FractionalGeometry-Chap2

For every positive integer n de bruijn sequences give

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Unformatted text preview: the pair 41, otherwise paint the square grey. Addresses through length 7 are shown. Figure 2.63: Coloring squares by addresses This example demonstrates the method of coloring, but the images of Fig. 2.63 are not particularly interesting, nor do they fill us with joy at having learned this method. Perhaps another IFS will at least give us some satisfaction, if no real joy. Example 2.10.2 Coloring a tree 97 2.10. COLORING IFS BY ADDRESSES Consider the first IFS of Sect. 2.6, the IFS generating the tree image on the left side of Fig. 2.33. The trunk of the tree is generated by T5 and T6 ; T1 (T5 ) and T1 (T6 ) give the image of the trunk in the lower left branch; T1 (T1 (T5 )) and T1 (T1 (T6 )) give the image of the trunk in the lower subbranch of the lower left branch; and so on. So to color the trunk and branches of the tree brown, and the rest of the tree (the leaves) green, simply keep track of the address of each region, down to some specified level. If the address contains a 5 or a...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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