Good resources for learning fractal mathematics
bena...@my-deja.com
creating 2D and 3D fractals, especially L-System trees. Does anyone know of
any decent books / web sites, etc. If so I would be very grateful.
TIA
Ben Arnold
Sent via Deja.com http://www.deja.com/
Before you buy.
Donald Cameron
this is a great link
"The Fract-ED Information Pages"
Fract-ED is an introductory fractal tutorial intended for high school or
college entry-level students. It is an informal discussion of some of the
elements of fractal geometry, and includes interactive programs which
demonstrate the techniques of fractal generation.
http://www.ealnet.com/ealsoft/fracted.htm
"Paul N. Lee" <NOS...@Worldnet.att.net> wrote in message
news:39EFD8...@Worldnet.att.net...
> Ben Arnold <bena...@my-deja.com> wrote:
> >
> > Hi, I am looking for resources to help me
> > understand the maths behind creating 2D and
> > 3D fractals, especially L-System trees.
> > Does anyone know of any decent books / web
> > sites, etc. If so I would be very grateful.
> > TIA
> >
>
>
> ----------------------------------------------------------------------
> Online Documentation (URL alphabetical order):
> ----------------------------------------------------------------------
> ftp://anon...@rtfm.mit.edu/pub/usenet/news.answers/fractal-faq
> http://archives.math.utk.edu/topics/fractals.html
> http://cassiopaea.org/quantum_future/papers/garda.htm
> http://faqs.colombianet.net/sci/fractals-faq/
> http://fractal.mta.ca/sci.fractals-faq/
> http://homepages.force9.net/calresco/
> http://hypertextbook.com/chaos/
> http://library.advanced.org/11679/
> http://library.thinkquest.org/3493/main.html
> http://linas.org/art-gallery/escape/escape.html
> http://math.bu.edu/DYSYS/FRACGEOM/FRACGEOM.html
> http://math.bu.edu/DYSYS/FRACGEOM2/FRACGEOM2.html
> http://members.aol.com/calresco/
> http://mitpress.mit.edu/books/FLAOH/cbnhtml/
> http://non.com/news.answers/fractal-faq.html
> ftp://pit-manager.mit.edu/pub/usenet/news.answers/fractal-faq
> ftp://pit-manager.mit.edu/pub/usenet/news.answers/sci/fractals-faq
> ftp://rtfm.mit.edu/pub/usenet-by-hierarchy/sci/fractals/
> ftp://rtfm.mit.edu/pub/usenet/news.answers/fractal-faq
> ftp://rtfm.mit.edu/pub/usenet/news.answers/sci/fractals-faq/
> ftp://rtfm.mit.edu/pub/usenet/sci.fractals/
> http://spanky.triumf.ca/pub/fractals/docs/SCI_FRACTALS.FAQ
> http://spanky.triumf.ca/www/quartet-info.html
> http://spanky.triumf.ca/www/whats-new.html
> http://sprott.physics.wisc.edu/pickover/home.html
> http://sprott.physics.wisc.edu/sprott.html
> http://tftnrlb.tripod.com/
> http://webpages.marshall.edu/~stepp/fractal-faq/faq.html
> http://w1.111.telia.com/~u11109996/CubTut/cubictut.html
> http://www.ceremade.dauphine.fr/~vojak/
> http://www.chaos-theorie.de
> http://www.cis.ohio-state.edu/hypertext/faq/usenet/fractal-faq/faq.html
> http://www.cis.ohio-state.edu/hypertext/faq/usenet/sci
> http://www.columbia.edu/~gae4/chaos/
> http://www.cribx1.u-bordeaux.fr/fractals/faq/
> http://www.cygnus-software.com/theory/theory.htm
> http://www.eecs.wsu.edu/~hart/
> http://www.efg2.com/Lab/FractalsAndChaos/
> http://www.geocities.com/CapeCanaveral/5003/
> http://www.home.aone.net.au/sci-gal/sci-gal.htm
> http://www.ipm.sci-nnov.ru/~DEMIDOV/MSet/Contents.htm
> http://www.lib.ox.ac.uk/internet/news/faq/sci.fractals.html
> http://www.mta.ca/~mctaylor/sci.fractals-faq/
> http://www.olympus.net/personal/dewey/mandelbrot.html
> http://www.shop.de/priv/hp/3133/fr_4d.htm
> http://www.swin.edu.au/astronomy/pbourke/
> http://www.swin.edu.au/chem/bio/fractals/refslist.htm
> http://www.teknet.net.au/~plavers/
> http://www.ugr.es/CRYSLAB/Fractals.html
> http://www.users.zetnet.co.uk/rgirvan/udo.htm
> http://www3.bc.sympatico.ca/moormank/abstract.html
>
>
> ----------------------------------------------------------------------
> Books, Magazines, Articles, etc.
