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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
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
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
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
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
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)
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
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
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
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
other meridians as complex curves, and parallels as circular arcs. Azimuthal In standard presentation, azimuthal projections map meridians as straight
List_of_map_projections
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)
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
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
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
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)
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
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
Underground hideouts used by Jewish rebels
known refuge systems have been examined and mapped. According to the researchers, most of these refuge complexes were used or prepared by Jews for times of
Bar_Kokhba_hiding_complexes
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
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
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
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
Fortified complex in Moscow, Russia
The Moscow Kremlin, commonly known as the Kremlin, is a fortified complex (kremlin) in Moscow, Russia. Located in the historic centre of the country's
Kremlin
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
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
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
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
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
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
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
Square in Tashkent, Uzbekistan
rendering of a map of Uzbekistan. Before the pedestal there is a statue of a seated mother with a baby in her arms. The monumental complex represent the
Mustaqillik_Maydoni
Matrix operation which flips a matrix over its diagonal
^{\text{T}}=-\mathbf {A} .} A square complex matrix whose transpose is equal to the matrix with every entry replaced by its complex conjugate (denoted here
Transpose
Skyscraper 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
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
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
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
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)
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
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)
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)
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
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)
Business district in Mumbai, India
The Bandra Kurla Complex is a commercial area located in the Bandra East area of the city of Mumbai, the financial capital of India. It is a prominent
Bandra_Kurla_Complex
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
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
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
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
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
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
Sports complex in New Jersey, U.S.
The Meadowlands Sports Complex is a sports complex located in East Rutherford, New Jersey, United States. The facility is owned and operated by the New
Meadowlands_Sports_Complex
Branch of mathematics
+ a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b,} linear maps such as ( x 1 , … , x n ) ↦ a 1 x 1 + ⋯ + a n x n , {\displaystyle (x_{1}
Linear_algebra
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)
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
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)
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
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
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
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
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
Register of real estate boundaries
origins of this in Early Modern Europe, where taxation became more complex. Cadastral maps, he argues, are always a great simplification, but they in themselves
Cadastre
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
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)
J_{x}:E_{x}\to E_{x}} is the map on fiber-level, then J x 2 = − 1 {\displaystyle J_{x}^{2}=-1} as a linear map. If E {\displaystyle E} is a complex vector bundle, then
Complex_vector_bundle
United States historic place
Places in 1982 as the South Bushwick Reformed Protestant Dutch Church Complex, the complex consists of the church and attached Sunday School building. The original
South Bushwick Reformed Church
South_Bushwick_Reformed_Church
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
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
Residence of the President of the Republic of Turkey
The Presidential Complex (Turkish: Cumhurbaşkanlığı Külliyesi) is the presidential residence of the Republic of Turkey. The complex is located in the Beştepe
Presidential_Complex_(Turkey)
Sports complex in Walt Disney World
