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Filling in the details would be cumbersome, but these are the components of
the proof.
Practice problems
The practice problems 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. 2.60. As
in example 2.9.2, each transformation can involve reﬂection across the xaxis,
reﬂection across the y axis, or rigid rotation by π/2, π , or 3π/2. Translations
place each image in the appropriate location.
Prxs 2.9.1 The attractor without rotations or reﬂections (right side of Fig.
2.60) is multiplyconnected. Find an example with a dendrite attractor.
Prxs 2.9.2 Given that the transformations TA , TB , and TC have a dendrite
attractor, must every four function IFS also have a dendrite attractor?
Prxs 2.9.3 Find a four function IFS with a disconnected attractor. Is the
attractor totally disconnected?
Practice problem solutions 94 CHAPTER 2. ITERATED FUNCTION SYSTEMS PrxsSol 2.9.1 Looking at the attractor on the right side of Fig. 2.60, the m...
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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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