FractionalGeometry-Chap2

6 ifs forgeries of natural fractals 69 way to

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Unformatted text preview: ijn sequences 1 1 2 16 2048 67108064 14415188075855872 ... ≈ 1.31 × 10350 IFS forgeries of natural fractals If IFS just generated the gasket and its relatives, this approach would be of interest to geometers (including me), but maybe not to many others. We remember that a large part of Mandelbrot’s motivation was to understand the 2.6. IFS FORGERIES OF NATURAL FRACTALS 67 roughness of objects in nature. His insight was that much of physical roughness could be explained by by using symmetry under magnification. Benoit’s thinking never strayed far from Nature. Mirroring this, Michael Barnsey interested many, many people in IFS by Fig. 3 of [8], a realistic image of a black spleenwort fern constructed using only four transformations. This generated much interest, and at least indirectly prepared the way for fractal landscape systhesis and many other visual effects. In this section we learn to make fractal forgeries of some simple natural iamges. The left side of Fig. 2.33 shows a fractal tree, two branches left, two branches right, each of these having tw banches on each side, and so on. This is straightforward except possibly for the trunk. The right side, a fractal fern, involves a more subtle decomposition, so will be treated more extensively....
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