FractionalGeometry-Chap2

68 chapter 2 iterated function systems r 060 050 050

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Unformatted text preview: l an Eulerian cycle in a graph is a path that traverses each edge of the graph exactly once, and begins and ends at the same vertex. Then an Eulerian cycle in an order N − 1 de Bruijn graph is an order N de Bruijn sequence. An example illustrates this correspondence. To build this example, we describe the prefer 1 algorithm for generating binary order N de Bruijn sequences. By an N -string we mean a string of length N . 1. Begin with an empty list L of N -strings visited so far, and with the N string 00 . . . 0, called the current N -string. 2. Add the current N -string to L. 3. Append 1 to the left of, and remove the right-most entry of, the current string, if this gives a string not already in L, then loop to step 2. 4. If the operation of step 3 gives an N -string already in L, append 0 to the right of, and remove the right-most entry of, the current string. If this gives a string not already in L, then loop to step 2. 66 CHAPTER 2. ITERATED FUNCTION SYSTEMS 5. If neither steps 3 or 4 gives rise to...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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