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Unformatted text preview: de Bruijn and Tanja van ArdenneEhrenfest. 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...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.
 Fall '14
 AmandaFolsom
 Geometry, Fractal Geometry, Limits, The Land

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