FractionalGeometry-Chap2

Figure 264 left an ifs tree with color assigned by

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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

Ask a homework question - tutors are online