In mathematics, the complex squaring map, a polynomial mapping of degree two, is a simple and accessible demonstration of chaos in dynamical systems. It...

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...

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...

from complex quadratic map Koch snowflake - special case of de Rham curve Lyapunov fractal Mandelbrot set - derived from complex quadratic map Menger...

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...

the principal square root. Square roots of negative numbers can be discussed within the framework of complex numbers. More generally, square roots can be...

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...

} 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...

together) as when a covering map degenerates at a point of a space, with some collapsing of the fibers of the mapping. In complex analysis, the basic model...

conformal map. Each is hosted by its own real algebra, ordinary complex numbers, split-complex numbers, and dual numbers. The conformal maps are described...

2012. Sieczkowski, Cavan (January 29, 2013). "Google Maps North Korea: Prison Camps, Nuclear Complexes Pinpointed In New Images (PHOTOS)". The Huffington...

trace squared as a proxy for the eccentricity squared, as was done above; these classifications (but not the exact eccentricity values, since squaring and...

^{n}} , such that the transition maps are holomorphic. The term "complex manifold" is variously used to mean a complex manifold in the sense above (which...

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...

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);...

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...

other meridians as complex curves, and parallels as circular arcs. Azimuthal In standard presentation, azimuthal projections map meridians as straight...

facades characteristic of Newar architecture. The central square is surrounded by palace complexes built during the Malla and Shah periods. The most well...

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...

the square. When the forces of the Eight-Nation Alliance besieged Beijing during the Boxer Rebellion in 1900, they badly damaged the office complexes and...

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...

an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. The map was initially utilized by Edward...

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...

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...

(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....

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...

result in complex differential geometry that estimates the (squared) pointwise norm | ∂ f | 2 {\displaystyle |\partial f|^{2}} of a holomorphic map f : (...

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...

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...

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...