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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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
3D scene and model file format
easily memorized as a text file) or .glb (binary). Both .gltf and .glb files may reference external binary and texture resources. Alternatively, both
GlTF
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
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
Shape with three equal sides
tessellation's instances are the triangular tiling where six equilateral triangles surrounds a common vertex, and the sphinx tiling as a special case of the polyiamond
Equilateral_triangle
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)
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
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)
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
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)
Dynamic window manager for X Window System
dwm's xinerama support: tiling on two screens simultaneously
Dwm
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)
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
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
Editing technique for video games
specifically used for a method known as decompilation, where the game's binary executable is decompiled to recreate the game's source code in a high-level
ROM_hacking
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
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
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
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
Distinctive Software Konami April 1991NA Unreleased April 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
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
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
Natural number
and angle trisector. The lowest number of squares needed for a perfect tiling of a rectangle is 9. Ne Win, the leader of Myanmar from 1962 to 1988, was
9
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
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)
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
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)
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
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
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
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
Natural number
solvable configuration of the 15 puzzle can be solved in no more than 80 single-tile moves. In Northern Europe, there have traditionally been words for eighty
80_(number)
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)
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
Mapping function that preserves data point locality
are also known as quadkey values; see Tiled web map. The Z-values of the x coordinates are described as binary numbers from the Moser–de Bruijn sequence
Z-order_curve
English mathematician, mathematical physicist (born 1931)
his Waterfall and Ascending and Descending. Penrose's eponymous aperiodic tiling presaged Dan Shechtman's discovery of quasicrystals. Penrose won the Royal
Roger_Penrose
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
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
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)
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
Free software project
set, plot (graphics), portable bitmap format meteor-contest: hexagonal tiling, puzzle solving n-body: N-body simulation, Jovian planets, symplectic integrator
The Computer Language Benchmarks Game
The_Computer_Language_Benchmarks_Game
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
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
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
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)
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)
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
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
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
Puzzle video game genre
infinite Minesweeper is Turing-complete. Board puzzles with algebra of binary variables 1990s in video games Edwards, Benj (8 October 2020). "30 Years
Minesweeper_(video_game)
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
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
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
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
64-bit extension of the ARM architecture
Multi-vector instructions. Multi-vector predicates. 2b/4b weight compression. 1b binary networks. Range Prefetch. Guarded Control Stack (GCS) (ARMv9 only). Confidential
AArch64
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
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)
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
Ancient Mesopotamian board game
successive rolls of 4 (the royal game discovered by Woolley was found with 3 binary tetrahedral dice, which when rolled together can only produce 4 different
Royal_Game_of_Ur
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)
11". Gematsu. Retrieved June 13, 2026. Romano, Sal (February 5, 2026). "Binary Haze Interactive and Adglobe announce multi-genre action game Tokyo Scramble
List of Nintendo Switch 2 games
List_of_Nintendo_Switch_2_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
Gematsu. Retrieved December 5, 2025. Romano, Sal (February 5, 2026). "Binary Haze Interactive and Adglobe announce multi-genre action game TOKYO SCRAMBLE
List of video games released in 2026
List_of_video_games_released_in_2026
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
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
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)
Natural number
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)
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. In September
Dokkaebi
Process to build apps for various mobile operating systems
build and test on the localhost Eclipse (software) (optional) All native binaries: Android, iOS, BlackBerry 10, Windows, OS X, Linux, OpenBSD, OpenWrt The
Mobile_app_development
Family of instruction set architectures
represented any 8086-compatible CPU. Today, however, x86 usually implies binary compatibility with the 32-bit instruction set of the 80386. This is due
X86
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
Solid-dissection puzzle
currently sold as a logic game by Piet Hein Trading and by ThinkFun (formerly Binary Arts) under the name Block by Block. Online assembling of Soma Cube pieces
Soma_cube
RAM, ROM, flash and cache sizes as well as file sizes are specified using binary meanings for K (10241), M (10242), G (10243), etc. Common features of the
List_of_Intel_processors
Australian science fiction author and mathematician
Baez, Dan Christensen and Greg Egan Conic-Helical Orbits of Planets around Binary Stars do not Exist by Greg Egan The production of a short film inspired
Greg_Egan
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
Study of discrete mathematical structures
collections of geometrical objects. A long-standing topic in discrete geometry is tiling of the plane. In algebraic geometry, the concept of a curve can be extended
Discrete_mathematics
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