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The original Windows version of Genuine Fractals was designed and developed by Altamira Group in Burbank, California under team leader Steven Bender in 1996. In 1997, Altamira released the Robert McNally-developed Version 2.0 on the Macintosh Platform and the redesigned Windows Version 2.0 product.
Sierpiński Carpet - Infinite perimeter and zero area Mandelbrot set at islands The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
L-Systems branching pattern having 4 new pieces scaled by 1/3. Generating the pattern using statistical instead of exact self-similarity yields the same fractal dimension. Calculated: 1.2683: Julia set z 2 − 1: Julia set of f(z) = z 2 − 1. [9] 1.3057: Apollonian gasket
Fractal fern in four states of construction. Highlighted triangles show how the half of one leaflet is transformed to half of one whole leaf or frond.. Though Barnsley's fern could in theory be plotted by hand with a pen and graph paper, the number of iterations necessary runs into the tens of thousands, which makes use of a computer practically mandatory.
Starting in the 1950s Benoit Mandelbrot and others have studied self-similarity of fractal curves, and have applied theory of fractals to modelling natural phenomena. Self-similarity occurs, and analysis of these patterns has found fractal curves in such diverse fields as economics, fluid mechanics, geomorphology, human physiology and linguistics.
A Jerusalem cube is a fractal object first described by Eric Baird in 2011. It is created by recursively drilling Greek cross-shaped holes into a cube. [15] [16] The construction is similar to the Menger sponge but with two different-sized cubes. The name comes from the face of the cube resembling a Jerusalem cross pattern. [17]
Created Date: 8/30/2012 4:52:52 PM
Fractal expressionism is used to distinguish fractal art generated directly by artists from fractal art generated using mathematics and/or computers. [1] Fractals are patterns that repeat at increasingly fine scales and are prevalent in natural scenery (examples include clouds, rivers, and mountains). [ 2 ]