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In mathematics, the complex squaring map, a polynomial mapping of degree two, is a simple and accessible demonstration of chaos in dynamical systems. It
Complex_squaring_map
Quadratic polynomial
c=0} (see complex squaring map) f c {\displaystyle f_{c}} planes (all other planes for c ≠ 0 {\displaystyle c\neq 0} ) The extended complex plane plus
Complex_quadratic_polynomial
from complex quadratic map Koch snowflake - special case of de Rham curve Lyapunov fractal Mandelbrot set - derived from complex quadratic map Menger
List_of_chaotic_maps
Complex-differentiable (mathematical) function
a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate
Holomorphic_function
Number whose square is a given number
the principal square root. Square roots of negative numbers can be discussed within the framework of complex numbers. More generally, square roots can be
Square_root
Number with a real and an imaginary part
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary
Complex_number
Web mapping service
2012. Sieczkowski, Cavan (January 29, 2013). "Google Maps North Korea: Prison Camps, Nuclear Complexes Pinpointed In New Images (PHOTOS)". The Huffington
Google_Maps
Shape with four equal sides and angles
multiplying a number by itself is called squaring. Equal squares can tile the plane edge-to-edge in the square tiling. Square tilings are ubiquitous in tiled floors
Square
Mathematical function that preserves angles
conformal map. Each is hosted by its own real algebra, ordinary complex numbers, split-complex numbers, and dual numbers. The conformal maps are described
Conformal_map
Fundamental operation on complex numbers
} that leave the real numbers fixed are the identity map and complex conjugation. Once a complex number z = x + y i {\displaystyle z=x+yi} or z = r e
Complex_conjugate
Discrete (i.e., incremental) version of infinitesimal calculus
outputs six, and if the squaring function is given the input three, then it outputs nine. The derivative, however, can take the squaring function as an input
Discrete_calculus
Graphical method to simplify Boolean expressions
donut or torus shape. The four corners of the square drawn by the k-map are adjacent. Still more complex maps are needed for 5 variables and more. Σm(0);
Karnaugh_map
Cylindrical conformal map projection
Mercator projection is just the complex logarithm, z ↦ log z {\displaystyle z\mapsto \log z} , a conformal map of the complex plane (with the exception
Mercator_projection
Branching out of a mathematical structure
geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign
Ramification_(mathematics)
Geometric representation of the complex numbers
quadratic spaces. For a point z = x + iy in the complex plane, the squaring function z2 and the norm-squared x2 + y2 are both quadratic forms. The former
Complex_plane
Manifold
ball in the complex coordinate space C n {\displaystyle \mathbb {C} ^{n}} , such that the transition maps are holomorphic. The term "complex manifold" is
Complex_manifold
other meridians as complex curves, and parallels as circular arcs. Azimuthal In standard presentation, azimuthal projections map meridians as straight
List_of_map_projections
Apartment complex in London, England
Highbury Square is an apartment complex in Highbury, London. It is a redevelopment of the old Highbury Stadium site, the home stadium of Arsenal F.C. until
Highbury_Square
Array of numbers
rotations by an angle zero. The complex analog of an orthogonal matrix is a unitary matrix. The trace, tr(A) of a square matrix A is the sum of its diagonal
Matrix_(mathematics)
Systematic representation of the surface of a sphere or ellipsoid onto a plane
a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection
Map_projection
Historic site in Split, Croatia
pǎlatʃa]; Latin: Palatium Diocletiani) is an ancient Roman palace and fortress complex in Split, Croatia. It was built at the end of the third century AD by the
Diocletian's_Palace
Skyscraper complex in Melbourne Australia
Square is a A$2.8 billion building complex of residential mixed-use towers in the Southbank precinct of Melbourne, Victoria, Australia. The complex will
Melbourne_Square_(complex)
Square in Kathmandu, Nepal
facades characteristic of Newar architecture. The central square is surrounded by palace complexes built during the Malla and Shah periods. The most well
Kathmandu_Durbar_Square
Data visualization technique
A heat map (or heatmap) is a two-dimensional data visualization technique that represents the magnitude of individual values within a dataset as a color
Heat_map
Office building complex in Toronto, Ontario, Canada
Canada Square is a complex of three interconnected office buildings located at Yonge and Eglinton in Toronto, Ontario, Canada, including a small shopping
Canada_Square_(Toronto)
Corporate Offices in Somers, NY
1984, the modernist 1,200,000-square-foot (110,000 m2) complex has been described as a "futuristic fortress". The complex was originally conceived in 1983
IBM_Somers_Office_Complex
Abandoned Hotel Complex
near Baħar iċ-Ċagħaq. Covering an area of approximately 450,000 square meters, the complex offers stunning views of the Mediterranean Sea but has fallen
White_Rocks_Complex
Simple polynomial map exhibiting chaotic behavior
