Fractal art

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Image:Fractal.arp.750pix.jpg

Fractal art is created by calculating fractal mathematical functions and transforming the calculation results into still images, animations, music, or other art media. Fractal images are graphs of the calculation results, and fractal animations are sequences of these graphs. Fractal music maps the calculation results to music pitches or other sounds. Fractal art is usually created with the assistance of a computer, in order to speed up the process of calculating the fractal function.

Traditionally, fractals fall into four broad categories relevant to fractal art:

Fractals of all four kinds have been used as the basis for vast sections of digital art and animation. Starting with 2-dimensional details of fractals such as the Mandelbrot Set, fractals have found artistic application in fields as varied as texture generation, plant growth simulation and landscape generation.

Image:InterstellarDoilies-1024.jpgFractals are also being used in context with evolutionary algorithms in the Electric Sheep project, as people use fractals rendered with distributed computing as their screensaver, and "rate" the flame they are viewing. Then the server reduces the traits of the undesirables, and increases those of the desirables to produce a computer-generated, community-created piece of art.

Many fractal art galleries can now be found on the Internet, for example at this Tierazon and Sterling fractal gallery page. Perhaps a good starting point would be the fractal pages of Stephen C. Ferguson who has made several fractal generators like Sterling Fractal, an example image from which is shown to the left. His more classic fractal generators include Iterations et Flarium (et means "and").

The two most popular fractal image creation programs are thought to be Ultra Fractal and Apophysis. The latter being a fractal flame editor and the former a more general purpose fractal program with a lot of features. During the 1990s Fractint for DOS was the most popular fractal rendering software for the PC.

Fractal music is able to produce more realistic natural sounds and subtle tunes than conventional approaches.

Contents

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Gallery

Burning Ship fractal by Michael Michelitsch and Otto E. Rössler

Fractal by Michael Michelitsch

Fractal by Michael Michelitsch

Fractal by Michael Michelitsch

Circus Table

Sunhorses - a composite fractal image

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Art and the Mandelbrot set

Some people have a hobby of searching the Mandelbrot set for interesting pictures and using them in fractal art. They have a collection of pictures, along with the coordinates for generating that picture.

Further examples below are regions, to the right is a min-cardioid, connected by filaments (too thin to be seen) to the main set (and other cardioids, some of which are actually in this image but too small to be seen).:

Image:Rfl-mandel002-out-p02.ps.rgb.bmp-fv-ls.2-gq90op.jpg Image:Rfl-mandel003-out-p03.ps.rgb.bmp-fv-ls.2-gq90op.jpg Image:Fract027.gif Image:Michelmset.jpg
There are many free fractal-generating programs available, such as those by Stephen Ferguson (Sterling Fractal and the Tierazon series) and many people write such programs themselves for the highest level of control over their pictures.

Since the set (unlike nature) has unlimited detail, it appears less noisy when calculated on a fine grid and down-sampled with anti-aliasing. Here are two color codings of the same calculation and two images made by combining two calculations for each image.

Image:Mandelbrot Spiral Cleft 2.jpg

Image:Mandelbrot Spiral Cleft.jpg

Image:Mandelbrot Islands of Consciousness.jpg

Image:Mandelbrot Cypress Underbrush.jpg

Following the left of one valley and the right of another cancels out most of the spiraling found on the sides of valleys.

In the following three images, the distance estimator has been used to help in anti-aliasing by eliminating unrepresentative samples. In the last three, these pixels were replaced by bleeding in their neighbors. "Deep Re Twisted" has been processed to enhance the edges, similarly to some in the previous row. 

     Image:Mandelbrot Pachyfractal.jpg

     Image:Mandelbrot Deep Re-Twisted.jpg

     Image:Wayne's Pachifractal very large bright.jpg

     Image:Mandelbrot Budding turbines.jpg

      Image:Mandelbrot Persian Rug.jpg

The main artistic challenge is that simple mathematical forms are boring, like classical Greek pottery (without the painting), or like classical music sounds to a jazz fan without classical training. To make it more like classical Chinese pottery, or like the way classical music sounds to a classical fan or jazz to a jazz fan, there needs to be a greater variety of shapes. This is achieved by taking a varied path while zooming in, near a point, down a cleft, right and left sides of valleys, etc., and by picking dense areas where most of the pixels are blends of the colors of different dwell values. The difficulty is that deeper dwells, fine detail, and large calculations to be down sized, all increase the computer time, so what one can do without parallel arithmetic is limited.

Also, oil paintings tend to be around a meter square, or larger, so serious computer art should really use many megapixels.

"Persian Rug" was found by selecting a star near the body of the set and then a puff on a horizontal part of a ray of the star (an arm of the candelabra), twice. It is similar with reflection and almost identical with 180 degree rotation. The dwell values are very high, so only the top half was calculated, and that was rotated to approximate the bottom.

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Some details of the Mandelbrot set

(made using a JAVA applet)

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References

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External links

sv:Fraktalkonst

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