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Tiling of the hyperbolic plane
In geometry, a binary tiling (sometimes called a Böröczky tiling) is a tiling of the hyperbolic plane, resembling a quadtree over the Poincaré half-plane
Binary_tiling
Non-periodic tiling of the plane
Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is
Penrose_tiling
Tiling of the plane by pentagons
geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. A regular pentagonal tiling on the Euclidean
Pentagonal_tiling
Question about single-shape aperiodic tiling
ratio. Binary tiling, a weakly aperiodic tiling of the hyperbolic plane with a single tile Schmitt–Conway–Danzer tile, in three dimensions Two tiles have
Einstein_problem
Window manager with non-overlapping frames
1985) also used tiling (see sections below). In 1986 came Digital Research's GEM 2.0, a windowing system for the CP/M which used tiling by default. One
Tiling_window_manager
Uniform tiling of the hyperbolic plane
related to Uniform tiling 4-5-4-5. Binary tiling, an aperiodic tiling of the hyperbolic plane by pentagons Uniform tilings in hyperbolic plane List of regular
Tetrapentagonal_tiling
the tiles). A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself. Such a tiling is
List of aperiodic sets of tiles
List_of_aperiodic_sets_of_tiles
Independent video game
truncated order-7 triangular tiling by default (with a few exceptions). The player can also choose to play on some other tilings and honeycombs in two and
HyperRogue
Tree data structure that partitions a 2D area
return pointsInRange; } } Adaptive mesh refinement Binary space partitioning Binary tiling k-d tree Octree R-tree UB-tree Spatial database Subpaving
Quadtree
Term in group theory mathematics
campaign against referring to BS(1, 2) as a Baumslag–Solitar group." Binary tiling Solv geometry See Nonresidually Finite One-Relator Groups by Stephen
Baumslag–Solitar_group
Non-periodic tiling of the plane
In geometry, an Ammann A1 tiling is a tiling from the 6-piece prototile set shown on the right. They were found in 1977 by Robert Ammann. Ammann was inspired
Ammann_A1_tilings
Graphical calculator used in electrical engineering
3D Riemann sphere. The resulting sphere has the following features: Binary tiling Bode plot cis (mathematics) Circle diagram Nyquist plot Transversal
Smith_chart
Mathematical tree in the hyperbolic plane
Xerox in 1996, but the patent has since expired. Hyperbolic geometry Binary tiling Information visualization Radial tree – is also circular, but uses linear
Hyperbolic_tree
Tiling by squares of two sizes
A Pythagorean tiling or two squares tessellation is a tiling of the Euclidean plane by squares of two different sizes, in which each square touches four
Pythagorean_tiling
Geometric shape formed from squares
of Wang tiles to sets of polyominoes. Because the general problem of tiling regions of the plane with sets of polyominoes is NP-complete, tiling with more
Polyomino
Way to divide polygon into smaller parts
Substitution tilings are a well-studied type of subdivision rule. A subdivision rule takes a tiling of the plane by polygons and turns it into a new tiling by subdividing
Finite_subdivision_rule
Sub-field of pathology
Attribution-No Derivative 4.0 license. Key features include: Memory-mapped binary tile offset tables enabling direct random access without additional indexing
Digital_pathology
Digital circuit that produces sums from inputs
many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement
Adder_(electronics)
3D scene and model file format
file extensions: .gltf (JSON/ASCII) or .glb (binary). Both .gltf and .glb files may reference external binary and texture resources. Alternatively, both
GlTF
Sporadic simple group
original triangular tiling which bisect the squares and octagons". This can be visualized by coloring the triangles – the corresponding tiling is topologically
Mathieu_group_M24
Dynamic window manager for X Window System
xmonad is a dynamic window manager (tiling) for the X Window System, noted for being written in the functional programming language Haskell. Begun in March
Xmonad
Spatial index that partitions space based on the bit-representation of keys
inventor C++: GitHub repository C++: GitHub repository Binary space partitioning Binary tiling k-d tree Octree Quadtree R-tree UB-tree Spatial database
PH-tree
Field of geometry closely arranging circles on a plane
The truncated trihexagonal tiling with both types of gaps can be filled as a 4-uniform packing. The snub hexagonal tiling has two mirror-image forms.
