
Welcome to the wonderful world of Fractal Art! This relatively
new form of art utilizes the mathematical science of Fractals to generate
beautiful images. Since the discovery
of Fractal geometry in the 1980's, this mathematical science has been used by a
fastgrowing community of artists to generate beautiful images of various
complexity. These images are usually created on computers using
dedicated programs.
There are now several
programs available to generate fractal pictures. Most of these programs can be
downloaded from various sites. Some of these programs are free, and others need
to be purchased.

About Fractals
Fractal geometry was defined by Benoit Mandelbrot in
1975, but some of the basic concepts had existed in other forms even before
that. This branch of mathematics was formed in order to geometrically describe
indescribable objects. When a Geometer wanted to describe a perfect cone, he
could do so easily, but he could not use those principals to describe a
mountain. There were similarly no tools for describing clouds, trees, or
galaxies in standard Euclidean geometry. Fractals, however, when accurately
defined can turn out a near perfect picture of something like a leaf, tree or
fern. Almost everything in nature can be defined by a fractal. This fairly new
part of mathematics is already used in a huge variety of fields to describe many
different things.
There are three words essential to fundamental fractal geometry, and thus to
understanding fractals. They are self similarity, iteration, and the replacement
rule. Self similarity is a similar appearance at all scales. Iteration is to
repeat an operation, generally using the last result of that operation as the
input. The replacement rule states that in going from one stage of construction
of a fractal to the next, one graphical object is replaced with another, which
is usually more complex but which fits into the place of the original. In
general, a fractal can be defined as a fragmented object having a
selfsimilarity or symmetry of scale. The word was coined by Mandelbrot and was
derived from the Latin word fractus meaning "broken". To better understand what a fractal is though,
one needs to see some examples.

Examples of Fractals
The first and simplest fractal is the Cantor’s dust or
set. To generate this fractal, one starts with a finite line. This line is then
divided into three segments. Then the middle segment is erased. Next, each
remaining segment is divided into three segments, and the middle segments are
erased again. This is then reiterated as many times as possible to obtain a
Cantor’s dust. From this, one can see that this object will have a
selfsimilarity; that is it will look similar under any scale of observation.

Cantor’s dust after seven iterations from
www.wikipedia.org.


For more information about Fractals, we suggest the following links:
* Fractalus web site. A great source of
Fractal Art.
You will also find many links from each of the above sites.

Fractal Art
Fractal science can be used to generate beautiful images. Many artists all over the world have embraced this relatively new type of art. We suggest to visit the Fine Art America web site and serach for Fractal Art. You can also go directly to the fractal art digital art page or to the abstract fractal digital art page or even here.
To create our Fractal Art images, we are using 3
different programs: Ultra Fractal, Tierazon,
and Xenodream. The first two generate
2Dimensional images by resolving mathematical fractal formula in a complex
Cartesian plane. The third one generates 3Dimensional objects by applying
directly some scaling geometry in the 3Dimensional space to some solid
elements. Each program has its own set of specific features leading to different
types of Fractal images.

