Christy Wolfe

September 29, 1999

UNVR 197a – Sec. 11

The Basics of Fractals for Elementary Students

Do you ever look up into the sky and look at the clouds? Do you ever pull a leaf off of a tree and twirl it between your fingers? Do you ever gaze at the coastline and dream of amazing things? If you do, you are actually looking at patterns of fractals. Fractal shapes are found everywhere in nature, and only recently have they become widespread throughout the math world. Most students think math is boring, dull, and dead. They don’t realize that math affects things everywhere around us. I’m going to give you some helpful insight into some web pages and fractal ideas for the classroom. These ideas are generally for the 7^th and 8^th grades, but can also be incorporated into high school and younger classrooms as well.

Fractals are geometric figures. Yes! All those beautiful, brightly colored pictures are really just triangles, rectangles, circles, and squares. Fractals can appear in nature or can be mathematically made. Some examples of natural fractals are the shapes and patterns of clouds, trees, ferns, mountains, and coastlines. For more information on what fractals are, you can visit any of the web pages throughout this paper. Just a reminder though, all these web pages are primarily used for elementary students. More advanced pages can be found by using the search engine: www.yahoo.com

Fractals serve a variety of purposes. Fractals provide a simple solution for a very complex idea. You can break down the shapes of landscapes and clouds into fractals. Landscape designers use fractals when they are building parks, city streets, and yards for homes. They start with a simple design and repeat it over and over again. Science Fiction film designers also use fractals when making their backdrops. They can transport you to another world just by the use of fractals. Pretty neat, huh? If you would like to know more about the uses of fractals, visit: http://library.advanced.org/3288/usesfrac.html

Most math you study in school isn’t very exciting. Most of it was organized by men like Euclid in about 300 BC or Isaac Newton in the early 1700s! No wonder it’s boring, with all the technology we have today, old math just doesn’t seem any fun. But fractals are new math. You take a shape, do something to it, then do it again and again as long as you want and BAM! You have a fractal pattern! From Cynthia Lanius’ web page, you can learn more about fun with fractals. "You don’t see a lot of triangles, squares, and rectangles in the woods, but fractals show up in everything from cumulus clouds to fern fronds," said Lanius. Learning fractals should be fun. To look up some fractal lesson plans, visit Lanius’ web page at: http://math.rice.edu/~lanius/frac/

The Sierpinski Triangle is one of the easiest fractals there is to construct. Younger students will especially enjoy making these patterns. All they will need is a ruler, a piece of paper, and some crayons. Watch as they become fascinated as they make not only a beautiful picture, but also realize they are doing "high-tech" mathematics. For complete instructions on how to construct the Sierpinski Triangle, go to:

http://math.rice.edu/~lanius/fractals/

There are so many fractals found in nature, it would be impossible for me to try and name them all. From beautiful coastlines to swirling galaxies in the universe, you can find fractals everywhere in nature. Visit the following sight for pictures of wonderful natural fractal shapes and also some examples of how mathematics can remake these fractals.

http://hyperion.advanced.org/12740/netscape/landscape/index.html

Of course, we have to end this paper with my personal favorite fractal. To see just what it is, you’ll have to go to: http://www.oz.net/~alden/animpal/mandel.html

I hope I’ve given you some insight into the world of fractals and how you can incorporate their everyday existence into the classroom with their simplicity. If you can’t get your students to completely understand fractals and why they work, just get them to fully understand where they are found and how to do the simple ones. Next time you look into the sky or stare at the ocean, imagine what kind of fractals are actually there.