Circle_packing
Dynamic window manager for X Window System
dwm's xinerama support: tiling on two screens simultaneously
Dwm
Plane tiling corresponding to a polyhedron
tessellations or elliptic tilings, referring to the projective plane as (projective) elliptic geometry, by analogy with spherical tiling, a synonym for "spherical
Projective_polyhedron
Ordered chemical structure with no repeating pattern
quasicrystals. In 1961, Hao Wang asked whether determining if a set of tiles admits a tiling of the plane is an algorithmically unsolvable problem or not. He
Quasicrystal
Shape in mathematics of domino tiling
the number of domino tilings of the Aztec diamond of order n is 2n(n+1)/2. The Arctic Circle theorem says that a random tiling of a large Aztec diamond
Aztec_diamond
Natural number
Kevin. "Shield - a 3.7.42 tiling". Imperfect Congruence. Retrieved 2023-01-09. 3.7.42 as a unit facet in an irregular tiling. Poonen, Bjorn; Rubinstein
7
Logic puzzle
Atsumari is similar to Nurikabe but based upon a hexagonal tiling rather than a square tiling. Mochikoro is a variant of the Nurikabe puzzle: Each numbered
Nurikabe_(puzzle)
Natural number
Kevin. "Shield - a 3.7.42 tiling". Imperfect Congruence. Retrieved 2023-01-09. 3.7.42 as a unit facet in an irregular tiling. Andrews, William Symes (1960)
42_(number)
Index of articles associated with the same name
Order in mathematics may refer to: Total order and partial order, a binary relation generalizing the usual ordering of numbers and of words in a dictionary
Order_(mathematics)
Natural number
tiling. This tiling is one of eight Archimedean tilings that are semi-regular, or made of more than one type of regular polygon, and the only tiling that
8
Circuit that performs subtraction
and it can be designed using the same approach as that of an adder. The binary subtraction process is summarized below. As with an adder, in the general
Subtractor
English mathematician, mathematical physicist (born 1931)
his Waterfall and Ascending and Descending. Penrose's eponymous aperiodic tiling presaged the discovery of quasicrystals by Dan Shechtman. Penrose won the
Roger_Penrose
Series of image file formats
entering the budding desktop scanner market. In the beginning, TIFF was only a binary image format (only two possible values for each pixel), because that was
TIFF
A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have
Redundant binary representation
Redundant_binary_representation
2024 operating system version
draft email responses, and a system-wide integration with ChatGPT. Window tiling is now automatically suggested by macOS when dragging a window to the edges
MacOS_Sequoia
Visualisation method for hierchical data
items on the screen simultaneously. To create a treemap, one must define a tiling algorithm, that is, a way to divide a region into sub-regions of specified
Treemapping
Solid with six equal square faces
meeting at the center. Bhargava cube, a configuration to study the law of binary quadratic form and other such forms, of which the cube's vertices represent
Cube
Editing technique for video games
Similar to assembly hacking, this method involves decompiling the game's binary executable to recreate the game's source code in a high-level, human-readable
ROM_hacking
Natural number
on 12 vertices 1,278,818 = Markov number 1,290,872 = number of 26-bead binary necklaces with beads of 2 colours where the colours may be swapped but turning
1,000,000
Sliding puzzle with fifteen pieces and one space
matter how many moves are made. This is done by considering a binary function of the tile configuration that is invariant under any valid move and then
15_puzzle
Standardized means of organizing and storing digital images
allowing WebP support for animation, ICC profile, XMP and Exif metadata, and tiling. The support for animation allowed for converting older animated GIFs to
Image_file_format
Property of being an even or odd number
and Schuster, pp. 273–274, ISBN 9780671795023. Mendelsohn, N. S. (2004), "Tiling with dominoes", The College Mathematics Journal, 35 (2): 115–120, doi:10
Parity_(mathematics)
Natural number
and angle trisector. The lowest number of squares needed for a perfect tiling of a rectangle is 9. Nine is a number that appears often in Indian culture
9
Solid with twenty equal triangular faces
icosahedron is a cell for the honeycomb in a hyperbolic three-dimensional space. Binary icosahedral group, a double cover of the group of rotations of the icosahedron
Regular_icosahedron
Mapping function that preserves data point locality
interleaving the binary representations of its coordinate values. However, when querying a multidimensional search range in these data, using binary search is
Z-order_curve
Dutch graphic artist (1898–1972)
squares); creating tile shapes; local versus global definitions of regularity; symmetry of a tiling induced by the symmetry of a tile; orderliness not induced
M._C._Escher
Space-filling system of square prisms
tetrastix structure form a tiling of space by cubes, combinatorially equivalent to the Weaire–Phelan structure for tiling space with unit volumes of low
Tetrastix
In mathematics, a Riemann surface
