Update 5-February-2012 Patterns, Fractals and Attractors ^{© 2000}

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Patterns Quotes

Norbert Wiener (1954) "The Human Use of Human Beings", Da Capo Press.

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.

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

Our conscious representations are sometimes ordered (or arranged in a pattern)
before they have became conscious to us. p. 308,

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

All Movement, all change, is a pattern of the interaction of yin and yang. p. 23.

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

Mathematics is the study of pure pattern, and everything in the cosmos is a kind of pattern. p. 3.

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

As in all matter organized into biological units, there is a pattern, an order, in human bodies. p. 15,

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

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. p. 35,

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

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. p. 84.

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

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. p. 229.

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

We live in a universe of patterns. p. 1.

Nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes. p. 1.

Patterns possess utility as well as beauty. p. 3.

Each of nature's patterns is a puzzle, nearly always a deep one. p. 16.

Mathematics is the science of patterns, and nature exploits just about every pattern that there is. p. 21.

Even when the consequence of natural laws seem to be patternless, the laws are still there and so are the patterns. p. 142.

Nature's patterns are "emergent phenomena." They emerged from an ocean of complexity ... p. 168.

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

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. p. 403.

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

Understanding of life begins with the understanding of patterns. p. 80.

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

Fractals are to chaos what geometry is to algebra. p. 272.

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

Patterns are the fool's gold of financial markets. p. 21.

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

Humans are pattern-seeking animals. p. 220.

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Stephan Wolfram (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.

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Fractalization of the Language (added 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 ( 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 (added: 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, a dded 15-July-2010)

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:

iberian Trap                        Wadi Hadramaw         Lake Erepecu                     Namibia                    Utah                    Manantah Reservoir, Mali Jeff Alu

Volcano                            Fiji Island s                                      The Zagros Mountains, Iran           the pole                       HéctorGarrido      Christchurch, New Zealand

Zeph Van Allen     Springs      Scotch Macaskill - Sand Patterns Pete Hanson - Pele Fingerprints Alluvial Fan In Southern 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

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

Drops, Splashes and Bubbles:

Harold Edgerton

Flow, Whirlpools, Swirls, Vortices and Symmetry:

NASA Jupiter                     NASA                                                                                                                                   Alexander Lillevik              symmetry

Short Movies of Water Patterns:

Double Swirl                        Water Moon Light           Water Flaw   Water Gold lines         Water Patterns                   Water stars                      Water Interference
video: Ben Tamari
music: Mordechai Cohen

Clouds:

NASA                                             NASA mount Cleveland               J. Warren                                Atom bomb                              Sarychev Peak Volcano Rockywave

MultiFractals:

$Multi fractal$

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, Cymatics:

SubAtomic Particles Atom                                                 Berenice Abbott      Cymatics                                                  Chladni                 sound waves

Self Organization, Emergence and Complexity:

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

Astronomy       Microscopic fungus Diffusion Cellular Automata        NanoTech.:

Saturn                            Sordaria fimicola          Cell               Jonathan McCabe                          Nanotechnology 1               Nanotechnology 2

Sea Creatures:

Diatoms                             Maurice Burton    Jellyfish 1                        Jellyfish 2                    Tina Carvalho William White Bisson brothers

Emiliania Huxley               Radiolarian

Trees :

Leaves :

Antonio Franchi

Plants :

Animals :
$fractal$ $fractal$

Human Body :

The Brain, Aasen                            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:

The Nautilus             Egypt                                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 :
$Hokusai fractal Like$ $Hiroshige fractal like$ $persian art fractal like$ $African fractal$
                         | Hokusai                                                               | Hiroshige      |                      | Salvador Dali - visage of war |African fractal | Poul 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

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

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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 .

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Cobwebs:

g Natural Fractals:

Natural Attractors :

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

Attractors in Brain and Music :

Walter J. Freeman                          Rolf Wallin             Beethoven - Stephen Malinowski

Attractors in Computer 3 Dimensions: figured with software Eco2 (to download Eco0 , only Lorenz and Tamari attractors) .

     Ikeda Attractor                Lorenz Attractor          Pickover Attractor          Rossler Attractor        Tamari Attractor

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MiniFractal              Babushka