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4.3 Special Two-Dimensional Plots
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Discrete functions, i.e., functions defined on a discrete set, can be visualized using the special plotting function ListPlot.
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ListPlot[{y1, y2,...}] plots points whose y-coordinates are y1, y2, . . . The x-coordinates are taken to be the positive integers, 1, 2, . . . ListPlot[{{x1, y1}, {x2, y2},...}] plots the points (x1, y1), (x2, y2), . . .
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Standard graphics options are permitted. The form of the command would then be
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ListPlot[{y1, y2, ...}, options] or ListPlot[{{x1, y1}, {x2, y2},...}, options]
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The most useful graphics options used with ListPlot are
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PlotStyle PointSize[d] where d specifies the diameter of the point as a fraction of the overall width of the graph. The default value is .008. In addition, the following symbolic forms can be used: Tiny, Small, Medium, and Large. These specify point sizes independent of the total width of the graphic. 1 PlotStyle AbsolutePointSize[d] where d is measured in printer s points, equal to 72 of an inch. PlotMarkers Automatic will cause the point markers to take different shapes, e.g., circles, squares, diamonds, etc. This is useful when two or more sets of points are to be plotted. Filling Axis fills the graph vertically to the horizontal axis. Filling Bottom fills the graph vertically to the bottom of the graph. Filling Top fills the graph vertically to the top of the graph. Filling v fills the graph vertically to the value v.
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EXAMPLE 31 The following plots a list of the squares of the positive integers 1 through 20.
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squares = Table[k2, {k, 1, 20}]; ListPlot[squares]
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400 300 200 100
ListPlot[squares, PlotStyle PointSize[.03]]
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EXAMPLE 32
randomintegers = Table[RandomInteger,[{1, 20}], {k, 1, 30}]; ListPlot[randomintegers]
The Table command generates a list of 30 random integers, each between 1 and 20.
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ListPlot[randomintegers,Filling Axis]
ListLinePlot[{y1, y2,...}] plots points whose y-coordinates are y1, y2, . . . and connects them with line segments. The x-coordinates are taken to be the positive integers. ListLinePlot[{{x1, y1}, {x2, y2},...}] plots the points (x1, y1), (x2, y2), . . . and connects them with line segments. ListLinePlot[list 1, list 2, ...] plots multiple lines through points defined by list 1, list2, . . .
The options for ListPlot may be used for ListLinePlot. The Filling option may be used to create a filled polygon that describes the data.
EXAMPLE 33 (Continuation of Example 32)
ListLinePlot[randomintegers]
ListLinePlot[randomintegers, Filling Axis]]
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Different types of bar graphs can be drawn with Mathematica, using the command BarChart. Note: Starting with version 7, BarChart can be found in the Mathematica kernel. If you are using version 6, you will find BarChart in the package BarCharts` which must be loaded prior to use. See the Documentation Center for appropriate usage.
BarChart[datalist] draws a simple bar graph. datalist is a set of numbers enclosed within braces. BarChart[{datalist1, datalist2,...}] draws a bar graph containing data from multiple data sets. Each data list is a set of numbers enclosed within braces.
EXAMPLE 34
dataset1 = {1, 2, 3, 4, 5}; dataset2 = {6, 5, 4, 3, 2}; g1 = BarChart[dataset1]; g2 = BarChart[{dataset1, dataset2}]; GraphicsArray[{g1, g2}]
5 4 3 2 1 6 5 4 3 2 1
If a customized look is desired, there are a variety of options that can be invoked. The format of the command with options becomes
BarChart[datalist, options] BarChart[{datalist1, datalist2,...}, options]
Some of the more popular options are Chartstyle g specifies that style option g should be used to draw the bars. Examples of style options are GrayLevel, Hue, Opacity, RGBColor, and Colors (Red, Blue, etc.). Chartstyle {g1, g2,...} specifies that style options g1, g2, . . . should be used cyclically. ChartLayout "layout" specifies that a layout of type layout should be used to draw the graph. Examples of layouts are "Stacked", in which case the bars are stacked on top of each other rather than placed side by side, and "Percentile", which generates a stacked bar chart with the total height of each bar constant at 100%. BarSpacing controls the spacing between bars and between groups of bars. The default is BarSpacing Automatic which allows Mathematica to control the spacing. BarSpacing s allows a space of s between bars within each data set. The value of s is measured as a fraction of the width of each bar. BarSpacing {s, t} allows a space of s between bars within each data set and a value of t determines the space between data sets. The values of s and t are measured as a fraction of the width of each bar. In each of the preceding BarSpacing commands, the values of s and t may be replaced by the predefined symbols None, Tiny, Small, Medium and Large.
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