Welcome to "An Exploration of Fractals", a site brought to you courtesy
of a Senior Honors Thesis in Computer Science at Wittenberg University. Over
the course of the last academic year, I have been learning and researching
Fractals and Chaos. This site will summarize what I believe are some of the
more important aspects of Fractals and Chaos that I have found in my learning.
Computer generated pictures and animation have been used whenever possible to
better illustrate ideas. Most pictures have been generated with Turbo Pascal
code and imported into a couple of graphics packages for retouching and file conversions.
The following section elaborates on the table of contents. It describes
what each section of the table will discuss.
- Introduction and forward
- This section familiarizes the user with the site as a whole and
provides a brief description of the other sections in the site.
- What is a Fractal?
- This section introduces the user to Fractals and Fractal terminology.
A brief dictionary of terms is included.
- This section defines "self-similarity" and shows how it applies to
fractals. One of the goals of this section is to enable the user to
distinguish between self-similar and non-self-similar objects.
- "Classic" Fractal Examples
- This is the picture section of the site. It showcases numerous examples
- Measuring Fractal Dimensions
- This section discusses two ways of measuring fractal dimensions:
self-similar dimension and box-counting dimension.
These two ways are compared and contrasted.
- Iterated Function Systems
- This section demonstrates the most popular way to build fractals.
Iterated Function Systems (a.k.a. Multiple Reduction Copy Machine algorithms)
are discussed and pictorially demonstrated in detail.
- Chaos and Iterated Function Systems
- This section shows how chaos and IFS can produce fractals with much less
computing time and better quality. Discussion from the section on iterated
function systems will motivate this section.
- Other Resources
- This section points the user to other references on the subject,
including additional web sites. The author's email address is also given for
Final notes: For the most part, graphics on the site were generated with
code written in Borland's Turbo Pascal 7.0 for DOS. The graphics were
compiled and imported into JASC's "Paint Shop Pro" (for conversion
and cropping) and RTLsoft's "Animagic GIFs" (for animation when needed).
If you have any questions about any of the material contained in this site,
please feel free to email. Hope
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Copyright Eric Green, 1998