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Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
Parametric equation. Representation of a curve by a function of a parameter. The butterfly curve can be defined by parametric equations of x and y. In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. [1] Parametric equations are commonly used to express the ...
The formula is a general-purpose method of decoding a bitmap stored in the constant , and it could be used to draw any other image. When applied to the unbounded positive range , the formula tiles a vertical swath of the plane with a pattern that contains all possible 17-pixel-tall bitmaps. One horizontal slice of that infinite bitmap depicts ...
Semi-log plot of the Internet host count over time shown on a logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved. Unlike a linear scale where each unit of distance ...
A cobweb plot, known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the logistic map. The technique was introduced in the 1890s by E.-M. Lémeray. [1] Using a cobweb plot, it is possible to ...
For quadratic Bézier curves one can construct intermediate points Q 0 and Q 1 such that as t varies from 0 to 1: Point Q 0 (t) varies from P 0 to P 1 and describes a linear Bézier curve. Point Q 1 (t) varies from P 1 to P 2 and describes a linear Bézier curve. Point B(t) is interpolated linearly between Q 0 (t) to Q 1 (t) and describes a ...
Escape time algorithm. The simplest algorithm for generating a representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel.
The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve. The notation curl F is more common in North America.