Patterns, Fractals and Attractors

Published 2000, Update 13-Januar-2013

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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."

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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."

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

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

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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."

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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."

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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."

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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."

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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."

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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 ..."

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

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

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

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

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

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

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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.

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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."

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

"Humans are pattern-seeking animals."

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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'."

Fragments
Fractalization of the Language I (29-April 2002)

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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.

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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."

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

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

Patterns in Nature:

Siberian Trap              Wadi Hadramaw     Lake Erepecu             Namibia                    Utah            Manantah Reservoir, Mali Jeff Alu Greenland 2012

Volcano                          Fiji Islands                                 The Zagros Mountains, Iran   the pole                         Héctor Garrido Christchurch, New Zealand

Zeph Van Allen           Springs               Macaskill-Sand Patterns Hanson-Pele Fingerprints Alluvial Fan In Iran  Himalaya               Bill Burton - Puma

Denovich-Napoleonite   Beijing Oncolites - Shanan

Dendrites:

Diffusion Limited Aggregation (DLA)

Rivers and Deltas:

Mesopotamia Ganges               Aerial Snaking Delta Selenga River Nasser Lake                Greenland delta                  Missouri             NYukon delta - NASA


Cracked: glass, mud, metal, rocks and wood respectively:

Drops, Splashes and Bubbles:

Harold Edgerton

Flow, Whirlpools, Swirls, Vortices and Symmetry:

Jupiter                       NASA                                                                                                                                        Alexander Lillevik                 Symmetry

Short Movies of Water Patterns: video: Ben Tamari, music: Mordechai Cohen

Double Swirl                      Water Moon Light      Water Flaw   Water Gold lines    Water Patterns          Water stars                   Water Interference

Clouds:

NASA                              NASA Mount Cleveland       J. Warren                          Atom bomb                                         N                              Sarychev Peak Volcano

Multi Fractals:
$Multi fractal$
$multifractal$

Electricity:

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

Diffractions and Interferences:
$Diffractions$ $Diffractions$ $Diffractions$ $Diffractions$ $Diffractions$ $Diffractions$

Vibrations:

SubAtomic Particles Atom                                                  Berenice Abbott   Peter Cadogan

Cymatics:

Cymatics                                                    Chladni                      sound waves

Self Organization, Emergence and Complexity:

Space: The finel frontier Gardhaia, Algeria          Robert B. Haas                                     Jerry Matchett

Astronomy,

Saturn                                   spiral star                                     Sun

Microscopic fungus, Diffusion, Cellular Automata, Nano Technology:

Sordaria fimicola      Cell                               Jonathan McCabe                                   Nanotechnology 1   Nanotechnology 2

Sea Creatures:

Diatoms                                     Jellyfish 1                         Jellyfish 2                               Tina Carvalho   William White

Emiliania Huxley               Radiolarian                                               Maurice Burton

Shells:

Trees:

Leaves:

Antonio Franchi

Plants:

Animals:
$fractal$ $fractal$

Human Body:

The Brain                       The Brain Scan    The Heart, McNally The Eye, McClenaghan The Ear, Nilsson The Kidney, Kage Cyst

Fractal 5D-2L  Comroe         Blood in The Brain              Blood in The Head                       The Nerves in Brain      DNA molecule Vitamin

Architecture:
$fractal$
The Nautilus         Egept                            Laos            Australia, Sydney Opera House Belgrade India    Myanmar      Morocco        France

$fractal$ $chandelier fractal$
India                               Muqarnas Dome, Baghdad Iran Vila        Italy, floor mosaic Roman Vila        MIQEL                                                          chandelier

Arts:
$Hokusai fractal Like$ $Hiroshige fractal like$ $persian art fractal like$ $African fractal$ Mandelbroth set Hokusai                                                            Hiroshige     Iran art    Salvador Dali - visage of war African fractal Klee-Fugue in Red

Graphics:
$eltic circle fractal$ $Jos Leys fractal$
Escher                    William T. Shaw       Peitgen and Saupe Yuzo Nakano          Felipe Arte         Celtic circle fractal Tom Shannon      Jos Leys

Religion:
$fractal hand Blue Stellaluna$
Yin and Yang            Mandala:                                                                                                                               Hamsa Mira Krispel BlueStellaluna

Fractals in Computer 2 Dimensions (figured with FractInt).

KAM, Kolmogorov-Arnold-Moser Dynamic                      Barnsley                               Circle                                  Complex Newton

Mandelbrot set                    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 Walru s - Graph Visualization Tool .

Cobwebs

Almost Mathematical Creatures in Nature:
Mandelbrot Set

Dendi Caldera, Ethiopia Paul Chesley, Yellowstone North pole of Saturn John Mumaw Campello Boris - Ice Thing Antartica's Moving Ice

Mobius Strip                                      Sierpinski fractal

Drew Patrick                         Martin Richard

Natural Fractals:

Pickover                                         Designin Nature

Natural Attractors

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:

Walter J. Freeman                        Rolf Wallin               Beethoven - Stephen Malinowski N A sand earthquake tracing pendulum

Attractors in Computer 3 Dimensions: figured with software Eco2.

N Chua attractor               Ikeda Attractor              Lorenz Attractor         Pickover Attractor Rossler Attractor         Tamari Attractor

Humor in Chaos, Fractals and Attractors:
$homur- fractal$ $Humor - elevator fractal$ $Humor - fractal$
MiniFractal                  Babushka                              Giraffe Farley Katz Elevator fractal                                          Norway economics

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.

Links

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

http://www.bathsheba.com/

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

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

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