an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. The map was initially utilized by Edward
Logistic_map
Rational function of the form (az + b)/(cz + d)
trace squared as a proxy for the eccentricity squared, as was done above; these classifications (but not the exact eccentricity values, since squaring and
Möbius_transformation
Parallel programming model
many kinds of data use, especially on complex processing or where the data is used across an enterprise, but that MapReduce may be easier for users to adopt
MapReduce
Function that maps matrices to matrices
can be used for defining a matrix function that maps square matrices with complex entries to square matrices of the same size. This is used for defining
Analytic_function_of_a_matrix
History and style of cartography in Japan
a feudal manor, or orientation within a temple complex. An example might be an Edo era pilgrimage map depicting the route and location of lodges on the
Japanese_maps
Fortified complex in Moscow, Russia
The Moscow Kremlin, commonly known as the Kremlin, is a fortified complex, known by the same name, in Moscow, Russia. Located in the historic centre of
Kremlin
Type of data visualization for geographic regions
they can make the map overly complex, especially if there is not a meaningful geographic pattern in the variable (i.e., the map looks like randomly
Choropleth_map
Real estate complex in Yangon, Myanmar
The complex is located near Shwedagon Pagoda, at the intersection of Shwedagon Pagoda Road and U Wisara Roads. Y Complex will encompass 92,000 square metres
Y_Complex
Type of map that visualizes data
A thematic map is a type of map that portrays the geographic pattern of a particular subject matter (theme) in a geographic area. This usually involves
Thematic_map
Component of Tolkien's writings
his often complex stories, and contributed to the impression of depth and worldbuilding in his writings. Tolkien stated that he began with maps and developed
Tolkien's_maps
Multi-purpose indoor arena in New York City, U.S.
and retail complex, named for the railway station. Several other operating entities related to the Garden share its name. Madison Square is formed by
Madison_Square_Garden
Public square in Beijing, China
north, which separates it from the Forbidden City imperial palace complex. The square holds the Monument to the People's Heroes, the Great Hall of the
Tiananmen_Square
Sum of elements on the main diagonal
of A can be real numbers, complex numbers, or more generally elements of a field F. The trace is not defined for non-square matrices. Let A be a matrix
Trace_(linear_algebra)
Mathematical function, denoted exp(x) or e^x
how the domain complex plane is mapped into the range complex plane: zero is mapped to 1 the real x {\displaystyle x} axis is mapped to the positive
Exponential_function
Corporate headquarters complex of Google
complex of Google and its parent company, Alphabet Inc. It is located at 1600 Amphitheatre Parkway in Mountain View, California. The original complex
Googleplex
Representation of mathematical space
complex as a set or as a topological space. A map f : K → L {\displaystyle f:{\mathcal {K}}\rightarrow {\mathcal {L}}} between simplicial complexes is
Triangulation_(topology)
Matrix operation which flips a matrix over its diagonal
components thereof) as the set of all linear maps X → X for which the adjoint equals the inverse. Over a complex vector space, one often works with sesquilinear
Transpose
Association of one output to each input
Serge Lang, use "function" only to refer to maps for which the codomain is a subset of the real or complex numbers, and use the term mapping for more general
Function_(mathematics)
Fractal named after mathematician Benoit Mandelbrot
for each sampled complex number c. The real and imaginary parts of c {\displaystyle c} are mapped as image coordinates on the complex plane and colored
Mandelbrot_set
Medieval European maps of the world
Zonal maps (sometimes called Macrobian maps) Tripartite maps (including "T-O" and "V-in-◻" maps) Quadripartite maps (including the Beatus maps) Complex maps
Mappa_mundi
Field of mathematics and science based on non-linear systems and initial conditions
logistic map alike ψ → G ψ [ 1 − tanh ( ψ ) ] {\displaystyle \psi \rightarrow G\psi [1-\tanh(\psi )]} or complex map. For examples of complex maps the Julia
Chaos_theory
Imperial complex of religious buildings in Beijing, China
pinyin: Tiāntán) is a complex of imperial religious Confucian buildings situated in the southeastern part of central Beijing. The complex was visited by the
Temple_of_Heaven
version of the map was introduced on January 30, 2012. The official version of the map, based on the Tauranac redesign, incorporated a complex cartography
New_York_City_Subway_map
Arithmetic operation, inverse of nth power
is also a square root of 9, since (−3)2 = 9. A negative real number −x has no real-valued square roots, but when x is treated as a complex number it has
Nth_root
Vector space with generalized dot product
numbers rather than complex numbers. The real part of the complex inner product ⟨ x , y ⟩ {\displaystyle \langle x,y\rangle } is the map ⟨ x , y ⟩ R = Re
Inner_product_space
Large city square in Baku, Azerbaijan
(7.4 acres), the square prominently displays national symbols of Azerbaijan, including the state coat of arms, anthem, and a bronze map of the country.
