Applications of Fractal Geometry

An Honors Project at the University of Rhode Island, Spring 2002

by Joe DeAlmo

Faculty Sponsor: Mustafa Kulenovic, Ph.D.

This site was created as a presentation medium for my honors project on fractals. It also is intended to serve as a reference tool for others who may be studying the exciting field of fractal geometry.

When I began this project, I had almost no knowledge of fractal geometry. I had to learn some basic theory, and then I learned some of the many fractal applications to the non-mathematical world. Then, I needed to find a way to take what I had learned and present it in such a way that people could understand fractals without having to know all of the theory behind them.

Along the way, the idea of a website as a presentation medium began to manifest itself. Many mathematical programs such as Mathematica and Sicentific Notebook allow direct saving as HTML files. Thus, making a website out of my work would be simpler than, say, making presentation using PowerPoint.

I then realized the potential that this site could have. This site is a published piece of work, and it could very well be on this server long after I graduate. Technology thus has given me the unique opportunity to publish a major work with fairly little effort. I can use this site to present my work, and then other people can access the site on their own to learn more.

This is what I hope to accomplish with this site. I hope that it fulfills whatever purpose you, the user, hope that it will serve. If you have any comments about the site, please feel free to pass them along using the email links on the top of this page.

I have written this site to be read almost as a textbook; this also provides ease in presentation. Section 1 gives a breif overview and introduction to some basic fractals. Section 2 provides some basic theory; those of you who are uninterested in theory can bypass this section. Section 3 discusses a few of the many applications of fractals. And Section 4 simply gives some additional resources one may wish to explore.

  1. Fractals: An Introduction
  2. Some Theory and Definitions
  3. Applications
  4. Other Sources of Information