Fractal Links/References
The following links/references provide a wealth of information about fractals.
Fractal Links
The following web sites provide an excellent introduction to fractals and fractal geometry:
Eric W. Weisstein. "Fractal."
From MathWorld--A Wolfram Web Resource.
"Fractal."
From Wikipedia, the free encyclopedia.
Yale University's Fractal Geometry site.
Paul Bourke's Fractals, Chaos site.
Clifford A. Reiter's Gallery of Fractals, Chaos and Symmetry.
Lafayette College
Curtis T McMullen's Gallery site.
Harvard University
Sprott's Fractal Gallery (Clint Sprott).
University of Wisconsin - Madison
Paul Nylander's Fractals site.
The Spanky Fractal Database (Noel Giffin).
Mandelbrot / Julia / Newton Fractal Links
For additional details on Mandelbrot fractals, Julia fractals, and Newton fractals, see the following:
Eric W. Weisstein. "Mandelbrot Set."
From MathWorld--A Wolfram Web Resource.
Eric W. Weisstein. "Julia Set."
From MathWorld--A Wolfram Web Resource.
Eric W. Weisstein. "Newton's Method."
From MathWorld--A Wolfram Web Resource.
From Wikipedia, the free encyclopedia.
"Julia Set."
From Wikipedia, the free encyclopedia.
From Wikipedia, the free encyclopedia.
"3. The Mandelbrot Set and Julia Sets."
From Yale University's Fractal Geometry site.
"3G. Complex Newton's Method."
From Yale University's Fractal Geometry site.
David E. Joyce's Newton Basins site.
Clark University
Sekino's Fractal Gallery (Junpei Sekino).
Willamette University
Ingvar Kullberg's Fractal World.
Lifesmith Classic Fractals (Jeff Berkeley).
Kleinian Group Links
For additional details on the Apollonian Gasket, Schottky Groups, and Kleinian Groups, see the following:
David Wright's Indra's Pearls site.
Oklahoma State
Orbital / IFS / Strange Attractor Links
For additional details on Orbital fractals, including Sierpinski N-gons, IFS fractals, the Apollonian Gasket, strange attractors, Rep-Tiles, symmetric icons, symmetric attractors, frieze groups, wallpaper groups, hyperbolic attractors, and circle inversion fractals, see the following:
Eric W. Weisstein. "Iterated Function System."
From MathWorld--A Wolfram Web Resource.
Eric W. Weisstein. "Strange Attractor."
From MathWorld--A Wolfram Web Resource.
From Wikipedia, the free encyclopedia.
"Attractor."
From Wikipedia, the free encyclopedia.
"1E. Iterated Function Systems."
From Yale University's Fractal Geometry site.
Eric W. Weisstein, "Rep-Tile."
From MathWorld--A Wolfram Web Resource.
Stewart R. Hinsley's Rep-Tiles site.
"9. Circle Inversions."
From Yale University's Fractal Geometry site.
Yale University's Kitchen Science Fractals site.
David Wright's Indra's Pearls site.
Oklahoma State
Mike Field's Symmetric Icons site.
University of Houston
Clifford A. Reiter's Gallery of Fractals, Chaos and Symmetry.
Lafayette College
Larry Riddle's Classic Iterated Function Systems site.
Agnes Scott College
L-System Links
For additional details on L-System fractals, see the following:
Eric W. Weisstein. "Lindenmayer System."
From MathWorld--A Wolfram Web Resource.
"L-System."
From Wikipedia, the free encyclopedia.
Fractint L-System Documentation.
Fractint L-System Tutorial by William McWorter.
Fractint L-System Space-filling Curves Tutorial by William McWorter.
L-System Programs on the Internet
For many L-System programs that can be used with the Fractal Science Kit, see the following:
The Spanky Fractal Database (Noel Giffin).
Fractint L-System Tutorial by William McWorter.