State_Flag_Square_(Baku)
Complex matrix A* obtained from a matrix A by transposing it and conjugating each entry
is a linear map from a complex vector space V {\displaystyle V} to another, W {\displaystyle W} , then the complex conjugate linear map as well as the
Conjugate_transpose
Skyscrpaer complex in Istanbul, Turkey
Emaar Square Complex is a mixed-use skyscraper complex in the Ünalan district of Istanbul, Turkey. Overall built between 2012 and 2020, the complex consists
Emaar_Square_Istanbul
Notable events in the history of geometry
the first known approximate values of π at 3.16, the first attempt at squaring the circle, earliest known use of a sort of cotangent, and knowledge of
Timeline_of_geometry
Building in New Brunswick, Canada
Brunswick Square is a mixed-use complex located in uptown Saint John, New Brunswick, Canada. Built by Robert McAlpine in 1976, it is owned by Slate Office
Brunswick Square (building complex)
Brunswick_Square_(building_complex)
Type of mathematical functions
theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space C n {\displaystyle
Function of several complex variables
Function_of_several_complex_variables
Type of stable macromolecular complex
than 2500 square Ås. Protein complex formation can activate or inhibit one or more of the complex members and in this way, protein complex formation can
Protein_complex
Algebraic operation on coordinate vectors
norm; it is a vector generalization of the absolute square of a complex scalar (see also: Squared Euclidean distance). The inner product generalizes the
Dot_product
Study of complex manifolds and several complex variables
complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
Iron age map engraved into rock
Italian side, Lombardy region) petroglyph complex. It is known as one of the most ancient topographic maps, interpreted as a depiction of cultivated plots
Bedolina_Map
Sports complex in Springfield, Virginia
20-acre (8.1 ha) 450,000-square-foot multi-purpose sports complex located in Springfield, Virginia, United States. The complex includes a private health
The St. James (sports complex)
The_St._James_(sports_complex)
Shopping mall in South Shore, Pittsburgh
Station Square is a 52-acre (210,000 m2) entertainment complex located in the South Shore neighborhood of Pittsburgh, Pennsylvania, United States. It sits
Station_Square
Construct in algebraic geometry
mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such
Cotangent_complex
Complex of buildings in Iqaluit, Nunavut, Canada
The Astro Hill Complex is a four building structure in Iqaluit, Nunavut, Canada, and includes the W. G. Brown Building, the Frobisher Inn hotel and two
Astro_Hill_Complex
Mathematical object
of those square-free monomials of S {\displaystyle S} that are not in I {\displaystyle I} determine an abstract simplicial complex via the map a ∈ { 0
Abstract_simplicial_complex
Skyscraper in Jersey City, New Jersey
Journal Squared, or J2, is a three-tower retail and residential complex at Journal Square in Jersey City, New Jersey. The site of the project is adjacent
Journal_Squared
Length in a vector space
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance
Norm_(mathematics)
Map projection in which every angle between two curves that cross each other is preserved
often appended. In complex projections such as of oblique aspect. Contour charts of scale factors are sometimes appended. List of map projections (Euler
Conformal_map_projection
Tabular summary of genetic combinations
than if only analyzing for phenotypic ratio. Mendelian inheritance Karnaugh map, a similar diagram used for Boolean algebra simplification Mendel, Gregor
Punnett_square
Conformal mapping in complex analysis
In complex analysis, a Schwarz–Christoffel mapping is a conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon
Schwarz–Christoffel_mapping
Map distorting size to show another value
cartogram (also called a value-area map or an anamorphic map, the latter common among German speakers) is a thematic map of a set of features (countries,
Cartogram
Thematic map based on symbol size
