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The position of the image of the large gap [0, 1/2] × [1/2, 1] is a clue. Pieces B
and C are obtained by reﬂection across the y  and xaxes, respectively, followed
by appropriate translations, given in IFS 2.
For fractal (c), pieces B , C , D, and E are in the same orientation as the whole
fractal. Pieces A and F are rotated by π , or reﬂected across the xaxis. With
the appropriate translations, we have IFS 3. 31 2.1. ITERATED FUNCTION SYSTEM FORMALISM
A F B C E C A B A (b) (a) C B D (c) Figure 2.8: Fractals for Prxs 2.1.1.
r
1/2
1/2
1/2 s
1/2
1/2
1/2 θ
ϕ
e
π
π
1/2
π/2
π/2
1
−π/2 −π/2 0
IFS 1 for PrxsSol 2.1.1 f
1/2
0
1 r
1/2
1/2
1/2 s
1/2
1/2
1/2 θ
ϕ
e
π/2
π/2
1/2
0
0
1
0
0
0
IFS 2 for PrxsSol 2.1.1 f
1/2
0
1 r
1/4
1/4
1/2
1/2
1/4
1/4 s
1/4
1/4
1/2
1/2
1/4
1/4 θ
ϕ
e
π
π
1/4
0
0
0
0
0
0
0
0
1/2
0
0
3/4
π
π
1
IFS 3 for PrxsSol 2.1.1 f
1
1/2
0
0
1/2
1 PrxsSol 2.1.2 Because the square is taken to another square, this is a similarity transformation. That is, r = s. To ﬁnd the con...
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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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