FractionalGeometry-Chap2

# Two examples are given in the bottom of fig 237 the

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Unformatted text preview: r copies above those, a row of four still smaller copies above those, and so on. Clearly, this is not a useful decomposition. The right side of Fig. 2.35 shows a much better approach: take the four smaller copies in the bottom row, each scaled by r = s = .25, and everything else, a copy scaled by r = s = .75. That is, this fractal is generated by this IFS r 1/4 1/4 1/4 1/4 3/4 s 1/4 1/4 1/4 1/4 3/4 IFS for the θ ϕ e f 0 0 0 0 0 0 1/4 0 0 0 1/2 0 0 0 3/4 0 0 0 1/8 1/4 gasket relative of Fig. 2.35. Figure 2.35: Left: a relative of the gasket Right: a decomposition into ﬁve pieces. This example suggests another decomposition of the fern. The bottom left and right fronds are small copies of the fern, scaled, the right copy is reﬂected across the y -axis to achieve the proper orientation, both are rotated, counterclockwise for the left copy, clockwise for the right, then translated vertically, the left copy higher than the right. By making the shrinkings aﬃnities instead of similarities, and by rotating through angles...
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