A proportional symbol map or proportional point symbol map is a type of thematic map that uses map symbols that vary in size to represent a quantitative
Proportional_symbol_map
Type of group in mathematics
group O(n) are, up to a uniform scaling (homothecy), the linear maps from E to E that map orthogonal vectors to orthogonal vectors. The orthogonal O(n)
Orthogonal_group
Construction in homological algebra
so forth. Let A be a commutative ring and s: Ar → A an A-linear map. Its Koszul complex Ks is ⋀ r A r → ⋀ r − 1 A r → ⋯ → ⋀ 1 A r → ⋀ 0
Koszul_complex
Skyscraper complex in Kuala Lumpur, Malaysia
"Berjaya Times Square Tower A". CVU Skyscraper Center. "Berjaya Times Square Tower B". CVU Skyscraper Center. "Emporis building complex ID 101020". Emporis
Berjaya_Times_Square
Mathematical theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number
Riemann_mapping_theorem
Entertainment complex in Shanghai, China
and entertainment complex in Shanghai, China. Located in Fuxing Park in the Huangpu District, it covers approximately 20,000 square metres across six
INS_Land
New York City Subway station in Manhattan
The Times Square–42nd Street station is a major New York City Subway station complex located under Times Square, at the intersection of 42nd Street, Seventh
Times Square–42nd Street station
Times_Square–42nd_Street_station
Doubling map on the unit interval
transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)
Dyadic_transformation
Public housing apartment complex in Miami, Florida, United States
Liberty Square, often referred to as the Pork & Beans, is a 753-unit Miami-Dade public housing apartment complex in the Liberty City neighborhood of Miami
Liberty_Square_(Miami)
Fundamental trigonometric functions
their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic
Sine_and_cosine
Office building in Michigan, United States
(204 ha) complex is located next to Interstate 75 in Auburn Hills, Michigan, a northern suburb of Detroit. The complex has 5,400,000 square feet (500
Chrysler World Headquarters and Technology Center
Chrysler_World_Headquarters_and_Technology_Center
Complex in Salt Lake City operated by The Church of Jesus Christ of Latter-day Saints
Welfare Square is a complex in downtown Salt Lake City, Utah owned and operated by the Church of Jesus Christ of Latter-day Saints (LDS Church), to provide
Welfare_Square
In mathematics, invariant of square matrices
the field of real or complex numbers. Moreover, the characterization of the determinant as the unique alternating multilinear map that satisfies det (
Determinant
Mathematical functions of split-complex numbers
function is equivalent to a squeeze mapping. The squaring function has no analogy in ordinary complex arithmetic. Let f ( z ) = z 2 {\displaystyle f(z)=z^{2}\
Motor_variable
Railway station in Maharashtra, India
Bandra Kurla Complex high-speed railway station, also known as Mumbai BKC station, is an under-construction high-speed railway station on the Mumbai–Ahmedabad
Bandra Kurla Complex high-speed railway station
Bandra_Kurla_Complex_high-speed_railway_station
Central square of Athens, Greece
Athens at the square. The square is also a hub for buses to the northern suburbs and the Athens Olympic Complex in Maroussi. The square is located near
Syntagma_Square
Sizes of palaces around the world
fortified walls is held by China's Forbidden City complex in Beijing, which covers an area of 728,000 square metres (180 acres). The 980 buildings of the Forbidden
List_of_largest_palaces
Method of environment mapping in computer graphics
the six faces of a cube as the map shape. The environment is projected onto the sides of a cube and stored as six square textures, or unfolded into six
Cube_mapping
Complex of three historically renovated 1930-completed high-rises located in Cleveland
The Landmark Office Towers is a complex of three historically renovated 1930-completed 259 foot 22 story high-rises that are located on the property of
Landmark Office Towers Complex
Landmark_Office_Towers_Complex
Skyscraper in Rwanda
Green Complex Development in Rwanda". Construction Review Online. Nairobi, Kenya. Retrieved 19 January 2024. "Location of the Kigali Green Complex" (Map).
