The Fascinating World of Fractals
A new perspective
Pat Brewster


For centuries we have viewed the world, using the line as a basic perspective.  Fractals provide a new and different way to look at what we encounter in life.  Fractal Geometry is a new language which is helping us understand and perhaps control some of the mystifying chaotic aspects of nature.
Fractals can also make beautiful and intricate designs. 

 
What are Fractals? Fractals are shapes which have similar details at many different sizes. That is, when you look at a small piece of the fractal shape, you see small copies of the overall large fractal shape. There are many different kinds of fractals, and at the heart of fractals is mathematics.   The word, "fractal", was coined in 1975 by Benoit B. Mandalbrot.  It comes from the Latin verb, frangere, meaning "to break or fragment."

Fractals in Nature and the world around us.

The featherlike frond of the fern is composed of rows of smaller fronds, and the smaller fronds have their rows of even smaller fronds, too. The whole plant and the smaller parts are "self-similar," like each other.

Some other things that 
fractals can model:
  • the weather
  • fluid flow 
  • geologic activity
  • planetary orbits
  • human body rhythms
  • animal group behavior
  • socioeconomic patterns
  • music
  • coastlines
  • storm clouds
  • soil erosion
  • seismic patterns
Real-world problems.

People use fractals to analyze chaotic behavior and solve real-world problems.
Engineers have begun designing and constructing fractals in order to solve practical engineering problems. For example take a look at Amalgamated Research Inc.'s Fractal Control of Fluid Dynamics.  Fractals are being used to control the turbulent flow of fluid through pipe systems.

Physicists use fractals. Strange attractors with Fractal turbulence appear in celestial mechanics.  Biologists diagnose dynamical diseases.

Fractals as Art
Fractal geometry mixes art with mathematics and shows us that there is indeed beauty in Mathematics.  Fractals win prizes at graphics shows. See Fractals as Art, by Melissa Binde.


Fractal Gallery
Points of Light
This page from Melissa Binde's site is a good page to go to, to view
thumbnails of 26 beautiful fractals.
When you go there, click on the names of the fractals, and view them FULL SCREEN. (Click on the small fractal, in the column at the left.)
Animations.

You can see some amazing fractal animations at the World of Fractals site by Adam Lerer.   (Click on the small fractal, in the column at the left.)  Once there, click on the left arrow on the progress bars to start the animation. 

Fractal Art Contest 		 World of Fractals is proud to be the home of the monthly Fractal Art Contest. This contest is for anybody who enjoys creating their own artistic works of fractals. A winner will be chosen by a team of judges based on appearance, depth, colour, interest, and overall appeal.

Click on the fractal at the left, to go to the site and find out more.

SOME FRACTAL LINKS:

http://www.math.umass.edu/~mconnors/fractal/intro.html Introduction: Exploring Fractals
http://www.cs.swarthmore.edu/~binde/fractals/index.html Melissa Binde’s Fractals as Art
http://archive.ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html The Fractal Microscope and
Why Fractals?
http://math.rice.edu/~lanius/fractals/WHY/ Why Study Fractals?
Amalgamated Research Inc.'s Fractal Control of Fluid Dynamics.  Constructing fractals in order to solve practical engineering problems.
(Advanced discussion)
http://mathforum.org/library/topics/fractals/ Many articles discussing fractals.
https://www.angelfire.com/art2/fractals/animations.htm Animations: By Adam Lerer
https://www.angelfire.com/art2/fractals/contest.htm Fractal Art Contest

 

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