Fractal
From The Art and Popular Culture Encyclopedia
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- A geometric figure that repeats itself under several levels of magnification, a shape that appears irregular at all scales of length, e.g. a fern.
- A geometric figure, built up from a simple shape, by generating the same or similar changes on successively smaller scales; it shows self-similarity on all scales
In nature
Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature.
Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. The connection between fractals and leaves are currently being used to determine how much carbon is contained in trees.
In 1999, certain self similar fractal shapes were shown to have a property of "frequency invariance"—the same electromagnetic properties no matter what the frequency—from Maxwell's equations (see fractal antenna).
In creative works
Fractal patterns have been found in the paintings of American artist Jackson Pollock. While Pollock's paintings appear to be composed of chaotic dripping and splattering, computer analysis has found fractal patterns in his work.
Decalcomania, a technique used by artists such as Max Ernst, can produce fractal-like patterns. It involves pressing paint between two surfaces and pulling them apart.
Cyberneticist Ron Eglash has suggested that fractal-like structures are prevalent in African art and architecture. Circular houses appear in circles of circles, rectangular houses in rectangles of rectangles, and so on. Such scaling patterns can also be found in African textiles, sculpture, and even cornrow hairstyles.
In a 1996 interview David Foster Wallace admitted that the structure of his novel Infinite Jest was inspired by fractals, specifically the Sierpinski triangle.
The song "Hilarious Movie of the 90's" from Pause (album) by the artist Four Tet employs the use of fractals.
