The boundaries of self-similar tiles in ℝn

Topology and its Applications

Volumn 94, Issue 1-3, 1999, Pages 195-205

  Keesling, James ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

Attractors; Fractal geometry; Hausdorff dimension; Iterated function systems; Tilings

Indexed keywords

EID: 0002096231     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-8641(98)00031-5     Document Type: Article

References (15)

1. n, Proc. Amer. Math. Soc. 112 (1991) 549-562.
2. P. Duvall and J. Keesling, Computing the dimension of the boundary of the Levy Dragon, preprint.
3. P. Duvall, J. Keesling and A. Vince, The Hausdorff dimension of the boundary of a self-similar tile, submitted.
4. G.A. Edgar, Measure, Topology, and Fractal Geometry (Springer, New York, 1990).
5. G.A. Edgar, Classics on Fractals (Addison-Wesley, New York, 1993).
6. K.J. Falconer, The Geometry of Fractal Sets (Cambridge Univ. Press, 1985).
7. K.J. Falconer, Fractal Geometry (Wiley, New York, 1990).
8. K.J. Falconer, Sub-self-similar sets, Trans. Amer. Math. Soc. 347 (1995) 3121-3129.
9. P. Gummelt, Self-similar sets and tilings, in: C. Bandt, ed., Topology, Measures, and Fractals (Akademie-Verlag, 1992) 58-65.
10. J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981) 713-747.
11. C. Krishnamurthi, A natural boundary for a self-similar set, Ph.D. dissertation, University of Florida, 1998.
12. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces (Cambridge Univ. Press, 1995).
13. A. Schief, Separation properties for self-similar sets, Proc. Amer. Math. Soc. 122 (1994) 111-115.
14. A. Schief, Self-similar sets in complete metric spaces, Proc. Amer. Math. Soc. 124 (1996) 481-490.
15. A. Vince, Reptiling Euclidean space, Aequationes Math. 50 (1995) 191-213.