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Unformatted text preview: ement of the four transformations. Right: the attractor witout rotations or reﬂections.
Exercises
Prob 2.9.1 In Example 2.9.1 ﬁnd a value of θ1 = ϕ1 slightly larger than π/4
so the attractor is connected.
Prob 2.9.2 Modify Example 2.9.1 in this way
r
1/2
1/2
1/2 s
1/2
1/2
1/2 θ
ξ
−ξ
0
Table for ϕ
ξ
−ξ
0
the IFS e
0
1 − cos(−ξ/2)
1/4
of Prob. 2.9.2. f
1/2
− sin(−ξ/2)
√
3/4 Certainly, for ξ = 0 the attractor is an equilateral gasket. Find another value
of ξ for which the attractor is an equilateral gasket. Is it the same size as the
ξ = 0 gasket?
Prob 2.9.3 Using the four function placements of the practice problems, ﬁnd
a four function IFS with hybrid attractor.
Probs 4 – 7 use a four function IFS, three scaling by 1/2, one scaling by 1/4,
placed according to the schematic on the left side of Fig. 2.62. As in example
2.9.2, the each transformation can involve reﬂection across the xaxis, reﬂection
across the y axis, or rigid rotation by π/2, π...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.
 Fall '14
 AmandaFolsom
 Geometry, Fractal Geometry, Limits, The Land

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