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Fractal artis a form ofalgorithmic artcreated by calculatingfractalobjects and representing the calculation results as still images, animations, andmedia. Fractal art developed from the mid-1980s onwards.It is a genre ofcomputer artanddigital artwhich are part ofnew media art.

Themathematical beautyof fractals lies at the intersection ofgenerative artandcomputer art. They combine to produce a type ofabstract art.

Fractal art (especially in the western world) is rarely drawn or painted by hand. It is usually created indirectly with the assistance offractal-generating software, iterating through three phases: setting parameters of appropriate fractal software; executing the possibly lengthy calculation; and evaluating the product. In some cases, othergraphics programsare used to further modify the images produced. This is called post-processing. Non-fractal imagery may also be integrated into the artwork.TheJulia setandMandelbrot setscan be considered asiconsof fractal art.

It was assumed that fractal art could not have developed without computers because of thecalculativecapabilities they provide.Fractals are generated by applyingiterativemethods to solving non-linear equations orpolynomial equations. Fractals are any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size.

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In mathematics, afractalis a subset of a Euclidean space for which theHausdorff dimensionstrictly exceeds thetopological dimension. Fractals tend to appear nearly the same at different levels, as is illustrated here in the successively small magnifications of theMandelbrot set;Because of this, fractals are encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales calledself-similarity,also known asexpanding symmetryorunfolding symmetry; If this replication is exactly the same at every scale, as in theMenger sponge,it is called affine self-similar.

One way that fractals are different from finitegeometric figuresis the way in which theyscale. Doubling the edge lengths of apolygonmultiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the dimension of the space the polygon resides in). Likewise, if the radius of a sphere is doubled, itsvolumescales by eight, which is two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere resides in). However, if a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily aninteger.

This power is called thefractal dimensionof the fractal, and it usually exceeds the fractal'stopological dimension.
Analytically, fractals are usually nowheredifferentiable.An infinite fractal curve can be conceived of as winding through space differently from an ordinary line although it is still1-dimensional, its fractal dimension indicates that it also resembles a surface.

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