- Easier - A fractal
is a shape, often drawn by a computer, that repeats
itself in a pattern. The design shapes usually
reoccur in different sizes.
- Harder - Fractals
are endlessly repeating patterns that vary
according to a set formula, a mixture of art and
geometry. Fractals are any pattern that reveals
greater complexity as it is enlarged A real-life
example of fractals is ice crystals freezing on a
glass window. You can see countless variations of
the same pattern emerge in the crystals over
Fractals (Grades 9-12) by M.A.
- This website explores fractal dimensions of
strictly self-similar fractals, from Cantor Dust to
the Fractal Skewed Web. Includes a teacher
- Related Websites:
- 2) Fract-ED (Grades 8 and Above) http://www.ealnet.com/ealsoft/fracted.htm
- 3) Fractals by C. Lanius http://math.rice.edu/~lanius/frac/
- 4) Fractals from Math Archives
Fractals by J. Sheu and M. Turvey
- This comprehensive site on fractals first began
as a ThinkQuest project. It still includes a
kid's section that uses audio clips to explain the
basics of fractals in an interesting manner, and
the rest of the site has just about any fact or
explanation a high school student might need on the
topic. Also has quizzes, downloadable files, links,
- Another Comprehensive Fractal
- 2) Amazing Seattle Fractals! http://www.fractalarts.com/ASF/index.html
by S. Alejandre from Math Forum
- This is an introduction to fractals. It also
has some good links.
- This website provides very simple methods to
construct fractals, to do and practice some math,
to appreciate the beauty of fractals, and finally
to have fun with math.
- Related Website:
- 2) Fractals (Grades 5-8) http://math.rice.edu/~lanius/frac/
- Websites By Kids for Kids
and Chaos (1999 ThinkQuest Internet
- This website will describe certain basic
concepts of chaos theory including fractal
Unleashed (1999 ThinkQuest Internet
- This is a comprehensive website about
World by E. Hanson, Lock Haven High
- You have the choice of three fractal topic
pages plus "Fractal Links" to other related
sites. In "What is a Fractal?" you find
basic information on the formulas and origins of
fractal geometry. Under "What is a Fractal?
2" you access more complicated information like
the Mandelbrot function and imaginary numbers.
Finally, examine some computer generated fractals
under "Sample Pictures".
- Fractory (1996
ThinkQuest Internet Challenge)
- This page will help you learn about fractals:
what they are and how to design them.
Internet Fractal and Chaos Education (1997
ThinkQuest Internet Challenge)
- InterFACE offers a series of lessons and
quizzes on fractals and chaos theory. You can hear
a fractal symphony, see a fractal movie, send a
fractal postcard, and download two freeware
Order Out of Chaos (1997 ThinkQuest
- The most well-known aspects of chaos theory are
fractal images. Fractals appear to be complex and
hard-to-comprehend at first glance, but the
underlying code is very simple.
Fractal Universe: Mandelbrot and
More (1999 ThinkQuest Internet
- This page is a study of fractals, both simple
and complex and the basic mathematical concepts
- More Fractal Websites
Music: The Sound of Chaos
- Nowadays, the mathematics behind fractals is
better known as chaos. An amateur musician creates
his music using nothing more than a desktop
computer and a mathematical entity called the
Mandelbrot set, a simple equation better known for
generating complex and haunting fractal images.
(Requires Real Audio program, free download link
- Other Fractal Music Site:
- 1) Fractal Music http://www.ozemail.com.au/~davesag/snd.html
Microscope at the National Center for
Supercomputing Applications (NCSA)
- This site explains about the bizarrely
beautiful images known as fractals.
of the Web from Chaffey High
- Here you find fractal information, programs,
articles and other fractal related pages on the
- Other School Webpages for Fractals:
- 2) Chaos from Minnesota Tech Prep and
Intermediate School District 287
Chaos by P. Bourke
- This fractals site contains images and
information for the more advanced learner.
- Another Fractal Site for Advanced Level
- 2) Fractals and Scale by D.G. Green http://life.csu.edu.au/complex/tutorials/tutorial3.html
of Linear Fractals
- This fractal gallery is divided into five parts
(use either text or images to navigate to them)
containing over 25 images.
- Related Website:
- 2) Presentations at fractals http://www.cs.uregina.ca/~hepting/art/present/
- This is the website of an applet that lets you
explore the Mandelbrot set.
- Similar Websites:
- 2) Julia and Mandelbrot Set Explorer http://aleph0.clarku.edu/~djoyce/julia/explorer.html
- 3) Java Julia Set Generator http://www.unca.edu/~mcmcclur/java/Julia/
- 4) Interactive Fractal Generation Using
Iterative Function Systems http://www.bridgewater.edu/departments/physics/ISAW/FracMain.html
- Here you can explore a huge resource of fractal
images, software and information.
- Other Fractal Images:
- 2) Dance of Chance http://polymer.bu.edu/museum/
- 3) Fractal Domains Gallery by D.C. De Mars
- 4) Fractal eXtreme http://www.cygnus-software.com/gallery/stampindex.htm
- 5) Linas' Art Gallery by L. Vepstas http://www.linas.org/art-gallery/
- 6) Fractal Galleries http://www.glyphs.com/art/fractals/
- 7) Sprott's Fractal Gallery http://sprott.physics.wisc.edu/fractals.htm
- Websites for Teachers
- Computer Generated (Grades 6-12) by D.
- This lesson includes a BASIC program that
generates a right triangle fractal.
- Other Fractal Lessons by D.
- 2) Fractals - Computer Generated 2
- 3) Fractals - Computer Generated 3
- 3) Fractals - Koch and Canter (Grades
- 4) Fractals - Paper Folding (Grades 6-12)
Self-Similarity and Recursion (Grade
- This lesson introduces learners to line
deformation fractals, infinity, self-similarity and
recursion and leads them in practice of fraction,
pattern recognition, perimeter and area
- Other Lesson Plans in the Series:
- 2) Chaos http://www.shodor.org/interactivate/lessons/frac5.html
- 3) Fractals and the Chaos Game http://www.shodor.org/interactivate/lessons/frac3.html
- 4) Properties of Fractals http://www.shodor.org/interactivate/lessons/frac4.html
- 5) Introduction to Fractals: Geometric Fractals
- 6) Irregular Fractals http://www.shodor.org/interactivate/lessons/frac7.html
- 7) Mandelbrot Set http://www.shodor.org/interactivate/lessons/frac9.html
- 8) Pascal's Triangle http://www.shodor.org/interactivate/lessons/frac6.html
Fractal Lesson (Grades 7-12) by D.
- This lesson has students studying fractals
using the World Wide Web and generating their own
- Created by
Updated by Nancy Smith, 6/02.