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         Fractals:     more books (100)
  1. The Fractal Geometry of Nature by Benoit B. Mandelbrot, 1983
  2. Fractal Time: The Secret of 2012 and a New World Age by Gregg Braden, 2010-02-01
  3. The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot, Richard L. Hudson, 2006-03-07
  4. Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer, 2003-11-14
  5. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise by Manfred Schroeder, 2009-08-21
  6. The Science of Fractal Images
  7. Fractals: The Patterns of Chaos: Discovering a New Aesthetic of Art, Science, and Nature (A Touchstone Book) by John Briggs, 1992-11-01
  8. Introducing Fractals: A Graphic Guide by Nigel Lesmoir-Gordon, 2005-10-15
  9. Fractals, Googols, and Other Mathematical Tales by Theoni Pappas, 1993-02-16
  10. African Fractals: Modern Computing and Indigenous Design by Ron Eglash, 1999-03-01
  11. Fractals Everywhere by Michael F. Barnsley, 2000-04-18
  12. Chaos and Fractals: New Frontiers of Science by Heinz-Otto Peitgen, Hartmut Jürgens, et all 2004-02-03
  13. Gaussian Self-Affinity and Fractals by Benoit Mandelbrot, 2001-12-14
  14. The Beauty of Fractals: Images of Complex Dynamical Systems by Heinz-Otto Peitgen, 1986-08

1. Sprott's Fractal Gallery
Daily updated gallery of automatically created fractals. Fractal generating software.
http://sprott.physics.wisc.edu/fractals.htm
Sprott's Fractal Gallery
Awards Received
MIDI Fractal background music
courtesy of Forrest Fang
Fractal of the Day
Every day at a few minutes past midnight (local Wisconsin time), a new fractal is automatically posted using a variation of the program included with the book Strange Attractors: Creating Patterns in Chaos by Julien C. Sprott . The figure above is today's fractal. Click on it or on any of the cases below to see them at higher (640 x 480) resolution with a code that identifies them according to a scheme described in the book. Older Fractals of the Day are saved in an archive . If your browser supports Java, you might enjoy the applet that creates a new fractal image every five seconds or so. If you would like to place the Fractal of the Day on your Web page, you may do so provided you mention that it is from Sprott's Fractal Gallery and provide a link back to this page. If you want to make your own fractals, I recommend the Chaoscope freeware.

2. The Fractals On Myspace Music - Free Streaming MP3s, Pictures & Music Downloads
Myspace Music profile for The fractals. Download The fractals Rock / Rockabilly / Surf music singles, watch music videos, listen to free streaming mp3s, read The fractals's blog.
http://www.myspace.com/losfractals

3. The Beauty Of Fractal Magic Transformation
Four galleries of fractals, black and white art by Isidoros Printezis.
http://afterzed.com/fractals/index.html
http://www.afterzed.com/fractals Isidoros Printezis - Afterzed FRACTALS GALLERY 1
Imagination GALLERY 2
Jewel GALLERY 3
GALLERY 4

Fractal Photoshop Works GALLERY 5 NEW
Latest Fractal Works PHOTOCUBE
Fractal Java Photcube BIO EMAIL
Site created 11/1/1999
Isidoros Printezis - AfterZed http://www.afterzed.com/fractals/index.com

4. Cynthia Lanius' Lessons: A Fractals Lesson - Introduction
Mathematics lessons for elementary school, middle school fractals, fractals, fractals
http://math.rice.edu/~lanius/frac/
Cynthia Lanius
Fractals
Pictured: A Famous Fractal - The Mandelbrot Set
A Fractals Unit for Elementary and Middle School Students
That Adults are Free to Enjoy
Table of Contents
Introduction Why study fractals?
What's so hot about

fractals, anyway?
Making fractals
Sierpinski Triangle

Using Java

Math questions

Sierpinski Meets Pascal
...
Using Java
Fractal Properties
Self-similarity

Fractional dimension
Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Send mail Fractals on the Web The Math Forum Other Math Lessons by Cynthia Lanius Awards This Site has received
What are Fractals?
They're everywhere, those bright, weird, beautiful shapes called fractals. But what are they, really? Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have. There's lots of information on the Web about fractals, but most of it is either just pretty pictures or very high-level mathematics. So this fractals site is for kids, to help them understand what the weird pictures are all about - that it's math - and that it's fun! Teachers: Every lesson has a print version for classroom use.

5. Fractal Geometry - Crystalinks
Fractal Geometry A Fractal is generally a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reducedsize copy of
http://www.crystalinks.com/fractals.html
Fractal Geometry
A Fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoit Mandelbrot in 1975 and was derived from the Latin fractious meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion. A fractal often has the following features:
  • It has a fine structure at arbitrarily small scales.
  • It is too irregular to be easily described in traditional Euclidean geometric language.
  • It is self-similar (at least approximately or stochastically).
  • It has a simple and recursive definition.
  • It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals - for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics; for instance, it is regular enough to be described in Euclidean terms.

