
	Where results make sense

Topic: Hexagonal tiling

	Bingo-card Lattices, Equal-tempered Musical Scales
		The utility of the bingo-card lattices lies in their ability to show the "vanishing commas", i.e., the small intervals which are tempered out in a particular EDO.
		Below is a lattice using triangular geometry, resulting in a hexagonal cell representing each lattice-point, showing many of these intervals, with most of the more important ones labeled with the names in common use among tuning theorists c.
		In this and all of the "tiling" lattices below, the objective was to outline the periodicity-blocks which forms the source-cell at the center of the lattice -- i.e., all ratios as close as possible, by the taxicab metric, to the 1/1 at the origin point.
	tonalsoft.com /enc/b/bingo.aspx (2244 words)

	The Geometry Junkyard: Fractal Tilings (Site not responding. Last check: 2007-10-10)
		Oded Schramm's mathematical picture gallery primarily concentrating in square tilings and circle packings, many forming fractal patterns.
		Marina Khibnik computes the convex hulls and boundary dimensions of fractal tiles such as the twin dragon and fractal red cross.
		Snowflake reptile hexagonal substitution tiling (sometimes known as the Gosper Island) rediscovered by NASA and conjectured to perform visual processing in the human brain.
	www.ics.uci.edu /~eppstein/junkyard/fractile.html (83 words)

	Cellular automaton: Just the facts... (Site not responding. Last check: 2007-10-10)
		The edges are usually handled with a toroidal arrangement: when you go off the top, you come in at the corresponding position on the bottom, and when you go off the left you come in on the right (This essentially simulates an infinite periodic tiling).
		This can be visualized as taping the left and right edges together to form a tube, then taping the top and bottom edges of the tube together to form a torus (Commonly the lowest molding at the base of a column) (doughnut shape).
		For example, if a plane is tiled (additional info and facts about tiled) with equilateral triangles, those triangles could be used as the cells.
	www.absoluteastronomy.com /encyclopedia/c/ce/cellular_automaton.htm (2940 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		A 44, 678-688 (01SEP1988) Shows an explicit method for constructing tilings having the trivial space group p2^jmm as well as the not-at-all trivial space group p2^jgm.
		Although this paper's domain is a 2-dimensional grid space (and associated 2- dimensional tiling space), the generalization to 3-dimensional grids and tilings should not prove exceedingly difficult.
		This paper focuses on (3+1) modulated crystals where the modulation can be either commensurate (a rational ratio between the set of generating vectors) or incommensurate (an irrational ratio between the set of generating vectors).
	ewald.cas.usf.edu /quasibiblio.txt (4282 words)

	Untitled Document
		You can get my Chaos Tiles game from Cleverwood.com (makes a great gift, but I might be biased).
		At the official Mitre Tile site, you can see some of the marvelous things Adrian has been building with it.
		Approached up the only road with a hairpin bend in the Netherlands (everywhere else is too flat!), Three Lands Point is the highest point in the country, and the place where the borders of Germany, Belgium and the Netherlands meet.
	www.mathpuzzle.com /4Dec2001.htm (6140 words)

	Works Citing the On-Line Encyclopedia of Integer Sequences
		Bernstein, N. Sloane and P. Wright, On Sublattices of the Hexagonal Lattice, Discrete Math., 170 (1997) 29-39.
		Broughton, D. Haney, L. McKeough and B. Mayfield, Divisible Tilings in the Hyperbolic Plane, New York J. Math.
		Chyzak, I. Gutman and P. Paule, Predicting the number of hexagonal systems with 24 and 25 hexagons, Communications in Mathematical and Computer Chemistry, no. 40, p.
	www.research.att.com /~njas/sequences/cite.html (8835 words)

	Toolglass and Magic Lenses: The See-Through Interface
		Our sheets and lenses are already fast enough to be useful on current hardware, but need to be faster for smooth motion.
		For example, using our prototype on a SPARCstation 10, we measured the time it takes to redraw the screen after moving a wireframe lens of size 70 by 70 pixels over the Penrose tiling of figure 10, containing 117 filled and outlined shapes.
		For the MIMO implementation of the lens, once it has cached its output scene, it takes an average of 300 milliseconds to repaint the scene, of which 120 milliseconds are spent drawing the lens interior.
	www2.parc.com /istl/projects/MagicLenses/93Siggraph.html (7049 words)

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