FractionalGeometry-Chap2

Figure 264 left an ifs tree with color assigned by

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Unformatted text preview: n TB and add a reﬂection across the x-axis in TC . The bottom middle image of Fig. 2.61 is the attractor of the IFS {TA , TB , TC }, certianly a dendrite, and now containing the points (3/4, 1/2) and (1/2, 3/4). The top middle image of Fig. 2.61 is the attractor of the IFS {TA , TB , TC , TD }, clearly multiply-connected. PrxsSol 2.9.3 From our experience in the ﬁrst two practice problems, we start with a three function IFS with a totally disconnected attractor. For example, the bottom right image of Fig. 2.61, where TA includes rotation by π/2, TB reﬂection across the y -axis, and TC rotation by −π/2. To break apart TC (S ) and TD (S ), include a reﬂection across the y -axis in TD . The attractor of the four function IFS, the top right image of Fig. 2.61, certainly is disconnected. But is it totally disconnected? No line segments are obvious, but perhaps some pieces are connected by curves. This is an interesting problem. 95 2.9. SOME TOPOLOGY OF IFS ATTRACTORS C D B A Figure 2.62: Left: the plac...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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