn   The Cat's Eye Nebula
TRACE Project NASA                                                                                                                                                            Russell E. Cooley IV


Attractors in Brain, Music
and Earthquake:
Brain attractorRolf Wollin Music attractorgraphics of Beethoven 9 1 movement
Tamari Attractor.gifA sand earthquake tracing pendulum
Walter J. Freeman                           Rolf Wallin                  Beethoven - Stephen Malinowski    
N  Tamari attractor    A sand earthquake tracing pendulum


Attractors in Computer 3 Dimensions: figured with software
Eco2.
Chua attractorIkeda AttractorLorenz AttractorPickover AttractorRossler attractorTamari Attractor
Chua attractor                     Ikeda Attractor                Lorenz Attractor                Pickover Attractor       Rossler Attractor            Tamari Attractor


Humor in Chaos, Fractals and Attractors:
Humor - Mini Fractal
Humor - fractalHumorHumor-BabushkaHumor - elevator fractalhomur- fractalNorway economics
   

stoper

   

Speculation 1, 19-October-2013   On Patternness (y) as function of Aggregation [ y = f(x) ].

The three Law's regimes (3RSD) - The Random laws (gases-like), the Statistical (chaotic) laws (liquids-like) and the Deterministic laws (solids-like).

pattern aggregation determinism


exampels:

Deterministic Laws: Lagrangian
                                   Lorentz transformations

Statistical Laws: Weather      - Lorenz Attractor
                              Economics - Tamari Attractor

Random Laws: Cellular Automata - The rule 110 of Stephan Wolfram
                                                          - Games of life

   

stoper

 

Books and Articles:

John A. Adam (2003) "Mathematics In Nature: modeling patterns in the natural world", Princeton UP.

Donald M. Anderson (1961) "Elements of Design", Holt, Rinehart and Winston.

Michael F. Barnsley (1993) "Fractals EveryWhere", 2ed. Academic Press.

Michael F. Barnsley (2006) "SuperFractals: Patterns of Nature", Cambridge UP.

John Briggs (1992) "Fractals: The Patterns of Chaos", Simon and Schuster.

Peter Cadogan (1985) "From Quark to Quasar", Cambridge UP.

John L. Casti (1992) "Reality Rules: I Picturing the World in Mathematics - The Fundamentals", John Willey.

John L. Casti (1992) "Reality Rules: II Picturing the World in Mathematics - The Frontier", John Willey.

Keith Devlin (1998) "The Language Of Mathematics: Making the Invisible Visible", Freeman / Owl books.

Field and Golubitsky (1992) "Symmetry In Chaos: A Search for Pattern in Mathematics, Art and Nature", Oxford UP.

Priya Hemenway (2005) "Divine Proportion : F (Phi) In Art, Nature, and Science", Sterling Pub. NY.

Janus H. (1957) "Nature As Architect",  Frederick Ungar Pub. NY.

andelbrot B.B. (1983) "The Fractal Geometry of Nature", Freeman.

Mandelbrot B. B. (2004) "Fractals and Chaos", Springer.

Novak M. M. (Ed.), (2004) "Thinking in Patterns Fractals and related Phenomena in Nature", World Scientific.

Rucker R. (1987) "MIND TOOLS: The Five Levels of Mathematical Reality", Houghton Mifflin Company, Boston.

Peitgen and Saupe, (Ed.), (1988) "The Science of Fractal Images", Springer-Verlag.

Peitgen, Jurgens and Saupe (1992) "Chaos and Fractals, New Frontiers Of Science", Springer-Verlag.

Pickover C.A. (Ed.), (2005) "PATTERN BOOK: Fractals, Art and Nature", World Scientific.

Pickover C. A. (2009) "THE MATH BOOK: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics", Sterling.

Sprott J. C. (1993) "Strange Attractors: Creating Patterns in Chaos", M T Books, NY.

Stewart I (1995) "NATUR'S NUMBERS: Discovering Order and Pattern in the Universe", Phoenix.

Wille L. T. (Ed.), (2004) "New Directions in Statistical Physics: Econophysics, Bioinformatics, and Pattern Recognition", Springer.

Wolfram S. (2002) "A New Kind of  Science", Wolfram Media, Inc..


Links

http://easyweb.easynet.co.uk/~iany/patterns/index.htm

http://www.bathsheba.com/

http://www.bugman123.com/index.html

http://fractalfoundation.org/

http://www.nysm.nysed.gov/virtual/collections/splendor_in_stone/index.html

http://neurofuture.blogspot.com/2007/02/cellular-automata.html

www.fractalus.com

http://news.bbc.co.uk/2/hi/science/nature/7617191.stm

http://www.patternsinnature.org/index.html

http://photography.nationalgeographic.com/photography/photogalleries/patterns-in-nature< /p>

http://pespmc1.vub.ac.be/Photos/Cracks.html

http://pespmc1.vub.ac.be/Photos/patterns.html

http://polymer.bu.edu/ogaf/

http://www.josleys.com/index.php

http://www.tomshannon.com/

http://www.youtube.com/watch_popup?v=RWgg5-kUSho&vq=medium

http://www.physlink.com/education/essay_weinberg.cfm

 

Software:

http://www.fractalsciencekit.com/

http://www.fractint.org/

http://www.chaoscope.org/

http://cgi.ebay.com/ECO-2-Economic-Simulator

http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=437

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