Reptiles with holes

Francis Jordan; Sze Man Ngai

doi:10.1017/S001309150400001X

Reptiles with holes

Francis Jordan
, Sze Man Ngai

Mathematical Sciences

Georgia Southern University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in ℝ^d, especially reptiles with holes. In particular, we construct, for each even integer n≥4, an n-reptile in ℝ² with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.

Original language	English
Pages (from-to)	651-671
Number of pages	21
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	48
Issue number	3
DOIs	https://doi.org/10.1017/S001309150400001X
State	Published - Oct 2005

Scopus Subject Areas

General Mathematics

Keywords

Iterated function system
Reptile
Self-similar set

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10.1017/S001309150400001X

Cite this

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title = "Reptiles with holes",

abstract = "Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in ℝd, especially reptiles with holes. In particular, we construct, for each even integer n≥4, an n-reptile in ℝ2 with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.",

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AB - Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in ℝd, especially reptiles with holes. In particular, we construct, for each even integer n≥4, an n-reptile in ℝ2 with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.

KW - Iterated function system

KW - Reptile

KW - Self-similar set

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DO - 10.1017/S001309150400001X

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JF - Proceedings of the Edinburgh Mathematical Society

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Reptiles with holes

Abstract

Scopus Subject Areas

Keywords

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