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A self-similar tiling generated by the minimal Pisot number
| Content Provider | Semantic Scholar |
|---|---|
| Author | Akiyama, Shigeki |
| Copyright Year | 1998 |
| Abstract | Let β be a Pisot unit of degree 3 with a certain finiteness condition. A large family of self similar plane tilings can be constructed, by the digit expansion in base β. (cf. [7], [5], [8]) In this paper, we prove that the origin is an inner point of the central tile K. Further, in the case corresponds to the minimal Pisot number, we shall give a detailed study on the fractal boundary of each tile. Namely, a sufficient condition of ”adjacency” of tiles is given and the ”vertex” of a tile is determined. Finally, we prove that the boundary of each tile is a union of 5 self similar sets of Hausdorff dimension 1.10026 . . .. 1991 Mathematics Classification. Primary 11A68, 11R06 |
| Starting Page | 9 |
| Ending Page | 26 |
| Page Count | 18 |
| File Format | PDF HTM / HTML |
| Volume Number | 6 |
| Alternate Webpage(s) | http://math.tsukuba.ac.jp/~akiyama/papers/Min_pisot.pdf |
| Alternate Webpage(s) | https://dml.cz/bitstream/handle/10338.dmlcz/120535/ActaOstrav_06-1998-1_3.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
