Fractal Links

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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

 

The Geometry Junkyard - Fractals

 

Paul Nylander's Fractals site.

 

Fractal Foundation

 

The Spanky Fractal Database (Noel Giffin).

 

The Unravelling of the Real 3D Mandelbulb

by Daniel White

 

Tom Beddard's subblue site

 

Amazing Seattle Fractals

 

Fractal Art FAQ

 

Mathematical Art, Graphics, Chaos and Fractals

Bruno Kevius

 

A Unique Journey of Fractal Exploration

Quantum Enterprises

 

Fractal Software - Fractal Art Generators - Information About Fractals (About.com)

 


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.

 

"Mandelbrot Set."

From Wikipedia, the free encyclopedia.

 

"Julia Set."

From Wikipedia, the free encyclopedia.

 

"Newton Fractal."

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 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.

 

"Iterated function system."

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 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

Clark University

 

The Flame Algorithm

by Scott Draves and Erik Reckase

 


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:

Fractint L-System Examples.

 

Fractint L-System Tutorial by William McWorter.

 

Fractint L-System Space-filling Curves Tutorial by William McWorter.

 

Charlie Chernohorsky's FractInt@oblivion site.

 


Math/Science Links

For information related to mathematics and science, see the following:

Visual Dictionary of Special Plane Curves

Xah Lee

 

Famous Curves Index

The University of St Andrews

 

Mathematical Curves

Jan Wassenaar

 

List of curves

Wikipedia

 

Symmetry, Tilings and Polyhedra

Steven Dutch, Natural and Applied Sciences

 

Math Projects

Vladimir Bulatov

 

Algorithmic worlds

Samuel Monnier

 

David Bailey's World of Escher-like Tessellations

 

Virtual Math Museum

Richard Palais

 

The Bridges Organization: art and mathematics

 

Mathematical Imagery

 

Science Central

A large directory of science links

 

maths online - A gallery of multimedia learning material

English version / German version

 

KaBoL (Knot a Braid of Links)

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

ELA MATHEMATICS DIRECTORY

 


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

 

Symmetry in Chaos

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.

 

The Fractal Flame Algorithm

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 Forums

 

FracFan Forum

 


Fractal Resources

The following resources are related to math, fractals, and/or fractal art:

Spiral Graphics

Genetica Viewer - Seamless Textures

 

Public Domain Textures - Seamless Textures

 

Paul Bourke's Texture and Colour site.

 

deviantART gallery

The gallery contains a collection of fractals I have generated with the Fractal Science Kit fractal generator.

 

Flickr

My photostream on Flickr.

 

RedBubble

My gallery on RedBubble.

 

Fine Art America

My gallery on Fine Art America.

 

Facebook

My facebook page.

 

 

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