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abstract fire fractals
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abstract artwork circles digital art fractals
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Winterfell nebula
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abstract fractals grunge spikes
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artwork desks fractals hands notebook
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WINTER FROM NORWAY
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Abstract Fractals 3
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abstract fractals multicolor rainbows
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A Palace
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Blue fractals
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Hibiscus
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SeaHorse
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Amethyst
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3rd Dimension
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Colorful Fractals
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Milky Way
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Abstract Fractals
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Red Star
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3d Fractals
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Enigma
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EKG
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Fields of Gold
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Days of the Dragons
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A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern. An example of this is the Menger Sponge. Fractals can also be nearly the same at different levels. This latter pattern is illustrated in Figure 1. Fractals also includes the idea of a detailed pattern that repeats itself. Fractals are different from other geometric figures because of the way in which they scale. Doubling the edge lengths of a polygon multiplies 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, its volume scales 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). But if a fractal's one-dimensional lengths are all doubled, t...

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