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    Modeled fractals may be sounds, [21] digital images, electrochemical patterns, circadian rhythms , [50] etc. Fractal patterns have been reconstructed in physical 3-dimensional space [29] : 10 and virtually, often called " in silico " modeling. A limitation of modeling fractals is that resemblance of a fractal model to a natural phenomenon does not prove that the phenomenon being modeled is formed by a process similar to the modeling algorithms. Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges.

    The connection between fractals and leaves, for instance, is currently being used to determine how much carbon is contained in trees. Fractal basin boundary in a geometrical optical system [55]. A fractal is formed when pulling apart two glue-covered acrylic sheets. Romanesco broccoli , showing self-similar form approximating a natural fractal.

    Further Developments In Fractals And Related Fields Mathematical Foundations And Connections

    Fractal defrosting patterns, polar Mars. The patterns are formed by sublimation of frozen CO 2. Width of image is about a kilometer. Slime mold Brefeldia maxima growing fractally on wood. Decalcomania , a technique used by artists such as Max Ernst , can produce fractal-like patterns.

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    Cyberneticist Ron Eglash has suggested that fractal geometry and mathematics are prevalent in African art , games, divination , trade, 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.

    Ethnomathematician Ron Eglash has discussed the planned layout of Benin city using fractals as the basis, not only in the city itself and the villages but even in the rooms of houses. He commented that "When Europeans first came to Africa, they considered the architecture very disorganised and thus primitive. In a interview with Michael Silverblatt , David Foster Wallace admitted that the structure of the first draft of Infinite Jest he gave to his editor Michael Pietsch was inspired by fractals, specifically the Sierpinski triangle a.

    Sierpinski gasket , but that the edited novel is "more like a lopsided Sierpinsky Gasket". Humans appear to be especially well-adapted to processing fractal patterns with D values between 1. When two-dimensional fractals are iterated many times, the perimeter of the fractal increases up to infinity, but the area may never exceed a certain value. A fractal in three-dimensional space is similar; such a fractal may have an infinite surface area, but never exceed a certain volume.

    If done correctly, the efficiency of the emission process can be maximized. From Wikipedia, the free encyclopedia. For other uses, see Fractal disambiguation. A self-similar pattern or set in mathematics. Mandelbrot set : Self-similarity illustrated by image enlargements.

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    This panel, no magnification. The same fractal as above, magnified 6-fold. Same patterns reappear, making the exact scale being examined difficult to determine. The same fractal as above, magnified fold, where the Mandelbrot set fine detail resembles the detail at low magnification.

    See also: Fractal-generating software. Further information: Patterns in nature. Actin cytoskeleton [52] Algae Animal coloration patterns Blood vessels and pulmonary vessels [47] Coastlines Craters Crystals [53] DNA Earthquakes [30] [54] Fault lines Geometrical optics [55] Heart rates [22] Heart sounds [23] Lightning bolts Mountain goat horns Mountain ranges Ocean waves [56] Pineapple Psychological subjective perception [57] Proteins [58] Rings of Saturn [59] [60] River networks Romanesco broccoli Snowflakes [61] Soil pores [62] Surfaces in turbulent flows [63] [64] Trees Brownian motion generated by a one-dimensional Wiener process.