321281.} The symmetry of the Bolza surface can be understood in terms of its tiling by 16 equilateral hyperbolic triangles, 8 per vertex. Focusing on one particular
Bolza_surface
White_Space is a binary Unicode property. "Unicode PropList.txt". Unicode. 2025-06-30. Retrieved 2025-09-11. Although ​ is one HTML5 named
List_of_Unicode_characters
Natural number
134. "Shield - a 3.7.42 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 7 March 2022. "Dancer - a 3.8.24 tiling". Kevin Jardine's projects
17_(number)
Games February 22 Redemption Reapers WIN, NS, PS4 Strategy, RPG Adglobe Binary Haze Interactive February 22 Runner PS5 Action Truant Pixel February 22
List of video games released in 2023
List_of_video_games_released_in_2023
Natural number
18, 24, 36, 48, 72, 144 Greek numeral ΡΜΔ´ Roman numeral CXLIV, cxliv Binary 100100002 Ternary 121003 Senary 4006 Octal 2208 Duodecimal 10012 Hexadecimal
144_(number)
Distinctive Software Konami March 1991NA Unreleased March 1991 Unreleased Binary Land Hudson Soft Hudson Soft December 19, 1985JP December 19, 1985 Unreleased
List of Nintendo Entertainment System games
List_of_Nintendo_Entertainment_System_games
Overview of and topical guide to geometry
Sangaku Straightedge Symmedian Tessellation Prototile Aperiodic tiling Wang tile Penrose tiling Trapezoid (trapezium) Isosceles trapezoid Triangle Acute and
Outline_of_geometry
Numbers obtained by adding the two previous ones
different ways among the set of binary strings, or equivalently, among the subsets of a given set. The number of binary strings of length n without consecutive
Fibonacci_sequence
Natural number
six-sided polygon is a hexagon, one of the three regular polygons capable of tiling the plane. A hexagon also has 6 edges as well as 6 internal and external
6
Array containing every possible matrix of size m × n
possible binary "square" de Bruijn torus, depicted above right, denoted as (4,4;2,2)2 de Bruijn torus (or simply as B2), contains all 2×2 binary matrices
De_Bruijn_torus
24-dimensional repeating pattern of points
and 240 unit balls, respectively, based on the integer lattice, hexagonal tiling, and E8 lattice, respectively. It has no root system and in fact is the
Leech_lattice
Use of functions that call themselves
illustrates an in-order traversal of the binary tree. A Binary search tree is a special case of the binary tree where the data elements of each node
Recursion_(computer_science)
Visibility in 3D computer graphics
the number of primitives considered per region, e.g. tiling, or screen-space BSP clipping. Tiling may be used as a preprocess to other techniques. Z-buffer
Hidden-surface_determination
Decorative background on electronic devices
least as early as the X10R3 release in 1985 could tile the screen with any solid color or any binary-image X BitMap file. In 1989, a free software program
Wallpaper_(computing)
the systolic array, the sizes of the on-chip buffers, and the software's tiling strategy are derived from the same blocking parameters. The number of processing
Hardware/software_co-design
History of Apple's current Mac operating system
iPhone was included, along with a password manager app, system support for tiling and resizing windows, and various other minor updates to Safari, Maps, Messages
MacOS_version_history
3D computer graphics software
and was not updated to the GPLv3, as "no evident benefits" were seen. The binary releases of Blender are under GNU GPLv3 or later because of the incorporated
Blender_(software)
Hypermedia system for Apple Macintosh and Apple IIGS computers
abilities of the IIGS. Although stacks (HyperCard program documents) are not binary-compatible, a translator program (another HyperCard stack) allows them to
HyperCard
Database management system
that the tiling pattern is adjusted to the query access patterns; several tiling strategies assist in establishing a well-performing tiling. A geo index
Rasdaman
Combinational digital circuit
digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates
Arithmetic_logic_unit
Largest integer that divides given integers
gives gcd(48, 18) = 6. The binary GCD algorithm is a variant of Euclid's algorithm that is specially adapted to the binary representation of the numbers
Greatest_common_divisor
Mathematical puzzle game
positions after move m can be mapped from the binary representation of m by the following rules: There is 1 binary digit (bit) in m for each disk. The bitstring
Tower_of_Hanoi
Natural number
There are 15 perfect matchings of the complete graph K6 and 15 rooted binary trees with four labeled leaves, both of these being among the types of objects
15_(number)
File format used to present documents
The simplest is the tiling pattern in which a piece of artwork is specified to be drawn repeatedly. This may be a colored tiling pattern, with the colors
Natural number
"Archimedean Solid". MathWorld. Retrieved 2020-08-21. Weisstein, Eric W. "Domino Tiling". MathWorld. Retrieved 2020-08-21. "Sloane's A059756 : Erdős-Woods numbers"
36_(number)
Natural number
65\;537=4\;294\;967\;295.} The first 32 rows of Pascal's triangle read as single binary numbers represent the 32 divisors that belong to this number, which is also
32_(number)
Natural number
pentagon. The equilateral pentagon is the first regular polygon that does not tile the plane with copies of itself. The pentagon solid has the largest face
