Unformatted text preview: traction factor, consider the
scaling needed to take a side of the initial square to a side of the image square.
√
The initial square has side length 2, the image square 1/ 2, giving
√
1/ 2
1
image length
=
=√
r=
initial length
2
22
PrxsSol 2.1.3 Because the second iteration consists of 9 squares, the IFS consists of 3 transformations. Say T1 takes the unit square to S1 = [0, 1/2] × [0, 1/2],
T2 takes the unit square to S2 = [1/2, 1] × [0, 1/2], and T3 takes the unit square
to S3 = [0, 1/2] × [1/2, 1]. How care we to ﬁnd the parameters of the three
transformations?
Calling the unit square S , T1 (S ) is the corner of the L in the ﬁrst generation. 32 CHAPTER 2. ITERATED FUNCTION SYSTEMS In the second generation, the three corners of the L are T1 (T1 (L)), T2 (T1 (L))
and T3 (T1 (L)). Note that T1 (T1 (L)) is in the same orientation as L, so T1 is (i)
rotation by π , (ii) reﬂection across the xaxis, (iii) reﬂection across the y axis,
or (iv) reﬂection across the y axis and rotation by π/2. (Note from Eq 2.1 that
(iv) is...
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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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