Optional Quiz 4 - S , the Serpenski sponge. Iterates 0 , 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Name: Optional Quiz 4 Due Wednesday April 20, 2011 Staple your work 1. Consider the Serpenski sponge, constructed as follows. The zeroth iterate S 0 is a 1 × 1 square. The first iterate S 1 is a 1 × 1 square with the middle 1 3 × 1 3 square removed, leaving eight 1 3 × 1 3 squares. The second iterate S 2 is S 1 with the middle 1 9 × 1 9 of each of the eight 1 3 × 1 3 squares removed. Continuing this process an infinite number of times gives
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: S , the Serpenski sponge. Iterates 0 , 1 and 2 are shown below. S S 1 S 2 (a) Find the fractal dimension of S . fractal dimension 2 (b) Find the area of S n , the n th iterate in the construction of the Serpenski sponge. area of S n...
View Full Document

This note was uploaded on 01/08/2012 for the course MGF 1107 taught by Professor Staff during the Spring '08 term at University of Florida.

Page1 / 2

Optional Quiz 4 - S , the Serpenski sponge. Iterates 0 , 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online