- Ancient
Islamic Penrose Tiles. Peter Lu uncovers evidence that the
architects of a 500-year-old Iranian shrine used Penrose tiling to lay
out the decorative patterns on its archways. From Ivars Peterson's
MathTrek.
- Aperiodic
tiling and Penrose tiles, Steve Edwards.
- The
Art and Science of Tiling.
Penrose tiles at Carleton College.
- Cellular
automaton run on Penrose tiles, D. Griffeath.
See also Eric
Weeks' page on cellular automata over quasicrystals.
- Clusters and
decagons, new rules for using overlapping shapes to construct
Penrose tilings. Ivars Peterson, Science News, Oct. 1996.
- Five-fold symmetry in crystalline quasicrystal lattices, Donald L. D. Caspar and Eric Fontano.
- Gallery of interactive on-line geometry.
The Geometry Center's collection includes programs for generating
Penrose tilings, making periodic drawings a la Escher in the Euclidean
and hyperbolic planes, playing pinball in negatively curved spaces,
viewing 3d objects, exploring the space of angle geometries, and
visualizing Riemann surfaces.
- Goldene
Schnittmuster. Article in German on Penrose tiling and related topics.
- Irrational
tiling by logical quantifiers. LICS proceedings cover art by Alvy Ray Smith, based on the Penrose tiling.
- Kadon Enterprises,
makers of games and puzzles including polyominoes and Penrose tiles.
- Mathematical imagery by Jos Leys.
Knots, Escher tilings, spirals, fractals, circle inversions, hyperbolic
tilings, Penrose tilings, and more.
- Non
periodic tiling of the plane.
Including Penrose tiles, Pinhweel tiling, and more. Paul Bourke.
- Ozbird Escher-like tessellations
by John Osborn, including several based on Penrose tilings.
- Patterns within
rhombic Penrose tilings. Stephen Collins' program "Bob" generates
these tilings and explores the patterns formed by geodesic walks in them.
- Penrose
mandala and five-way Borromean rings.
- Penrose quilt on a
snow bank, M.&S. Newbold. See also
Lisbeth
Clemens' Penrose quilt.
- The penrose
tile and the golden mean: towards hyperdimensional intergeometry.
- Penrose-tiled
lace doily.
- Penrose-tiled swallow
- Penrose tiles
and how their visualization leads to strange looks from priests and
small children. Drew Olbrich.
- Penrose tiles and worse. This article from Dave Rusin's known math pages discusses the difficulty of correctly placing tiles in a Penrose tiling, as well as describing other tilings such as the pinwheel.
- Penrose
Tiles entry from E. Weisstein's treasure trove.
- Pentagonal coffee table with rhombic bronze casting related to the Penrose tiling, by Greg Frederickson.
- Quasitiler image, E. Durand.
- Santa Fe Ribbon,
painting by Connie Simon featuring a rhombic Penrose tiling.
- Tessellations,
a company which makes Puzzellations puzzles, posters, prints, and
kaleidoscopes inspired in part by Escher, Penrose, and Mendelbrot.
- Three-color the Penrose tiling?
Mark Bickford asks if this tiling is always three-colorable.
Ivars
Peterson reports on a new proof by Tom Sibley and Stan Wagon
that the rhomb version of the tiling is 3-colorable;
A proof of 3-colorability for kites and darts
was recently published by Robert Babilon
[Discrete Mathematics 235(1-3):137-143, May 2001].
This is closely related to my page on line
arrangement coloring, since every Penrose tiling is dual to
a "multigrid", which is just an arrangement of lines in parallel families.
But my page only deals with finite arrangements, while Penrose tilings are
infinite.
- Tilings.
Lecture notes from the Clay Math Institute, by Richard Stanley and
Federico Ardila, discussing polyomino tilings, coloring arguments for
proving the nonexistence of tilings, counting how many tilings a region
has, the arctic circle theorem for domino tilings of diamonds,
tiling the unit square with unit-fraction rectangles, symmetry groups,
penrose tilings, and more. In only 21 pages, including the annotated
bibliography. A nice but necessarily concise introduction to the subject.
(Via Andrei Lopatenko.)
- Toilet
paper plagiarism. A big tissue company tries to rip off Sir Roger P.
- The
trouble with five. Craig Kaplan explains why five-fold symmetry
doesn't work in regular plane tilings, but does work for the Penrose tiling.
- Voronoi
diagram of a Penrose tiling (rhomb version), Cliff Reiter.

From the Geometry Junkyard,
computational
and recreational geometry pointers.

Send email if you
know of an appropriate page not listed here.

David Eppstein,
Theory Group,
ICS,
UC Irvine.

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