A Survey on Topological Properties of Tiles Related to Number Systems
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[1] G. C. Shephard,et al. Tilings and Patterns , 1990 .
[2] Shigeki Akiyama,et al. On the boundary of self affine tilings generated by Pisot numbers , 2002 .
[3] W. Gilbert. Complex Numbers with Three Radix Expansions , 1982, Canadian Journal of Mathematics.
[4] Michael Baake,et al. Digit tiling of euclidean space , 2000 .
[5] THE BOUNDARY OF THE ATTRACTOR OF A RECURRENT ITERATED FUNCTION SYSTEM , 2002 .
[6] Arcwise connectedness of the boundaries of connected self-similar sets , 2003, math/0302279.
[7] J. J. P. Veerman,et al. Hausdorff Dimension of Boundaries of Self-Affine Tiles In R N , 1997, math/9701215.
[8] P. Arnoux,et al. Pisot substitutions and Rauzy fractals , 2001 .
[9] J. Thuswaldner,et al. On the characterization of canonical number systems , 2004 .
[10] J. Lagarias,et al. Integral self-affine tiles in ℝn part II: Lattice tilings , 1997 .
[11] Shigeki Akiyama,et al. Generalized radix representations and dynamical systems. I , 2005 .
[12] William J. Gilbert. Radix representations of quadratic fields , 1981 .
[13] Christoph Bandt,et al. Classification of Self-Affine Lattice Tilings , 1994 .
[14] Sze-Man Ngai,et al. A TECHNIQUE IN THE TOPOLOGY OF CONNECTED SELF-SIMILAR TILES , 2004 .
[15] Jörg M. Thuswaldner,et al. Neighbours of Self-affine Tiles in Lattice Tilings , 2003 .
[16] I. Kátai,et al. Canonical number systems in imaginary quadratic fields , 1981 .
[17] Masayoshi Hata,et al. On the structure of self-similar sets , 1985 .
[18] Nhu Nguyen,et al. The Heighway Dragon Revisited , 2003, Discret. Comput. Geom..
[19] Yang Wang,et al. Disk-Like Self-Affine Tiles in R2 , 2001, Discrete & Computational Geometry.
[20] Randolph B. Tarrier,et al. Groups , 1973, Algebra.
[21] Jörg M. Thuswaldner,et al. Canonical number systems, counting automata and fractals , 2002, Mathematical Proceedings of the Cambridge Philosophical Society.
[22] Andrew Vince,et al. Self-Replicating Tiles and Their Boundary , 1999, Discret. Comput. Geom..
[23] R. Ho. Algebraic Topology , 2022 .
[24] Jun Luo,et al. On the boundary connectedness of connected tiles , 2004, Mathematical Proceedings of the Cambridge Philosophical Society.
[25] Karlheinz Gröchenig,et al. Multiresolution analysis, Haar bases, and self-similar tilings of Rn , 1992, IEEE Trans. Inf. Theory.
[26] K. Falconer. Techniques in fractal geometry , 1997 .
[27] K. Lau,et al. On the Connectedness of Self‐Affine Tiles , 2000 .
[28] David Thomas,et al. The Art in Computer Programming , 2001 .
[29] Yang WANGAbstract,et al. GEOMETRY OF SELF � AFFINE TILES , 1998 .
[30] Hui Rao,et al. TOPOLOGICAL STRUCTURE OF SELF-SIMILAR SETS , 2002 .
[31] Yang Wang,et al. GEOMETRY OF SELF-AFFINE TILES II , 1999 .
[32] Shigeki Akiyama,et al. The topological structure of fractal tilings generated by quadratic number systems , 2005 .
[33] Shigeki Akiyama,et al. Connectedness of number theoretic tilings , 2004 .
[34] Jun Luo. A NOTE ON A SELF-SIMILAR TILING GENERATED BY THE MINIMAL PISOT NUMBER , 2002 .
[35] I. Kátai,et al. Number Systems and Fractal Geometry , 1992 .
[36] Yang Wang,et al. Wavelets, tiling, and spectral sets , 2002 .
[37] Christoph Bandt,et al. Self-similar sets. V. Integer matrices and fractal tilings of ⁿ , 1991 .
[38] J. Lagarias,et al. Integral self-affine tiles in ℝn I. Standard and nonstandard digit sets , 1996 .
[39] Sze-Man Ngai,et al. Topology of connected self-similar tiles in the plane with disconnected interiors , 2005 .
[40] Brenda Praggastis,et al. Numeration systems and Markov partitions from self similar tilings , 1999 .
[41] Jeffrey C. Lagarias,et al. Self-affine tiles in ℝn , 1996 .
[42] Yang Wang. INTEGRAL SELF-AFFINE TILES IN Rn II. LATTICE TILINGS , 1998 .
[43] Andrew Haas,et al. Self-Similar Lattice Tilings , 1994 .
[44] Shigeki Akiyama,et al. On canonical number systems , 2002, Theor. Comput. Sci..
[45] Shigeki Akiyama,et al. Topological properties of two-dimensional number systems , 2000 .
[46] Hyun-Jong Song,et al. DISCLIKE LATTICE REPTILES INDUCED BY EXACT POLYOMINOES , 1999 .
[47] Shigeki Akiyama,et al. Connectedness of number theoretical tilings , 2005, Discret. Math. Theor. Comput. Sci..
[48] Palle E.T. Jorgensen,et al. Iterated Function Systems and Permutation Representations of the Cuntz Algebra , 1996 .
[49] J. Lagarias. Self-Affine Tiles in , 1994 .
[50] Boris Solomyak,et al. Dynamics of self-similar tilings , 1997, Ergodic Theory and Dynamical Systems.
[51] Attila Pethö. On a polynomial transformation and its application to the construction of a public key cryptosystem , 1991 .
[52] K. Kuratowski. Topology - Volume I , 1966 .
[53] Gregory R. Conner,et al. On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane , 2005 .
[54] G. Rauzy. Nombres algébriques et substitutions , 1982 .
[55] Götz Gelbrich. Crystallographic reptiles , 1994 .
[56] Martin Greiner,et al. Wavelets , 2018, Complex..
[57] Donald E. Knuth,et al. The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .
[58] Scott Bailey,et al. Inside the Lévy Dragon , 2002, Am. Math. Mon..
[59] Nicolau C. Saldanha,et al. Remarks on Self-Affine Tilings , 1994, Exp. Math..