"... any finite patch that we choose in a tiling will lie inside a single inflated tile if we continue moving far enough up in the inflation hierarchy. This means that anywhere that tile occurs at that level in the hierarchy, our original patch must also occur in the original tiling. Therefore, the patch will occur infinitely often in the original tiling and, in fact, in every other tiling as well." Austin 2005a Austin, David (2005a). "Penrose Tiles Talk Across Miles". Providence: American Mathematical Society..
In Grünbaum & Shephard 1987, the term "inflation" is used where other authors would use "deflation" (followed by rescaling). The terms "composition" and "decomposition", which many authors also use, are less ambiguous. Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN978-0-7167-1193-3..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Luck 2000 Luck, R. (2000). "Dürer-Kepler-Penrose: the development of pentagonal tilings". Materials Science and Engineering. 294 (6): 263–267. doi:10.1016/S0921-5093(00)01302-2..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Baake, M.; Kramer, P.; Schlottmann, M.; Zeidler, D. (December 1990). "PLANAR PATTERNS WITH FIVEFOLD SYMMETRY AS SECTIONS OF PERIODIC STRUCTURES IN 4-SPACE". International Journal of Modern Physics B. 04 (15n16): 2217–2268. doi:10.1142/S0217979290001054.
"The rhombus of course tiles periodically, but we are not allowed to join the pieces in this manner." Gardner 1997, pp. 6–7 Gardner, Martin (1997). Penrose Tiles to Trapdoor Ciphers. Cambridge University Press. ISBN978-0-88385-521-8.. (First published by W. H. Freeman, New York (1989), ISBN978-0-7167-1986-1.)
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
"The rhombus of course tiles periodically, but we are not allowed to join the pieces in this manner." Gardner 1997, pp. 6–7 Gardner, Martin (1997). Penrose Tiles to Trapdoor Ciphers. Cambridge University Press. ISBN978-0-88385-521-8.. (First published by W. H. Freeman, New York (1989), ISBN978-0-7167-1986-1.)
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Chapter 1 (pp. 1–18) is a reprint of Gardner, Martin (January 1977). "Extraordinary non-periodic tiling that enriches the theory of tiles". Scientific American. Vol. 236, no. 1. pp. 110–121. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110..
Prange, Sebastian R.; Peter J. Lu (1 September 2009). "The Tiles of Infinity". Saudi Aramco World. Aramco Services Company. pp. 24–31. Retrieved 22 February 2010.