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Computer geometry: rep-tiles with a hole. (English) Zbl 1433.68480


MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
28A80 Fractals
52-04 Software, source code, etc. for problems pertaining to convex and discrete geometry
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
52C23 Quasicrystals and aperiodic tilings in discrete geometry

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References:

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[2] Bandt, Christoph; Mekhontsev, Dmitry, Elementary fractal geometry. New relatives of the Sierpiński gasket, Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 6, 063104 (2018) · Zbl 1394.28002
[3] Christoph Bandt, Dmitry Mekhontsev, and Andrei Tetenov. A single fractal pinwheel tile. Proc. Amer. Math. Soc. 146 (2018), 1271-1285. · Zbl 1382.52018
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[8] S. W. Golomb. Replicating figures in the plane. Math. Gaz. 48 (1964), 403-412. · Zbl 0125.38504
[9] Karl-Heinz Gröchenig and W. Madych. Multiresolution analysis, Haar bases, and self-similar tilings. IEEE Trans. Inform. Theory 38:2, Part 2 (1992), 558-568. · Zbl 0742.42012
[10] Branko Grünbaum and G. C. Shephard. Patterns and Tilings. Freeman, 1987. · Zbl 0601.05001
[11] Herman Haverkort. No acute tetrahedron is an 8-reptile. arXiv:1508.03773v2, 2018. · Zbl 1385.52008
[12] John E. Hutchinson. Fractals and self-similarity. Indiana University Mathematics Journal 30 (1981), 713-747. · Zbl 0598.28011
[13] Anwei Liu and Barry Joe. On the shape of tetrahedra from bisection. Mathematics of Computation 63:207 (2013), 141-154. · Zbl 0815.51016
[14] Jiři Matoušek and Zuzana Safernová. On the nonexistence of \(k\)-reptile tetrahedra. Discrete Comput. Geom. 46 (2011), 599-609. · Zbl 1270.52014
[15] Dmitry Mekhontsev. IFStile, version 1.8.1.4 (Jan. 2019). Available at www.ifstile.com.
[16] Marjorie Senechal. Quasicrystals and Geometry. Cambridge University Press, 1995. · Zbl 0828.52007
[17] Andrew Vince. Rep-tiling Euclidean space. Aequationes Math. 50 (1995), 191-213. · Zbl 0832.52005
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