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Article: Geometry of Self-Affine Tiles II
| Title | Geometry of Self-Affine Tiles II |
|---|---|
| Authors | |
| Issue Date | 1999 |
| Citation | Indiana University Mathematics Journal, 1999, v. 48, n. 1, p. 25-42 How to Cite? |
| Abstract | We continue the study in part I of geometric properties of self-similar and self-affine tiles. We give some experimental results from implementing the algorithm in part I for computing the dimension of the boundary of a self-similar tile, and we describe some conjectures that result. We prove that the dimension of the boundary may assume values arbitrarily close to the dimension of the tile. We give a formula for the area of the convex hull of a planar self-affine tile. We prove that the extreme points of the convex hull form a set of dimension zero, and we describe a natural gauge function for this set. |
| Persistent Identifier | http://hdl.handle.net/10722/362994 |
| ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 1.272 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Kenyon, Richard | - |
| dc.contributor.author | Li, Jie | - |
| dc.contributor.author | Strichartz, Robert S. | - |
| dc.contributor.author | Wang, Yang | - |
| dc.date.accessioned | 2025-10-10T07:43:56Z | - |
| dc.date.available | 2025-10-10T07:43:56Z | - |
| dc.date.issued | 1999 | - |
| dc.identifier.citation | Indiana University Mathematics Journal, 1999, v. 48, n. 1, p. 25-42 | - |
| dc.identifier.issn | 0022-2518 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/362994 | - |
| dc.description.abstract | We continue the study in part I of geometric properties of self-similar and self-affine tiles. We give some experimental results from implementing the algorithm in part I for computing the dimension of the boundary of a self-similar tile, and we describe some conjectures that result. We prove that the dimension of the boundary may assume values arbitrarily close to the dimension of the tile. We give a formula for the area of the convex hull of a planar self-affine tile. We prove that the extreme points of the convex hull form a set of dimension zero, and we describe a natural gauge function for this set. | - |
| dc.language | eng | - |
| dc.relation.ispartof | Indiana University Mathematics Journal | - |
| dc.title | Geometry of Self-Affine Tiles II | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.scopus | eid_2-s2.0-0347243310 | - |
| dc.identifier.volume | 48 | - |
| dc.identifier.issue | 1 | - |
| dc.identifier.spage | 25 | - |
| dc.identifier.epage | 42 | - |