Fractal Links 

Fractal Links/ReferencesThe following links/references provide a wealth of information about fractals. Fractal LinksThe following web sites provide an excellent introduction to fractals and fractal geometry: Eric W. Weisstein. "Fractal." From MathWorldA 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
The Geometry Junkyard  Fractals
Paul Nylander's Fractals site.
The Unravelling of the Real 3D Mandelbulb by Daniel White
Tom Beddard's subblue site
Mathematical Art, Graphics, Chaos and Fractals Bruno Kevius
A Unique Journey of Fractal Exploration Quantum Enterprises
Mandelbrot / Julia / Newton Fractal LinksFor additional details on Mandelbrot fractals, Julia fractals, and Newton fractals, see the following: Eric W. Weisstein. "Mandelbrot Set." From MathWorldA Wolfram Web Resource.
Eric W. Weisstein. "Julia Set." From MathWorldA Wolfram Web Resource.
Eric W. Weisstein. "Newton's Method." From MathWorldA 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.
Kleinian Group LinksFor 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 LinksFor additional details on Orbital fractals, including Sierpinski Ngons, IFS fractals, the Apollonian Gasket, strange attractors, RepTiles, symmetric icons, symmetric attractors, frieze groups, wallpaper groups, hyperbolic attractors, and circle inversion fractals, see the following: Eric W. Weisstein. "Iterated Function System." From MathWorldA Wolfram Web Resource.
Eric W. Weisstein. "Strange Attractor." From MathWorldA 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, "RepTile." From MathWorldA Wolfram Web Resource.
Stewart R. Hinsley's RepTiles 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 Images of Chaos and Symmetry site. Rice University
Clifford A. Reiter's Gallery of Fractals, Chaos and Symmetry. Lafayette College
Larry Riddle's Classic Iterated Function Systems site. Agnes Scott College
David E. Joyce's Geometric Pix Gallery
by Scott Draves and Erik Reckase
LSystem LinksFor additional details on LSystem fractals, see the following: Eric W. Weisstein. "Lindenmayer System." From MathWorldA Wolfram Web Resource.
"LSystem." From Wikipedia, the free encyclopedia.
Fractint LSystem Documentation.
Fractint LSystem Tutorial by William McWorter.
Fractint LSystem Spacefilling Curves Tutorial by William McWorter.
LSystem Programs on the InternetFor many LSystem programs that can be used with the Fractal Science Kit, see the following:
Fractint LSystem Tutorial by William McWorter.
Fractint LSystem Spacefilling Curves Tutorial by William McWorter.
Charlie Chernohorsky's FractInt@oblivion site.
Math/Science LinksFor information related to mathematics and science, see the following: Visual Dictionary of Special Plane Curves Xah Lee
The University of St Andrews
Jan Wassenaar
Wikipedia
Samuel Monnier
David Bailey's World of Escherlike Tessellations
Richard Palais
The Bridges Organization: art and mathematics
A large directory of science links
maths online  A gallery of multimedia learning material English version / German version
Cool math links from the Canadian Mathematical Society
XPLORA  European gateway to science education
Society for Chaos Theory in Psychology & Life Sciences
ELA Web Portal  a catalog of 1000s of links
ReferencesThe 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, Chaos, Solitons & Fractals, 9 12 (1998) 20312054; errata10 7 (1999) 12611264 Chaotic attractors with cyclic symmetry revisited Kevin C. Jones and Clifford A. Reiter (Lafayette College). Computers & Graphics 24 (2000) 271282.
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) 791796.
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 "RepTiles: 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 HansJochen Bartsch Translation by Hermert Liebscher
Fractal ForumsThe following forums are dedicated to fractals and/or fractal art:
Fractal ResourcesThe following resources are related to math, fractals, and/or fractal art: Genetica Viewer  Seamless Textures
Public Domain Textures  Seamless Textures
Paul Bourke's Texture and Colour site.
The gallery contains a collection of fractals I have generated with the Fractal Science Kit fractal generator.
My photostream on Flickr.
My gallery on RedBubble.
My gallery on Fine Art America.
My facebook page.
Additional ResourcesThe following are additional useful resources: Cyber security posters you can use to raise security awareness to your employees and how to effectively protect business data from cyber criminals.
A library of free excel templates that includes some of the most powerful and userfriendly spreadsheets you can find on the internet.

Copyright © 20042019 Ross Hilbert 