Grünbaum, B., Shephard, G.C.: Tilings and Patterns. W.H. Freeman, New York (1987) 18. Harriss, E.O., Lamb, J.S.W.: Canonical substitution tilings of Ammann–Beenker type. Theoret. Com- put. Sci. 319(1–3), 241–279 (2004) 19. Kannan, S., Soroker, D.: Tiling polygon...
1. Introduction In Tilings and Patterns [GS2], Gru¨nbaum and Shephard present in detail the full range of problems and methods associated with (mainly two-dimensional) tilings and patterns and discuss in depth their relevance for art and science. They address the problem of tiling three-...
Dense square-symmetry tilings of the plane by equilateral triangles and squares are described. Repeated substitution of a vertex of a tiling by groups of vertices leads asymptotically to a limiting density that is independent of the starting pattern and to a family of quasicrystalline patterns with...
Grünbaum, B., Shephard, G.C.: Tilings and Patterns. W.H. Freeman and Company, New York (1987) 3. Laczkovich, M.: Tilings of polygons with similar triangles. Combinatorica 10(3), 281–306 (1990) 4. Laczkovich, M.: Tilings of polygons with similar triangles. II. Discrete Comput....
Bandt, Self-similar tilings and patterns described by mappings, in The Mathematics of Aperiodic Order--Proceedings of NATO-Advanced Studies Institute, Waterloo, ON, August 1995, to appear. [BG] C. Bandt and G. Getbrich, Classification of self-affine lattice titings, J. London Math. Sac. ...
1. Introduction The well-known Apollonian circle packing can be constructed from a set of four base circles, and four dual circles, as shown in Fig. 1. The orbit of the base circles under the group generated by reflections through the dual circles is the packing, an infinite fractal set ...
Tilings and Patterns; W.H. Freeman and Company: New York, NY, USA, 1987. 9. Penrose, R. Remarks on a tiling: Details of a (1 + + 2)-aperiodic set. In The Mathematics of Long-Range Aperiodic Order; Moody, R.V., Ed.; NATO ASI Series C: 489; Kluwer Academic Publishers: ...