> ----------------------------------------------------------------------
> For a more complete list, you might want to do a Search on "Fractal" or
> "Chaos" at the following website:
> http://www.amazon.com/
> U.S. Standard Shipping (3 to 7 business days) $3 per shipment plus
> $0.95 per book. Many other shipping options available.
> http://www.astro.virginia.edu/~eww6n/books/Fractals.html
>
>
> Fractalia Magazine - Applied Mathematics and Recreational Computing.
> A lot of things about Fractal Theory, Chaos Theory, Dynamic Systems and
> more from Marius-F. Danca, editor. Website at:
> http://www.scs.ubbcluj.ro/~tt7316/fractalia/
> or (mirror pages):
> http://members.tripod.com/~fractalia/
> http://pages.codec.ro/fractalia/
> http://bavaria.utcluj.ro/~mdanca/fractalia/
> or e-mail:
> mailto:Marius...@aut.utcluj.ro
> mailto:tt7...@scs.ubbcluj.ro
>
>
> The Chaos Hypertextbook
> http://hypertextbook.com/chaos/
> It's a compact, four chapter book for those with a little bit of
> mathematical knowledge and a big curiosity about fractals and chaos. Of
> particular interest are the resource pages ...
> http://hypertextbook.com/chaos-links/92.shtml
> (chaos & fractal software for the Macintosh)
> http://hypertextbook.com/chaos-links/93.shtml
> (a collection of links)
>
>
> "The Computational Beauty of Nature", by Gary William Flake
> Computer Explorations of Fractals, Chaos, Complex Systems, and
> Adaptation
> http://mitpress.mit.edu/books/FLAOH/cbnhtml/
>
> "The Mandelbrot and Julia sets Anatomy"
> http://www.people.nnov.ru/fractal/MSet/Contents.htm
> or http://www.ipm.sci-nnov.ru/~DEMIDOV/MSet/contents.htm
>
> "Chaos and Fractals: A Computer Graphical Journey"
> (Ten Year Compilation of Advanced Research) by Cliff Pickover, 1998
>
> "The Science of Fractal Images" (Peitgen, 1988)
>
> "Chaos and Fractals" by Peitgen, Jurgens and Saupe
>
> "Chaos" by Gleick
>
> "The Fractal Geometry of Nature" by Benoit B. Mandelbrot
>
> "The Algorithmic Beauty of Plants", by Aristid Lindemayer & Przemyslaw
> Prusinkiewicz
>
> "Dynamical systems and fractals" by Becker & Dorfler
>
> "Fractal Music, Hypercards and More" by Martin Gardner
>
> "Fractal Geometry" by Edgar
>
> "Fractal Geometry" by Falconer
>
> "Fractals, Chaos & Power Laws" by Schuster
>
> "Fractals Everywhere" by Michael Barnsley (a college text book).
>
> "Fractal Programming in Turbo Pascal" Roger T. Stevens (1990) M & T
> Books
>
> "Iteration des polynomes quadratiques complexes" by A. Douady and J. H.
> Hubbard, CRAS Paris 294 (1982) 123-126.
>
> "Complex Variables and Applications, 5th Edition" by Churchill and
> Brown.
>
> "Difference Equations" by Kelly and Peterson.
>
> Brooks, R, Matelski, J. P. (1981) The dynamics of 2-generator
> subgroups of PSL(2,C). In Riemann Surfaces and Related Topics:
> Proceedings of the 1978 Stony Brook Conference. Kyra, I. and
> Maskit, B. (eds.) Princeton University Press: New Jersey.
>
> Author: Carleson, Lennart.
> Title: Complex dynamics / Lennart Carleson and Theodore W.
> Gamelin.
> Pub. Info.: New York : Springer-Verlag, 1993.
> LC Subject: Functions-of-complex-variables.
> Mappings-Mathematics.
> Fixed-point-theory.
>
> Author: Beardon, Alan F.
> Title: Iteration of rational functions : complex analytic
> dynamical
> systems / Alan F. Beardon.
