FractionalGeometry-Chap2

# R 12 12 12 e pi 12 2 2 1 2 2 0 ifs 1 for prxssol

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y -axis. For the corner in S3 , T3 has neither a reﬂection nor a rotation. Then we have the second candidate IFS 2. This gives the correct orientations and placements for all the second iteration squares. Figure 2.9: Initial image, ﬁrst and second iterates for Prxs 2.1.3. We need to ﬁnd the Ls in the ﬁrst iterate. r 1/2 1/2 1/2 θ ϕ e pi π 1/2 π/2 π/2 1 π/2 π/2 0 IFS 1 for PrxsSol 2.1.3 f 1/2 0 1/2 r -1/2 -1/2 1/2 Exercises s 1/2 1/2 -1/2 s 1/2 1/2 1/2 θ ϕ e pi/2 π/2 1/2 0 0 1 0 0 0 IFS 2 for PrxsSol 2.1.3 f 1/2 0 1/2 33 2.1. ITERATED FUNCTION SYSTEM FORMALISM Prob 2.1.1 Given any real numbers a, b, c, and d, show how to ﬁnd r, s, θ, and ϕ so that a c b r cos(θ) = d r sin(θ) −s sin(ϕ) s cos(ϕ) Prob 2.1.2 Prove T (x, y ) = (x/2, y/3) is a contraction and ﬁnd its contraction factor r. That is, show for all pairs of points (x1 , y1 ) and (x2 , y2 ), d(T (x1 , y1 ), T (x2 , y2 )) ≤ r · d((x1 , y1 ), (x2 , y2 )) and for any s &lt; r there are points (x1 , y1 ) a...
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