FractionalGeometry-Chap2

K kn for example for binary sequences n 1 2 3 4 5 6 7

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: de Bruijn and Tanja van Ardenne-Ehrenfest. Perhaps the most elegant way of generating de Bruijn sequences used finite fields. See [114], for example. We take a simpler approach, first showing a de Bruijn sequence B (k, N ) is an Eulerian cycle in an order N − 1 de Bruijn graph, both defined in a moment. This is a preview of the edge transition graphs central to the IFS with memory constructions of Ch 4. Next, we present the prefer 1 algorithm for constructing de Bruijn squences. For simplicity, we consider only binary sequences. For example, to construct an order N = 3 de Bruijn sequence, we begin with the order N = 2 de Bruijn graph. The vertices are the length 2 binary sequences; an edge goes from vertex ab to vertex cd if and only if a = d; the edge is labeled c. We interpret this graph as showing the effect of applying transformations on length 2 addresses. For example, applying T1 to a point in the region with address 00 gives a point in the region with address 10. This graph is shown on the left side of Fig. 2.32. Thin...
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