Prxssol 293 from our experience in the rst two

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: four iterates of the right IFS of Fig. 2.57. This list of types is not such a surprise: within these categories only one more possibility remains: disconnected and containing non-contractible loops. There appear to be no attractors of this type, at least using three functions of the form (2.18). The hybrid type was not mentioned on pg 237 of [125]. The be sure we haven’t imagined a nonexistent type of shape, observe in this hybrid IFS that T1 (x, y ) = (x/2, −y/2) + (0, 1/2) T3 (x, y ) = (x/2, y/2) + (0, 1/2) Denoting by L the line segment between (0, 0) and (0, 1), we see L = T1 (L) ∪ T3 (L) Because it is invariant under T1 and T3 , L is contained in the attractor A of {T1 , T2 , T3 }, and so A is not totally disconnected. On the other hand, Fig. 2.58 shows the first four iterations of this IFS applied to the illed-in unit square. This shows A is not connected. Recalling (2.19), we can always take s = 1/2. Consequently, the orientation of the image of each of the three transformations is determin...
View Full Document

Ask a homework question - tutors are online