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- Aperiodic_set_of_prototiles abstract "A set of prototiles is aperiodic if copies of them can be assembled to create tilings, and all such tilings are non-periodic. Consequently, aperiodicity is a property of the set of prototiles; the tilings themselves are just non-periodic. Typically, distinct tilings may be obtained from a single aperiodic set of tiles.The various Penrose tiles are the best-known examples of an aperiodic set of tiles. Today not many aperiodic sets of prototiles are known (here is a List of aperiodic sets of tiles). This is perhaps natural: the underlying undecidability of the Domino problem implies that there exists no systematic procedure for deciding whether a given set of tiles can tile the plane.A given set of tiles, in the Euclidean plane or some other geometric setting, admits a tiling if non-overlapping copies of the tiles in the set can be fitted together to cover the entire space. A given set of tiles might admit periodic tilings — that is, tilings which remain invariant after being shifted by a translation (for example, a lattice of square tiles is periodic). It is not difficult to design a set of tiles that admits non-periodic tilings as well (for example, randomly arranged tilings using a 2×2 square and 2×1 rectangle will typically be non-periodic). An aperiodic set of tiles, however, admits only non-periodic tilings.".
- Aperiodic_set_of_prototiles thumbnail Penrose_Rhombi_BR.svg?width=300.
- Aperiodic_set_of_prototiles wikiPageID "41287104".
- Aperiodic_set_of_prototiles wikiPageLength "7507".
- Aperiodic_set_of_prototiles wikiPageOutDegree "30".
- Aperiodic_set_of_prototiles wikiPageRevisionID "632182502".
- Aperiodic_set_of_prototiles wikiPageWikiLink Anisohedral_tiling.
- Aperiodic_set_of_prototiles wikiPageWikiLink Aperiodic_tiling.
- Aperiodic_set_of_prototiles wikiPageWikiLink Category:Aperiodic_tilings.
- Aperiodic_set_of_prototiles wikiPageWikiLink Effective_method.
- Aperiodic_set_of_prototiles wikiPageWikiLink Einstein_problem.
- Aperiodic_set_of_prototiles wikiPageWikiLink Euclidean_tilings_by_convex_regular_polygons.
- Aperiodic_set_of_prototiles wikiPageWikiLink Hans_Läuchli.
- Aperiodic_set_of_prototiles wikiPageWikiLink Hao_Wang_(academic).
- Aperiodic_set_of_prototiles wikiPageWikiLink Hilberts_eighteenth_problem.
- Aperiodic_set_of_prototiles wikiPageWikiLink Isohedral_figure.
- Aperiodic_set_of_prototiles wikiPageWikiLink Karel_Culik.
- Aperiodic_set_of_prototiles wikiPageWikiLink Karl_Reinhardt_(mathematician).
- Aperiodic_set_of_prototiles wikiPageWikiLink List_of_aperiodic_sets_of_tiles.
- Aperiodic_set_of_prototiles wikiPageWikiLink Penrose_tiling.
- Aperiodic_set_of_prototiles wikiPageWikiLink Prototile.
- Aperiodic_set_of_prototiles wikiPageWikiLink Raphael_M._Robinson.
- Aperiodic_set_of_prototiles wikiPageWikiLink Robert_Ammann.
- Aperiodic_set_of_prototiles wikiPageWikiLink Robert_Berger_(mathematician).
- Aperiodic_set_of_prototiles wikiPageWikiLink Roger_Penrose.
- Aperiodic_set_of_prototiles wikiPageWikiLink Tessellation.
- Aperiodic_set_of_prototiles wikiPageWikiLink Translation_(geometry).
- Aperiodic_set_of_prototiles wikiPageWikiLink Two-dimensional_space.
- Aperiodic_set_of_prototiles wikiPageWikiLink Undecidable_problem.
- Aperiodic_set_of_prototiles wikiPageWikiLink Wang_tile.
- Aperiodic_set_of_prototiles wikiPageWikiLink File:Penrose_Rhombi_BR.svg.
- Aperiodic_set_of_prototiles wikiPageWikiLink File:Penrose_tiling.svg.
- Aperiodic_set_of_prototiles wikiPageWikiLink File:Wang_tiles.svg.
- Aperiodic_set_of_prototiles wikiPageWikiLinkText "Aperiodic set of prototiles".
- Aperiodic_set_of_prototiles wikiPageWikiLinkText "aperiodic set of prototiles".
- Aperiodic_set_of_prototiles wikiPageWikiLinkText "aperiodic set".
- Aperiodic_set_of_prototiles wikiPageWikiLinkText "aperiodic".
- Aperiodic_set_of_prototiles wikiPageUsesTemplate Template:Reflist.
- Aperiodic_set_of_prototiles wikiPageUsesTemplate Template:Technical.
- Aperiodic_set_of_prototiles wikiPageUsesTemplate Template:Tessellation.
- Aperiodic_set_of_prototiles subject Category:Aperiodic_tilings.
- Aperiodic_set_of_prototiles comment "A set of prototiles is aperiodic if copies of them can be assembled to create tilings, and all such tilings are non-periodic. Consequently, aperiodicity is a property of the set of prototiles; the tilings themselves are just non-periodic. Typically, distinct tilings may be obtained from a single aperiodic set of tiles.The various Penrose tiles are the best-known examples of an aperiodic set of tiles.".
- Aperiodic_set_of_prototiles label "Aperiodic set of prototiles".
- Aperiodic_set_of_prototiles sameAs Q17002261.
- Aperiodic_set_of_prototiles sameAs m.0zgcbx0.
- Aperiodic_set_of_prototiles sameAs Q17002261.
- Aperiodic_set_of_prototiles wasDerivedFrom Aperiodic_set_of_prototiles?oldid=632182502.
- Aperiodic_set_of_prototiles depiction Penrose_Rhombi_BR.svg.
- Aperiodic_set_of_prototiles isPrimaryTopicOf Aperiodic_set_of_prototiles.