FractionalGeometry-Chap2

If we cant complete the ifs table to get the second

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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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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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