> Pub. Info.: New York : Springer-Verlag, 1991.
> LC Subject: Iterative-methods-Mathematics.
> Mappings-Mathematics.
>
> James D. Murray. How The Leopard Gets Its Spots / March, 1988 / page 80
> US,
> page 62 Intl. Abstract: A single pattern-formation mechanism could
> underlie the
> wide variety of animal coat markings found in nature. Results from the
> mathematical model open lines of inquiry for the biologist. Subjects:
> Chladni
> patterns, embryonic development, leopard, mathematical models,
> melanocytes,
> morphogens, reaction-diffusion mechanism, Turing.
>
> Heinz-Otto Peitgen's "Chaos and Fractals". It covers everything:
> M-set, dynamical systems, bifurcation diagrams, L-systems, etc.
> Other books at http://www.cevis.uni-bremen.de/fractals/
>
> Crowe, W., Hasson, R., Rippon, P., Strain-Clark, P. (1989) On the
> structure of the Mandelbar set. Nonlinearity. 2: 541-553.
>
> "Chapter 27, Turning a Universe Inside-Out" in Pickover, C. (1992)
> Computers in the Imagination. St. Martin's Press: New York.
>
>
> Hardbound books:
> "Fractals for the Classroom", National Teachers of Mathematics;
> Part I: Introduction to Fractals and Chaos; ISBN 0-387-97041-X,
> $38.50
> Part II: Complex Systems and Mandelbrot Set; ISBN 0-387-97722-8,
> $38.50
> http://poweredge.nctm.org/nctm/index.icl
> "Chaos and Fractals: New Frontiers of Science", by Springer;
> ISBN 0-387-97903-4, $64.95.
> http://www.springer-ny.com/catalog/np/updates/0-387-97903-4.html
> Softbound books:
> Strategic Activities, Vol. 1; ISBN 0-387-97346-X, $24.50
> Strategic Activities, Vol. 2; ISBN 0-387-97554-3, $24.50
> Strategic Activities, Vol. 3; ISBN 0-387-98420-8, $19.95
> http://poweredge.nctm.org/nctm/index.icl
>
>
> Fractals - Images of Chaos
> Hans Lauwerier; published in UK by Penguin Books.
>
> Fractals by Hans Lauwerier, Princeton Science Library
>
> Fractal Vision by Dick Oliver, Sams
>
> Fractal Horizons : The Future Use of Fractals
> Clifford A. Pickover; (1996) Hardcover Price: $20.97
>
> Chaos in Wonderland : Visual Adventures in a Fractal World
> Clifford A. Pickover; (1994) Hardcover Price: $20.97
> Clifford A. Pickover; (1995) Paperback Price: $15.16
>
> Computers, Pattern, Chaos and Beauty : Graphics from an Unseen World
> Clifford A. Pickover; (1991) Paperback Price: $19.95
>
> Mazes for the Mind : Computers and the Unexpected
> Clifford A. Pickover; (1992) Hardcover Price: $23.07
>
> Visions of the Future : Art, Technology and Computing in the
> Twenty-First Century Vol 1
> Clifford A. Pickover; (1994) Paperback Price: $13.56
>
> The Loom of God : Mathematical Tapestries at the Edge of Time
> Clifford A. Pickover; (1997) Hardcover Price: $29.95
>
> Frontiers of Scientific Visualization
> Clifford A. Pickover; (1994) Hardcover Price: $44.95
>
> Spiral Symmetry
> Clifford A. Pickover; (1992) Hardcover Price: $61.00
>
> The Pattern Book: Fractals, Art, and Nature
> Clifford A. Pickover; (1995) Hardcover Price: $51.00 (Back Ordered)
>
> Fractals: A Pattern Book
> Clifford A. Pickover; (1992) Paperback (Hard to Find)
>
> Visions of the Future : Art, Technology and Computing in the
> Twenty-First Century
> Clifford A. Pickover; (1992) Hardcover (Hard to Find)
>
> Advanced Fractal Programming in C--Stephens
> Archimedes' Revenge--Hoffman
> Beauty of Fractals, The--Peitgen and Richter
> Cellular Automata and Complexity--Wolfram
> Chaos: A Program Collection for the PC--Korsch & Jodl
> Chaos and Fractals: The Mathematics Behind...---Amer. Math. Soc.
