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 fast-growing 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 self-similarity 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 Cantorís 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 re-iterated as many times as possible to obtain a Cantorís dust. From this, one can see that this object will have a self-similarity; that is it will look similar under any scale of observation.

Cantorís 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 2-Dimensional images by resolving mathematical fractal formula in a complex Cartesian plane. The third one generates 3-Dimensional objects by applying directly some scaling geometry in the 3-Dimensional space to some solid elements. Each program has its own set of specific features leading to different types of Fractal images.

 

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Last updated Dec 2011- Reflections Of Infinity - email: reflectionsofinfinity@comcast.net