The ESPN Wide World of Sports Complex is an approximately 230-acre (90 ha) multi-purpose sports complex at Walt Disney World Resort in Osceola County
ESPN Wide World of Sports Complex
ESPN_Wide_World_of_Sports_Complex
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)
Temple in Yau Ma Tei, Kowloon, Hong Kong
front of the complex, and is surrounded by the popular Temple Street night market. The northern side of the complex is bordered by Public Square Street. At
Tin Hau Temple Complex, Yau Ma Tei
Tin_Hau_Temple_Complex,_Yau_Ma_Tei
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
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
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
Mathematical concept
for any nonzero complex number z {\displaystyle z} . In this context, it is often useful to consider meromorphic functions as maps into the Riemann
Infinity
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
Complex of buildings in New York City
buildings in the complex were the Marriott World Trade Center (3 WTC), 4 WTC, 5 WTC, 6 WTC, and 7 WTC. The complex contained 13,400,000 square feet (1,240
World Trade Center (1973–2001)
World_Trade_Center_(1973–2001)
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
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
Block of private apartments and business complex in Pimlico, London
Dolphin Square is a prominent estate of private flats near the River Thames in Pimlico, Westminster. Built between 1935 and 1937, it was, until the development
Dolphin_Square
Department store building in San Francisco
O'Farrell Street on the south to Geary Street and Union Square on the north. The entire complex including the Men's Store thus reached its peak size of
Macy's_Union_Square
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
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)
Cylindrical equidistant map projection
parallels on an ellipsoid is not constant. More complex formulae can be used to create an equidistant map whose parallels reflect the true spacing. λ =
Equirectangular_projection
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
Real numbers adjoined with a nil-squaring element
0 the subalgebra B is isomorphic to split-complex numbers, and when p < 0, B is isomorphic to the complex plane. One application of dual numbers is automatic
Dual_number
Skyscraper complex in Toronto, Ontario
The complex is intended to include 4,600 square metres (50,000 ft2) of community space, 7,400 square metres (80,000 ft2) for stores, and 93,000 square metres
Pinnacle_One_Yonge
Seat of the National Assembly of the Federal Republic of Nigeria
The National Assembly Complex is the seat of the National Assembly, the apex legislative body of the Federal Republic of Nigeria. It is a beehive of legislative
National_Assembly_Complex
American military region in Southern Nevada
GPX (secondary coordinates) The Nellis Air Force Base Complex (Nellis AFB complex, NAFB Complex) is the southern Nevada military region of federal facilities
Nellis_Air_Force_Base_Complex
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
Girl/Female
Hindu, Indian
Complex
Girl/Female
Muslim
Complex, Zigzag, Curling
Male
Chinese
soaring high.
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Biblical
sparing the people
Surname or Lastname
English
English : unexplained.
Boy/Male
Biblical Hebrew
Sparing the people.
Surname or Lastname
English
English : unexplained.
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.
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
African, Arabic, Australian, French, Muslim, Swahili
Sharing Together; Arrows
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Girl/Female
Indian, Tamil
Terrify; Scaring Others
Boy/Male
American, Australian, British, Dutch, English
Quaking Fen
Girl/Female
Bengali, Indian
Good Complex
Surname or Lastname
English
English : patronymic from Spear.
Boy/Male
Native American
Soaring turkey vulture.
Male
Chinese
flying, soaring.
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
Soaring Angel
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
Girl/Female
Muslim/Islamic
This was the name of a distinguished woman of her times she was Hajib known as Umm al-Hajib Abdul Malik
Girl/Female
Indian, Kannada
Rules
Girl/Female
Norse
Battle maiden.
Girl/Female
Indian
Offering, Gift
Girl/Female
Greek
Prophetess; oracle.
Girl/Female
African, Arabic, French, Indian, Muslim, Parsi
Faithful; Trustworthy
Girl/Female
Native American
Henna.
Boy/Male
Hindu, Indian
The Blameless One; One with No Faults; The Perfect Human Being
Girl/Female
Indian, Tamil
Gorgeous Flower
Boy/Male
Muslim/Islamic
Lion
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
COMPLEX SQUARING-MAP
imp. & p. p.
of Couple
adv.
In a complex manner; not simply.
a.
Complex, complicated.
n.
The act or operation of clipping with shears or a shearing machine, as the wool from sheep, or the nap from cloth.
a.
Not complex; uncompounded; simple.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
n.
One who complies, yields, or obeys; one of an easy, yielding temper.
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
n.
A complex; an aggregate of parts; a complication.
n.
The act or operation of dividing with shears; as, the shearing of metal plates.
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 Compile
n.
A feast at the time of sheep-shearing.
n.
Act of shearing sheep.
a.
See Couple-close.
n.
One who compiles; esp., one who makes books by compilation.
imp. & p. p.
of Comply
a.
Repeatedly compound; made up of complex constituents.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
a.
Intricate; entangled; complicated; complex.