6. Fractal Zoom Animations By Eric Bigas
Collection of short fractal animations in MPG format.
http://www.ericbigas.com/fractals/
20 high-quality fractal zoom movies. Zooms are 1 to 4 minutes each. Free downloads (MPG, XviD HD, H.264 HD).
Click on the small pictures

7. FractalNet Home Page
The Fractal Images Company 268 Arlington Road Kensington, CA 94707 . Voice 510528-0258 Fax 510-528-0243 e-mail marketing@fractals.com
http://fractals.com/
Best experienced with
Click here to start.
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FractalNet Commercial Links
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Fax: 510-528-0243
e-mail: marketing@fractals.com

8. Concepts: Fractals
fractals are entities that look the same under magnification, they are selfsimilar. More specifically, a geometric fractal is formed of parts, which, when magnified, are the
http://necsi.org/guide/concepts/fractals.html
Concepts in Complex Systems Yaneer Bar-Yam Fractals Fractals are entities that look the same under magnification, they are "self-similar." More specifically, a geometric fractal is formed of parts, which, when magnified, are the same as the original shape. Fractals can also involve randomness, so that the similarity of parts to the whole can be of a statistical or average property. An example of a geometric fractal is the Koch curve (an approximate version is shown below) which can be made using a simple algorithm: Take away the middle third of a line segment and insert two segments that are the same length as the one that was removed. Place them so they would make an equilateral triangle with the removed segment. Repeat this procedure with each of the line segments that now make up the curve. Fractals get their name because they can be seen to have fractional dimension. Length, area and volume measure the size of one, two and three dimensional shapes respectively. However, a Koch curve can be shown to be infinite in length and to cover no area. It has a dimension between one and two (strictly its dimension is d=ln(4)/ln(3)~1.2619). This means that if we use a ruler to measure the length of the curve, the length we find depends on how long the ruler is. The shorter the ruler, the longer is the length we measure. This is because a longer ruler cannot "get inside" smaller bumps. An example of a fractal-like shape found in nature is a coastline. How long is the coastline? Just as with the Koch curve, the length of the coastline depends on how long the ruler is used to measure it because there are inlets and peninsulas of many different sizes. A picture of the coastline of Cape Cod is shown below.

9. Fractals_by_Nous
Several galleries generated using Ultra Fractal, Tierazon, Grafzvizion, and Fractint.
http://www.sightsea.com/nous/fractals/
A Member of the Infinite Fractal Loop Fractint Gallerys I II III IV ... Technical and Acknowledgments UltraFractal UltraFractal Gallery 1 UltraFractal Gallery 2 Tierazon Tierazon Gallery 1 GrafZViZion GrafZViZion Gallery 1

10. Fractals
fractals 1 I am doing fractals next because that is how we usually see nonlinear systems. Fractal is a name coined by a fellow by the name of Mandelbrot in the 1960's.
http://www.paulbunyan.net/users/gsirvio/nonlinear/fractals.html
Fractals
I am doing fractals next because that is how we usually see non-linear systems. Fractal is a name coined by a fellow by the name of Mandelbrot in the 1960's. Fractals are the branch of geometry dealing with 'broken curves'. Remember that non-linear problems have graphs that have strange and unusual lines or ... 'broken curves'. There are two approaches to fractals: the natural lines (Has anyone ever seen a truly straight line or perfect curve in any natural object?) and the theoretical mathematical constructions. I will start with the lines occurring in nature since everyone here should be familiar with them and finally work our way into the mathematical curves.
An object in nature repeats itself. Consider a mountain. A peak on the shoulder of the mountain looks very much the same as the mountain. In fact a rock can be mistaken for a mountain if there is nothing next to it to show its size. A branch of a tree is a miniature of the tree. Some leaves are miniatures of branches. Each tributary of a river is a repetition of the whole river at a smaller scale. This repetition of structure with a change of scale is a characteristic of fractals.
If you seem to have any trouble understanding this idea of repetition of structure across scale, rent an old Godzilla movie from the video store. The effect is crude, but the repetition of structure between a branch and a tree, or hill and a mountain can easily be seen. You can also see another feature of natural curves. Although the imaging of structure across scale is very close to being a direct duplication it isn't exact. Waves in a bathtub are not quite the waves in an ocean, although they are very close.

11. Fractal Geometry
I find the ideas in the fractals, both as a body of knowledge and as a metaphor, an incredibly important way of looking at the world. Vice President and Nobel Laureate Al
http://classes.yale.edu/fractals/

12. NOVA | Hunting The Hidden Dimension | PBS
The Most Famous Fractal What exactly is the Mandelbrot set? Find out in this excerpt from the book fractals The Patterns of Chaos.
http://www.pbs.org/wgbh/nova/fractals/
document.write(unescape("%3Cscript src='" + (document.location.protocol == "https:" ? "https://sb" : "http://b") + ".scorecardresearch.com/beacon.js' %3E%3C/script%3E")); A Radical Mind
Benoit Mandelbrot is a true maverick, as his interview reveals. The Most Famous Fractal
What exactly is the Mandelbrot set? Find out in this excerpt from the book Fractals: The Patterns of Chaos Design a Fractal
Create and save your own wildly colorful fractals using our generator. A Sense of Scale
Explore the infinite detail of a Mandelbrot set as you zoom to a magnification of 250,000,000x. Watch a Preview
TV Program Description

