Unformatted text preview: equivalent to reﬂection across the x-axis and rotation by −π/2.) Of these,
only (1) and (iv) will orient correctly the three second iteration squares in S1 .
Keeping in mind some fractals are the attractors of several IFS, we’ll start with
the simplest choice, rotation by π . If we can’t complete the IFS table to get the
second iterate pictured, we’ll try another choice for T1 .
To produce the correct orientation for the second iteration corner square in S2 ,
T2 must be rotation by π/2. For the second iteration corner square in S3 , T3
must be reﬂection across the x-axis and rotation by π/2 (equivalent to reﬂection
across the y -axis and rotation by −π/2). So we have a candidate IFS 1.
This does not give the correct orientation for any of the six non-corner second
iteration squares. So, go back to our choice of T1 and take reﬂection across
the y -axis and rotation by π/2. To get the correct orientation of the second
iteration corner square in S2 , T2 must be reﬂection across the...
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