Data visualization

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Scatter diagram

A scatter diagram, also called a scatterplot or a scatter plot, is a visualization of the relationship between two variables measured on the same set of individuals. Scatter diagrams for lists of data , , ... can be generated with the Wolfram Language using ListPlot[x1, y1, x2, y2, ...].A scatter diagram makes it particularly easy to spot trends and correlations between the two variables. For example, the scatter diagram illustrated above plots wine consumption (in liters of alcohol from wine per person per year) against deaths from heart disease (in deaths per 100,000 people) for 19 developed nations (Moore and McCabe 1999, Ex. 2.5)There is clearly and inverse relationship between these two variables. Once such a relationship has been found, linear regression can be used to find curves of best fit. The graph above shows the same scatter diagram as above together with a line of best fit...

Level set

The level set of a differentiable function corresponding to a real value is the set of pointsFor example, the level set of the function corresponding to the value is the sphere with center and radius .If , the level set is a plane curve known as a level curve. If , the level set is a surface known as a level surface.

Web diagram

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function . In particular, the segments of the diagram connect the points , , , .... The diagram is so-named because its straight line segments "anchored" to the functions and can resemble a spider web. The animation above shows a web diagram for the logistic map with .

Recurrence plot

A recurrence plot is defined as a plot of the quantitywhere is the Heaviside step function and denotes a norm. A recurrence plot is therefore a binary plot. The figure above shows a recurrence plot for the Lorenz attractor with , , , , , , and .Recurrence plots were initially used to graphically display nonstationarity in time series (Eckmann et al. 1987, Gao and Cai 2000), but are also useful for visualizing functions.A so-called global recurrence plot or unthresholded recurrence plot of a function is a plot of (or ) in the - plane. Recurrence plots for a number of common functions are illustrated above.

Pólya plot

A Pólya plot is a plot of the vector field of of a complex function . Several examples are shown above.Pólya plots can be created in the WolframLanguage using the following code: PolyaFieldPlot[f_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_}, opts : OptionsPattern[]] := VectorPlot[Evaluate @ {Re[f], -Im[f]}, {x, xmin, xmax}, {y, ymin, ymax}, VectorScale -> {Automatic, Automatic, Log[#5 + 1]&}, opts ]

Function graph

Given a function defined on a domain , the graph of is defined as the set of points (which often form a curve or surface) showing the values taken by over (or some portion of ). Technically, for real functions,(1)(2)A graph is sometimes also called a plot. Unfortunately, the word "graph" is uniformly used by mathematicians to mean a collection of vertices and edges connecting them. In some education circles, the term "vertex-edge graph" is used in an attempt to distinguish the two types of graph. However, as Gardner (1984, p. 91) notes, "The confusion of this term with the 'graphs' of analytic geometry is regrettable, but the term has stuck [in the mathematical community]." In this work, the term "graph" will therefore be used to refer to a collection of vertices and edges, while a graph in the sense of a plot of a function will be called a "function graph" when any ambiguity arises.Two-..

Contour plot

A plot of equipotential curves. If desired, the regions between contours can be shaded or colored to indicate their magnitude. Contour plots are implemented in the Wolfram Language as ContourPlot[f, x, xmin, xmax, y, ymin, ymax].

Binary plot

A binary plot of an integer sequence is a plot of the binary representations of successive terms where each term is represented as a column of bits with 1s colored black and 0s colored white. The columns are then placed side-by-side to yield an array of colored squares. Several examples are shown above for the positive integers , square numbers , Fibonacci numbers , and binomial coefficients .Binary plots can be extended to rational number sequences by placing the binary representations of numerators on top, and denominators on bottom, as illustrated above for the sequence .Similarly, by using other bases and coloring the base- digits differently, binary plots can be extended to n-ary plots.

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