Patterns, Fractals and Attractors
Published 2000, Update 07-January-2014
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.
"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.
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'."
FragmentsFractalization 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)
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 hristchurch, 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
Diffusion Limited Aggregation (DLA)
Rivers and Deltas:
Mesopotamia Ganges Aerial Snaking Delta Selenga River Nasser Lake Greenland dela Missouri Yukon delta - NASA
Cracked: glass, mud, metal, rocks and wood respectively:
Drops, Splashes and Bubbles:
Flow, Whirlpools, Swirls, Vortices and Symmetry:
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
NASA NASA Mount C leveland J. Warren Atom bomb Sarychev Peak Volcano
Lightning Kirlian "lightning storm" Static Electric Ball Lichtenberg figure Electric spark Electric spark Positive discharge
Diffractions and Interferences:
SubAtomic Particles Atom Berenice Abbott Peter Cadogan Cymatics Chladni Sound waves
Self Organization, Emergence and Complexity:
Space: The finel frontier Gardhaia, Algeria Robert B. Haas Jerry Matchett
Saturn spiral star Sun
Microscopic fungus, Diffusion, Cellular Automata, Nano Technology:
Sordaria fimicola Cell Jonathan McCabe Nanotechnology 1 Nanotechnology 2
Diatoms Jellyfish 1 Jellyfish 2 Tina Carvalho William White
Emiliania Huxley Radiolarian Maurice Burton
he 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
The Nautilus Egept Laos Australia, Sydney Opera House Belgrade India Myanmar Morocco France
India Muqarnas Dome, Baghdad Iran Vila Italy, floor mosaic Roman Vila MIQEL Chandelier
Mandelbroth set Hokusai Hiroshige Iran art Salvador Dali - visage of war African fractal Klee-Fugue in Red
Escher William T. Shaw Peitgen and Saupe Yuzo Nakano Felipe Arte Celtic circle fractal Tom Shannon Jos Leys
Yin and Yang Mandala: Hamsa Mira Krispel N EthiopianCross
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 .
Almost Mathematical Creatures in Nature:
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
Pickover Designin Nature
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 Tamari attractor A sand earthquake tracing pendulum
Attractors in Computer 3 Dimensions: figured with software Eco2.
Chua attractor Ikeda Attractor Lorenz Attractor Pickover Attractor Rossler Attractor Tamari Attractor
Humor in Chaos, Fractals and Attractors:
Speculation 1, 19-October-2013 On Patternness (y) as function of Aggregation [ y = f(x) ].
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..