Patterns, Fractals and Attractors

Published in 2000, update August 23, 2014

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Texts in blue italics are "quotes."

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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."

●

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.

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'."

My Fragments - From My Personal Point of View, The Complete list see Tamari page:

MF1: Fractals relate to attractors like cobblestones in roads. Added 1 January 2000.

MF3: Fractalization of the Language I. Added 21 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 the sentence: "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**.

•

•

•

MF10: 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,
15 July 2010.

"An allocated number of words.
Never a needless one

Meaning - no poetry

And no philosophy and no religion."

MF9: Fractals and chaos is like sewing and cooking. Added 28 March 2009.

Patterns in Nature:

Dendrites:

Rivers and Deltas:

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

Drops, Splashes and Bubbles:

Flow, Whirlpools, Swirls, Vortices and Symmetry:

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

Clouds:

Multi Fractals:

Electricity:

Diffractions:

Interferences:

Vibrations and Cymatics:

Self Organization, Emergence and Complexity:

Astronomy,

Cellular Automata, Nano Technology:

Sea Creatures, Diatoms and Microscopic fungus

Shells:

Trees:

Leaves:

Plants:

Animals:

Human Body and ...:

Architecture:

Arts:

Graphics:

Religion and Symbols:

Fractals in Computer 2 Dimensions, figured with
**FractInt** software.

Fractals in Computer 3 Dimensions and more:

Cobwebs

Almost Mathematical Creatures in Nature:

Mandelbrot Set

Mobius
Strip Sierpinski
fractal

Natural Fractals:

Natural Attractors

Attractors in Brain, Music, Economics and Earthquake:

Attractors in Computer 3 Dimensions:
.

Chua, Ikeda, Lorenz, Pickover, Rossler and Tamari
attractors respectedly, figured with
software
Eco2.

Humor in Chaos,
Fractals and Attractors:

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

The Three Law's regimes: The **R**andom laws (gases-like), the **S**tatistical/chaotic laws (liquids-like) and the Deterministic laws (solids-like), RSD.

Exampels:

Deterministic Laws: Lagrangian and Lorentz transformations

Statistical Laws: Weather -Lorenz Attractor
and Economics -
Tamari Attractor

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

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.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

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

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

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

https://www.youtube.com/watch?v=rENyyRwxpHo

Software:

http://www.fractalsciencekit.com/

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

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