Kigali_Green_Complex
Mathematical concept
In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real
Complex_projective_space
American underground space leasing corporation
SubTropolis is a business complex located inside of a 14,000,000-square-foot (1,300,000 m2) limestone mine in the bluffs north of the Missouri River in
SubTropolis
Two-building skyscraper mixed use apartment complex in downtown Cleveland, Ohio
Reserve Square is a two-building skyscraper mixed use apartment complex in downtown Cleveland, Ohio, United States. Both buildings have 23 floors and
Reserve_Square
Skyscraper in Tokyo, Japan
Located above Shibuya Station, the complex consists of three buildings, including an eastern building, Shibuya Scramble Square (229.71 m height), a central
Shibuya_Scramble_Square
Smooth manifold
a smooth manifold. An almost complex structure J on M is a linear complex structure (that is, a linear map which squares to −1) on each tangent space
Almost_complex_manifold
Algebraic structure associated with a topological space
H_{n-2}(A)\to \cdots } All maps in this long exact sequence are induced by the maps between the chain complexes, except for the maps H n ( C ) → H n − 1 (
Homology_(mathematics)
Statement in complex analysis
result in complex differential geometry that estimates the (squared) pointwise norm | ∂ f | 2 {\displaystyle |\partial f|^{2}} of a holomorphic map f : (
Schwarz_lemma
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Surname or Lastname
English
English : unexplained.
Boy/Male
Biblical Hebrew
Sparing the people.
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Girl/Female
Indian, Tamil
Terrify; Scaring Others
Girl/Female
Indian
Soaring Angel
Male
Chinese
flying, soaring.
Girl/Female
Bengali, Indian
Good Complex
Surname or Lastname
English
English : unexplained.
Male
Chinese
soaring high.
Boy/Male
Native American
Soaring turkey vulture.
Girl/Female
Muslim
Complex, Zigzag, Curling
Biblical
sparing the people
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Surname or Lastname
English
English : patronymic from Spear.
Girl/Female
African, Arabic, Australian, French, Muslim, Swahili
Sharing Together; Arrows
Boy/Male
American, Australian, British, Dutch, English
Quaking Fen
Girl/Female
Hindu, Indian
Complex
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
Boy/Male
Celtic
From the alder grove.
Boy/Male
Latin
Helmeted.
Male
Arthurian
, (Sir) king Arthur's steward.
Boy/Male
Indian
Early morning fragrance, Entertaining companion, Wind
Boy/Male
Arthurian Legend
A Welsh king.
Male
Norwegian
Norwegian form of Old Norse Guðleifr, GUDLEIF means "divine heir."
Girl/Female
Indian, Sanskrit
The Mother
Girl/Female
Indian, Punjabi, Sikh
Without Fear; Fearless
Girl/Female
Indian
Light
Girl/Female
Tamil
Fire
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
imp. & p. p.
of Couple
n.
The product of the act or operation of clipping with shears or a shearing machine; as, the whole shearing of a flock; the shearings from cloth.
imp. & p. p.
of Comply
adv.
In a complex manner; not simply.
n.
The act or operation of clipping with shears or a shearing machine, as the wool from sheep, or the nap from cloth.
imp. & p. p.
of Compile
n.
A complex; an aggregate of parts; a complication.
n.
One who compiles; esp., one who makes books by compilation.
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
n.
Act of shearing sheep.
n.
One who complies, yields, or obeys; one of an easy, yielding temper.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Not complex; uncompounded; simple.
a.
Repeatedly compound; made up of complex constituents.
a.
See Couple-close.
a.
Complex, complicated.
a.
Intricate; entangled; complicated; complex.
n.
The act or operation of dividing with shears; as, the shearing of metal plates.
n.
A feast at the time of sheep-shearing.