FractionalGeometry-Chap2

But notice a consequence of fractality if the bottom

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Unformatted text preview: r left, upper right, and lower right branches. These are easy: scale the tree, rotate to achieve the orientation of each of the four main branches, translate to the location of these branches (translate so the base of the trunk is sent to where the branch joins the trunk). To make the tree appear more natural, the branches are scaled by diﬀerent amounts horizontally and vertically, destroying the exact similarity between the branches and the tree. The only diﬃculty is the trunk itself. A ﬁrst guess is to make the trunk by shrinking the tree a lot in the x-direction and by about half in the y -direction. This is the IFS made of the ﬁrst ﬁve rows of the table. The left side of Fig. 2.34 shows the resulting picture. A moment’s reﬂection reveals the diﬃculty. One repair, achieved with the sixth row of the table, is to shrink the tree again by the same amounts as in the ﬁfth row, reﬂect it vertically so the larger part is on the bottom, and then translate vertically. The right side of Fig. 2.34 shows the six copies of the tree...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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