Teacher's Guide

e-mail newsletter
... Program Participants This Web site was produced for PBS Online by WGBH.
Funding for NOVA is provided by David H. Koch, the Howard Hughes Medical Institute, the Corporation for Public Broadcasting, and public television viewers.
Major funding for "Hunting the Hidden Dimension" is provided by the Alfred P. Sloan Foundation. Support provided by

13. A@a__frActAl__a@a
Numerous fractal images, various categories. Screensavers.
http://fractales.free.fr/

14. Fractal -- From Wolfram MathWorld
Weisstein, E. W. Books about fractals. http//www.ericweisstein.com/encyclopedias/books/fractals.html. Yamaguti, M.; Hata, M.; and Kigami, J. Mathematics of fractals.
http://mathworld.wolfram.com/Fractal.html
Algebra
Applied Mathematics

Calculus and Analysis

Discrete Mathematics
... Interactive Demonstrations
Fractal A fractal is an object or quantity that displays self-similarity , in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension . The prototypical example for a fractal is the length of a coastline measured with different length rulers . The shorter the ruler , the longer the length measured, a paradox known as the coastline paradox Illustrated above are the fractals known as the Gosper island Koch snowflake box fractal Barnsley's fern , and Mandelbrot set SEE ALSO: Attractor Backtracking Barnsley's Fern Box Fractal ... Zaslavskii Map REFERENCES: Barnsley, M. F. and Rising, H. Fractals Everywhere, 2nd ed. Boston, MA: Academic Press, 1993. Bogomolny, A. "Fractal Curves and Dimension." http://www.cut-the-knot.org/do_you_know/dimension.shtml

15. Fractals - Fractal Recursions
Jock Cooper's gallery of still images and animations.
http://www.fractal-recursions.com/
Order: DVD Amazon or Createspace
Book Blurb Welcome to the ever-evolving exhibition of Jock Cooper's Fractal Art. A noteworthy recent addition to the site is the Zoomable Fractal Gallery; an interactive playground that allows one to zoom through six levels in each quadrant of a given fractal image. As always, the newer images are in the highest gallery numbers, and new images are added several every month or so.
Traditional Gallery
1029 images
Mechanical Gallery
281 images
Miscellaneous Gallery
246 images
Limited Palette Gallery
168 images
Fractal Animations Gallery
30 animations
Zoomables Gallery
6 Zoomable Fractal images
Please send comments to me at Jock.Cooper At Gmail Dot Com
For commercial use please contact Bruststrokes At Comcast Dot Net
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License You can now view gallery images on your Hires or Lores mobile device. Most recent images are shown first.

16. Cool Math - Fractals - Fractal Art, Lessons And Generators
Coolmath's Fractal Gallery Very cool art that's made from math!
http://www.coolmath.com/fractals/gallery.htm
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Coolmath's
Fractal Gallery
Very cool art that's made from math!
Sorry, your browser doesn't support Java. Your browser does not support the IFRAME tag. Your browser does not support the IFRAME tag. Your browser does not support the IFRAME tag. Back in the 1960's, a French mathematician named Benoit Mandelbrot started thinking about simple pretty simple: How long is the coast of Britain? Sure, it seems easy enough... But, think about how you'd really measure it... Would you fly over the coast in an airplane and measure how far you flew? Or would you take a ruler (or meter stick) and get down on your hands and knees and crawl around the edge? It would be different! In 1975, he made up the word "fractal" because he thought these figures would look fractured or broken up. It wasn't until he had a computer that he could SEE a picture of what he'd been thinking about! To learn about what a fractal is

17. Linda Bucklin S Fractals
Galleries of Ultra Fractal, Frax Flames, and collage.
http://www.lindabucklin.com/fractals/
NEW! Gallery One Gallery Four Frax Flame Gallery Click on a picture to enter a gallery Three NEW Galleries added 6/24/04 NEW! GalleryTwo Gallery Five Frax Flame 2 NEW! Gallery Three Apophysis One Fractal Collage Visit ‘Linda’s Universe’ - My Main Page, with links to all of my sites, including ‘Cats! Cats! Cats! and ‘Linda’s World’. Visit Linda’s World to see my paintings, drawings and digital images. There are also two galleries that exhibit mental illness - related art. My photos, paintings, drawings and digital images of cats. Visit my Renderosity Gallery to see a wide selection of my artwork. Lots of links to some gorgeous fractal galleries! Contact Linda Bucklin Linda's Fractals Gallery One Frax Flame1 ... Frax Flame 2

18. Fractals | Define Fractals At Dictionary.com
–noun Mathematics, Physics . a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale
http://dictionary.reference.com/browse/fractals

19. Fractals For IPhone, IPod Touch, And IPad On The ITunes App Store
Learn more, read reviews, and download fractals by Pomegranate Software on the iTunes App Store.
http://itunes.apple.com/us/app/fractals/id300542371?mt=8

20. Fractals
The primary focus of the Community Learning Network (CLN) is to help K12 teachers integrate Information Technology into their classrooms. This CLN menu page provides links to
http://cln.org/themes/fractals.html

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