Fractint L-System Space-filling Curves Tutorial by William McWorter.
Charlie Chernohorsky's FractInt@oblivion site.
References
The following books/papers have been invaluable to me in my ongoing quest to understand fractals and the math behind them:
The Fractal Geometry of Nature
(An earlier edition of this book was titled: Fractals: Form, Chance, and Dimension)
Benoit B. Mandelbrot
The Beauty of Fractals
H.-O. Peitgen, P.H. Richter
The Science of Fractal Images
M.F. Barnsley, R.L. Devaney, B.B. Mandelbrot,
H.-O. Peitgen, D. Saupe, R.F. Voss
with contributions by Y. Fisher, M. McGuire
Fractals Everywhere
Michael F. Barnsley
Chaos and Fractals
Peitgen, Jurgens, Saupe
Strange Attractors: Creating Patterns in Chaos
J. C. Sprott
Indra's Pearls - The Vision of Felix Klein
David Mumford, Caroline Series, David Wright
Michael Field, Martin Golubitsky
Chaotic Attractors with Discrete Planar Symmetries
Nathan C. Carter, Richard L. Eagles, Stephen M. Grimes,
Andrew C. Hahn, and Clifford A. Reiter (Lafayette College).
Chaos, Solitons & Fractals, 9 12 (1998) 2031-2054;
errata10 7 (1999) 1261-1264
Chaotic attractors with cyclic symmetry revisited
Kevin C. Jones and Clifford A. Reiter (Lafayette College).
Computers & Graphics 24 (2000) 271-282.
Iterated function systems with symmetry in the hyperbolic plane
Bruce M. Adcock, Kevin C. Jones, Clifford A. Reiter (Lafayette College)
and Lisa M. Vislocky. Computers & Graphics 24 (2000) 791-796.
by Scott Draves and Erik Reckase
Fractal Cosmos - The Art of Mathematical Design
Lifesmith Classic Fractals
Fractal art using variations on escape time algorithms in the complex plane
by P. D. Sisson
The Unexpected Hanging and Other Mathematical Diversions
Gardner, M., Ch. 19 "Rep-Tiles: Replicating Figures on the Plane."
Computers, Pattern, Chaos, and Beauty - Graphics from an Unseen World
Clifford A. Pickover
The Pattern Book - Fractals, Art, and Nature
Editor Clifford A. Pickover
Fractals for the Macintosh
Jesse Jones
Visual Complex Analysis
Tristan Needham
Introduction to Geometry
H. S. M. Coxeter, F. R. S.
Geometry
David A. Brannan, Matthew F. Esplen, Jeremy J. Gray
Geometry - A Comprehensive Course
Dan Pedoe
Mathematics - From the Birth of Numbers
Jan Gullberg
Connections - The Geometric Bridge Between Art and Science
E. H. Lockwood
Transformation Geometry - An Introduction to Symmetry
George E. Martin
A Book of Curves
E. H. Lockwood
Symmetries of Culture
Dorothy K. Washburn, Donald W. Crowe
CRC Standard Mathematical Tables 25th Edition
William H. Beyer
Handbook of Mathematical Formulas
Hans-Jochen Bartsch Translation by Hermert Liebscher
Fractal Forums
The following forums are dedicated to fractals and/or fractal art:
Fractal Resources
The following resources are related to fractals and/or fractal art:
Mathematical Art, Graphics, Chaos and Fractals
Bruno Kevius
A Catalog of Mathematics Resources on the WWW and the Internet
M. Maheswaran - University of Wisconsin Marathon County
Aussie Educator - 'a total education web page for Australia' (Mathematics)
Society for Chaos Theory in Psychology & Life Sciences
A Unique Journey of Fractal Exploration
Quantum Enterprises
Wayne L. Boucon
Tohsuke Urabe
InfiniteZoom A Fractal Gallery
Sarah Scotland
Filmer V2.0 - A program for creating fractal animation
Julian Haight