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Unformatted text preview: 488 Figure 2.5: A Sierpinski tetrahedron, the analog of the gasket in 3-dimensional
Before the exercises, we present several practice problems, together with
Prxs 2.1.1 Find the IFS rules to generate the fractals of Fig. 2.6.
Prxs 2.1.2 Find the contraction factor of the linear transormation taking the
square with vertices (0, 0), (2, 0), (2, 2), and (0, 2), to the square with vertices
(0, 0), (1/2, 1/2), (0, 1), and (−1/2, 1/2).
Prxs 2.1.3 Given the initial image, the unit square containing an L, on the
left side of Fig. 2.7, ﬁnd the IFS rules for which the image on the right side of
that ﬁgure is the second iteration of this IFS. 30 CHAPTER 2. ITERATED FUNCTION SYSTEMS (a) (b) (c) Figure 2.6: Fractals for Prxs 2.1.1. Figure 2.7: Images for Prxs 2.1.3. Practice problem solutions
PrxsSol 2.1.1 Decompositions of the fractals are shown in Fig. 2.8. Fractals
(a) and (b) each are divided into three pieces, scaled by 1/2. Fractal (c) is
divided into six pieces, two scaled by 1/2 and four scaled by 1/4.
None of the three piec...
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