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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