| Fractals
A fractal is a geometric pattern that repeats itself at smaller and smaller
scales to produce irregular shapes and surfaces that cannot be represented
by classical geometry......think about the spirals in some seashells.
That irregular pattern can be considered to be a fractal.
Fractals often exhibit the property of self-similarity and represent
the many irregularly shaped objects in nature. A self-similar object is
one whose component parts resemble the whole. Any of its smallest parts
are similar in shape to its larger structure---like a broccoli flower
or a fern leaf.
Sample some of the following activities to learn more about fractals.
Places To Go | People To See | Things To Do | Teacher Resources | Bibliography
Places To Go
The following are places to go (some real and some virtual) to find out
about fractals.
Dance of Chance
Visit the Museum of Science in Boston and check out their exhibit on fractals
and patterns in nature.
Fractal
World
An introduction to fractals created by an honors algebra class in Pennsylvania.
People To See
Benoit
Mandelbrot
Meet Benoit Mandelbrot. He is a French mathematician who helped develop
chaos theory. He also developed fractal geometry which is used to find
order in apparently erratic shapes and processes. Mandelbrot invented
the term fractal. He based the term on fractus, a Latin word meaning a
broken stone with an irregular surface.
Things To Do
Fractals
Check out the fractal of the day and view past fractals in the Fractal
Gallery.
A Fractals
Unit for Elementary and Middle School Students
This is a great site. It will lead you to fractal information and activities
that you can actually understand.
Sprott's
Fractal Gallery
Fractal music! Listen to fractal music while you view the Fractal of the
Day. The inventor of fractals, Benoit Mandelbrot, also is a proponent
of chaos theory. From this site, you can view a chaos demonstration and
experience "strange attractors".
An
Introduction to Fractals
Learn more about strange attractors.
Fractals
Figure out how a Koch snowflake is a fractal.
Spanky Fractal Database
Find lots o' fractals.
Making
Order out of Chaos
Remember the Jeff Goldblum character in the movie, Jurassic Park? He was
a believer in chaos theory which deals with complexity in nature. He was
proven right when an island full of female dinosaurs somehow laid and
hatched eggs, broke fences, chased jeeps, ate gamekeepers, and opened
kitchen doors. Find out more.
The
Leap Fractal Game
Choose your own difficulty level in this challenging game of Leap Fractal.
Mandelbrot
Explorer
Create your own Mandelbrot sets. In case you've forgotten, a Mandelbrot
set is the set of all complex c such that iterating z -> z^2+c does
not go to infinity (starting with z=0). See the creations that other Mandelbrot aficionados have made.
Julia
and Mandelbrot Set Explorer
After you knock yourself out making Mandelbrot sets, make some Julia sets.
The
Fibonacci Sequence
Apparently the Fibonacci sequence can be found in the Mandelbrot set.
Check it out.
What
Is a Fractal? And Who Is This Guy Mandelbrot?
See how this site calls fractals "worlds within worlds".
Fractals
Theme Page
Oh boy! Join the Chaos Club!
Fractals
Overload on fractals---fractal clouds, fractal music, fractal software,
fractal pancakes, and more.
The
Fract-ED Information Pages
Explore this introductory fractal tutorial.
NCTM
Interactive Fractal Tool
Use this online tool to play with and create fractals.
Teacher Resources
Lesson Plans/Webquests
Bibliography
- Crownover, Richard M. Introduction to Fractals and Chaos. Boston :
Jones and Bartlett, c1995.
- Dixon, Robert. Mathographics. New York : Dover Publications, 1991.
- Laplante, Phillip A. Fractal Mania. Blue Ridge Summit, PA : Tab Books,
1993.
- Peitgen, Heinz-Otto. Chaos and Fractals :New Frontiers of Science.
New York : Springer-Verlag, c1992.
- Pickover, Clifford A.Chaos in Wonderland : Visual Adventures in a
Fractal World. New York : St. Martin's Press, c1994.
- Turcotte, Donald Lawson. Fractals and Chaos in Geology and Geophysics.
Cambridge, U.K. ; New York : Cambridge University Press, c1997.
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