FractionalGeometry-Chap2

The bottom left image of fig 261 is the attractor of

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: CTORS Inspection of the examples on pgs 232-7 of [125] suggest that these fractals fall into four topological types, illustrated in Fig. 2.57. • Cantor sets: totally disconnected, perfect sets • Dendrites: connected sets without loops • Multiply-connected: connected sets containing non-contractible loops • Hybrid: disconnected but not totally disconnected sets, each component without loops. By loop we mean a closed curve, a path that ends where it starts. Figure 2.57: Cantor set, dendrite, multiply-connected, and hybrid IFS attractors. The IFS tables for the attractors of Fig. 2.57 are r −1/2 1/2 1/2 s 1/2 −1/2 1/2 θ ϕ 0 0 0 0 π/2 π/2 Cantor set e 1/2 1/2 1/2 f 0 1/2 1/2 r 1/2 1/2 1/2 s 1/2 1/2 1/2 θ ϕ π π π/2 π/2 0 0 dendrite e 1/2 1 0 f 1/2 0 1/2 r 1/2 −1/2 −1/2 s 1/2 1/2 1/2 θ ϕ e π/2 π/2 1/2 π/2 π/2 1 −π/2 −π/2 0 multiply-connected f 0 1/2 1/2 r 1/2 1/2 1/2 s −1/2 1/2 1/2 θ ϕ 0 0 −π/2 −π/2 0 0 hybrid e 0 1/2 0 f 1/2 1/2 1/2 92 CHAPTER 2. ITERATED FUNCTION SYSTEMS Figure 2.58: The first...
View Full Document

Ask a homework question - tutors are online