FractionalGeometry-Chap2

To help determine the scaling rotation and

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Unformatted text preview: generated by this IFS. Here the pieces have been pulled apart to more clearly reveal their individual natures. Figure 2.34: Left: fractal tree with half-trunk. Right: fractal tree with its main pieces pulled apart. The fern is a bit more difficult. A first guess at decomposing the fern might be discouraging: the bottom left and right fronds are small copies of the fern, as are the fronds left and right above those, as are the fronds left and right above those, and so on. Viewed this way, the fern is made of dozens, maybe hundreds (in fact, infinitely many, if we think of the image as a pixelated version of a mathematical fractal) of smaller copies of itself. Sometimes, the most obvious 2.6. IFS FORGERIES OF NATURAL FRACTALS 69 way to decompose a fractal does not lead to an IFS with the smallest number of rules. A simpler shape, a relative of the gasket, will guide us in decomposing the fern. The left side of Fig. 2.35 can be decomposed into a row of four smaller copies along the bottom, a row of four slightly smalle...
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