> Chaos and Fractals: New Frontiers of Science--Peitgen et al
> Chaos Cookbook, The--Pritchard
> Chaos, Fractals, and Dynamics: Computer Experiments...--Devaney
> Chaos in Dynamical Systems--Ott
> Chaos in Wonderland--Pickover
> Chaos: Making a New Science--Gleick
> Chaos: The New Science--Holte
> Chaos Under Control--Peak & Frame
> Chaotic and Fractal Dynamics--Moon
> Chaotic Dynamics--Baker & Gollub
> Computers and the Imagination--Pickover
> Computers, Pattern, Chaos, and Beauty--Pickover
> Differential Equations with Applications--Betz, Burcham & Ewing
> Does God Play Dice? The Mathematics of Chaos--Stewart
> Dynamical Systems and Fractals--Becker & Dorfler
> Elementary Number Theory--Uspensky & Heaslet
> Encounters with Chaos--Gulick
> Essence of Chaos, The--Lorenz
> Excursions in Number Theory--Ogilvy & Anderson
> Exploring Chaos--Hall
> Exploring the Geometry of Nature--Rietman
> Eye for Fractals, An--McGuire
> Fantasia Mathematica--Fadiman
> Fourth Dimension, The--Rucker
> Fractal Cosmos: The Art of Mathematical Design--Berkowitz
> Fractal Creations (1st ed.)--Wegner & Peterson
> Fractal Creations (2nd ed.)--Wegner & Tyler
> Fractal Geometry: Math Foundations & Applications--Falconer
> Fractal Geometry and Computer Graphics--Encarnacao, Peitgen et al
> Fractal Geometry of Nature, The--Mandelbrot
> Fractal Graphics for Windows--Oliver & Hoviss
> Fractal Mania--LaPlante
> Fractal Programming in C--Stevens
> Fractal Programming and Ray Tracing with C++--Stevens
> Fractal Vision: Put Fractals to Work for You--Oliver
> Fractals: A User's Guide ... Natural Sciences--Hastings/Sugihara
> Fractals and Chaos--Crilly, Earnshaw & Jones
> Fractals, Chaos, Power Laws--Schroeder
> Fractals: Endlessly Repeated Geometrical Figures--Lauwerier
> Fractals Everywhere (1st ed.)--Barnsley
> Fractals Everywhere (2nd ed.)--Barnsley
> Fractals for the Classroom, Part One: Intro...--Maletsky et al
> Fractals for the Classroom, Part Two: Complex Systems--Maletsky..
> Fractals: Images of Chaos--Lauwerier
> Fractals: The Patterns of Chaos--Briggs
> >From Five Fingers to Infinity--Swetz
> >From One to Zero--Ifrah
> >From Zero to Infinity--Reid
> Game, Set and Math--Stewart
> Godel, Escher, Bach--Hofstadter
> Infinity and the Mind--Rucker
> Journey Through Genius--Dunham
> Joy of Mathematics, The--Pappas
> Loom of God, The--Pickover
> Magic House of Numbers--Adler
> Martin Gardner's New Mathematical Diversions from Scientific American
> Mathematical Magic Show--Gardner
> Mathematical Tourist, The--Peterson
> Mathematician's Delight--Sawyer
> Mathematics Dictionary--James
> Mathematics: From the Birth of Numbers--Gullberg
> Mathematics in Civilization--Resnikoff & Wells
> Mathematics in the Making--Hogben
> Mathematics: Queen and Servant of Science--Bell
> Mazes for the Mind: Computers and the Unexpected--Pickover
> Men of Mathematics--Bell
> More Joy of Mathematics--Pappas
> New Scientist Guide to Chaos, The--Hall
> Of Men & Numbers--Muir
> Ordinary Differential Equations--Ince
> Pattern Book, The: Fractals, Art, and Nature--Pickover
> Real-World Fractals--Finlay & Blanton
> Recreations in the Theory of Numbers--Beiler
> Science of Fractal Images, The--Peitgen & Saupe
> Source Book in Mathematics, A (2 vols.)--Smith
> Strange Attractors: Creating Patterns in Chaos--Sprott
> Theory of Numbers--Stewart
> Turbulent Mirror--Briggs & Peat
> Turing Omnibus, The--Dewdney
> Understanding the New Mathematics--Rosenthal
> What is Mathematics?--Courant & Robbins
> World of Mathematics, The (4 vols.)--Newman
> You Are a Mathematician--Wells
> Your Chance to Win--Levinson
>
>
>
> P.N.L.
> --------------------------------------------------------------
> http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go