Geometric
abstract art is a form of abstract art based on the use
of simple geometric forms placed in nonillusionistic space and
combined into nonobjective compositions.
Artists who created geometric abstract works include Piet Mondriaan,
Victor Vasarely, Kazimir Malevich and Gordon Walters.
Fractal art is an algorithmic
approach for producing computer-generated art using fractal
mathematics. Traditionally, fractals fall into four broad categories
relevant to fractal art:
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Those for which membership of a point in a fractal set may be
determined by iterative application of a simple function. An example
of this type is the Mandelbrot set and the Lyapunov fractal. Those for which a geometric replacement rule exists. Examples include Cantor dust, the Sierpinski gasket, the Menger sponge and the Koch snowflake. Those created with iterated function systems, in particular fractal flames. Those which are generated by stochastic rather than deterministic processes (examples include fractal landscapes). |
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.
A fractal image generated by Sterling Fractal by Stephen
FergusonFractals 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").
For an example of the state of the art in fractal landscapes,
http://www.fractal-landscapes.com contains an excellent gallery and
a description of the mathematics behind fractal landscapes.
Additionally, a sub-category of fractal art is fractal music which
is able to produce more realistic natural sounds and subtle tunes
than conventional approaches.
The two most popular fractal art 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 1990's Fractint for DOS was the most popular
fractal rendering software for the pc.
This information and more can be found at WIKIPEDIA