Nicole Harper

UNVR 195A

Report #1

September 29, 1999

Fractals

In the American Heritage Dictionary: Third Edition the definition of a fractal is "a geometric pattern that is repeated at even smaller scales to produce irregular shapes that cannot be represented by classical geometry." Fractals are an amazing wonder and as strange as it may seem, this representation happens quite frequently in nature. Fractals are a major part of nature. Some examples of fractal like wonders in nature would be a leaf or a snowflake. But the wonder of fractal patterns doesn’t stop here. Nature is constantly forming things that have a natural nature to form a pattern.

A site specific for fractals can be found at www.users.bigpond.com/walkera/fractals.htm. At this site you will find some general information about fractals. There are some graphics to look at to help visualize the phenomenon of fractals. This site briefly discusses snowflakes and the Mandelbrot set. To read more information on these topics the next two links are helpfu. The Koch Snowflake is a prime example of how fractals work. At the site www.users.bigpond.com/walkera/koch.htm you will find a description of how the Koch Snowflake works and some detailed graphics for visual aide. This is a very interesting site and shows a lot about fractals. The Mandelbrot set can be found at a link from this site or at www.users.bigpond.com/walkera/mandset.htm. At this site you will find various different links to go to that will show you more about fractals and things related to fractals. Like the site before mentioned before, it has graphics. But at this site the graphics aren’t to show how the certain type of fractal is formed, instead simply to show what the image looks like. All of these sites and their links are free and you are welcomed to use the information and images.

Another interesting site where you can view the Mandelbrot set and also Julia set is www.geocities.com/CapeCanaveral/2854/. Unlike the other site about the Mandelbrot set, this site gives the mathematical definitions for both the Mandelbrot and Julia sets along with some other useful information about them. In contrast to the other site about the Mandelbrot set, this is a more technical view of the set. Something fun that the other site did not offer is the opportunity to produce fractals of your own. The fractal images that are at this site were produced using a free fractal generator program called Fractint. Something fun you might want to do is download this program. You can do this by going to the site about Fractint. From here you can either click on the link at the bottom of the Mandelbot and Julia Sets page or go to spanky.triumf.ca/www/fractint/fractint.html or fractal.mta.ca/fractint/fractint.html. With Fractint you can produce fractals, make fractal screen savers, and do all kinds of neat stuff.

All of these sites are about fractals in some sort of way but each in a different way. For instance, the first site mentioned is about the Koch snowflake. In contrast the geocities site is a mathematical view about the Mandelbrot and Julia sets. These are some of the most useful and informational sites about fractals that I found. Just as something to leave on, the best fractal image that I found was at the site homepage.dave-world.net/~toneill/fractal/fract009.htm. You won’t find anything informational or technical about this page, it is simply something fun to look at. At least ways that’s what I thought and this was my favorite!