5
Type of digital adder
save adder is typically used in a binary multiplier, since a binary multiplier involves addition of more than two binary numbers after multiplication. A
Carry-save_adder
Problems which attempt to find the most efficient way to pack objects into containers
general, but there are fast algorithms for solving small instances. In tiling or tessellation problems, there are to be no gaps, nor overlaps. Many of
Packing_problems
Public domain geocoding invented in 2008
is decoding it from textual "base 32ghs", as showed above, to obtain the binary representation: [ e ] 32 g h s = [ 13 ] 10 = [ 01101 ] 2 {\displaystyle
Geohash
Finite or infinite ordered list of elements
The set C = {0, 1}∞ of all infinite binary sequences is sometimes called the Cantor space. An infinite binary sequence can represent a formal language
Sequence
Formula that visually represents itself when graphed
{\displaystyle k} is a simple monochrome bitmap image of the formula treated as a binary number and multiplied by 17. If k {\displaystyle k} is divided by 17, the
Tupper's self-referential formula
Tupper's_self-referential_formula
Logic puzzle forming a picture in a grid
successive sets. These puzzles are often black and white — describing a binary image — but they can also be colored. If colored, the number clues are also
Nonogram
Season of television series
del Sur, due to Teeny Chirichillo participating in Survivor 47 as a non-binary person. Chirichillo would come out as a transgender man in April 2025. At
Survivor_47
Divide and conquer sorting algorithm
use as swap space. The space overhead can be reduced to O(√n) by using binary searches and rotations. This method is employed by the C++ STL library and
Merge_sort
Puzzle video game
infinite Minesweeper is Turing-complete. Board puzzles with algebra of binary variables Edwards, Benj (8 October 2020). "30 Years of 'Minesweeper' (Sudoku
Minesweeper_(video_game)
Season of television series
"Binary Bridge", participants had to cross a bridge by stepping on one of two tiles that would highlight red or green. When stepping on a green tile,
Big Brother 26 (American season)
Big_Brother_26_(American_season)
2001 fashion collection by Alexander McQueen
enables "the becoming-nonhuman of the wearer's body" and defies standard binary categories such as "human/animal". For Seely, McQueen's designs achieve
Voss_(collection)
smallest number greater than 1000 in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane. 1204 = 22 × 7 × 43. It is the magic constant for
1000_(number)
Natural number
can uniformly tile the plane alongside other regular polygons, as with the truncated hexagonal tiling or the truncated trihexagonal tiling. A regular dodecahedron
12_(number)
Family of algorithms used in procedural generation
Grammars (Video). Event occurs at 3:13. "Implementing Wave Function Collapse & Binary Space Partitioning for Procedural Dungeon Generation". Shaan Khan. 2021-03-21
Model_synthesis
List of Windows 10 operating system versions
new component that provides an environment for running Linux-compatible binary software in an Ubuntu-based user mode environment. This release also includes
Windows_10_version_history
2012 Microsoft operating system version
compatible with both Intel and ARM variants of Windows, otherwise they are not binary code compatible. Components may be compiled as Windows Runtime Components
Windows_8
Sultan of the Ottoman Empire (r. 1444–1446, 1451–1481)
was, itself, possibly an attempt to break down Western-Oriental cultural binaries in order for Mehmed to present himself as a Western-oriented ruler, among
Mehmed_II
Creatures from Korean folklore
She can also infiltrate CCTV cameras and observe the enemy. Sujin, a non-binary dokkaebi, is a character in the novel Dragon Pearl by Yoon Ha Lee.[citation
Dokkaebi
American daily newspaper
Philip B. Corbett, criticizing the paper's coverage of transgender, non-binary, and gender-nonconforming people; some of the Times's articles have been
The_New_York_Times
Multitasking operating system written in Oberon
support for OLE, Netscape Plugins, and the binary format named Oberon Module Interchange (OMI) or slim binaries, which allowed portable object code between
Oberon_(operating_system)
Natural number
110 and 112, which are the two smallest edge-lengths of squares that are tiled in the interior by smaller squares of distinct edge-lengths (see, squaring
111_(number)
Larabel (March 17, 2015). "BioShock Infinite Now Available For Linux, Demands Binary Graphics Drivers". Phoronix. Retrieved April 3, 2015. Eric Chetkauskas (February
List of video games released in 2015
List_of_video_games_released_in_2015
Type of two-dimensional barcode
use four standardized modes of encoding: numeric, alphanumeric, byte or binary, and kanji. Compared to standard UPC barcodes, the QR labeling system was
QR_code
Home video game console
of the SNES incorporates graphics and sound co-processors that perform tiling and simulated 3D effects, a palette of 32,768 colors, and 8-channel ADPCM
Super Nintendo Entertainment System
Super_Nintendo_Entertainment_System
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