# 24 More Forms of Visualization

 24 More Forms of Visualization
We’ve seen how to plot lists of data with ListPlot and ListLinePlot. If you want to plot several sets of data at the same time, you just have to give them in a list.
Plot two sets of data at the same time:
ListLinePlot[{{1, 3, 4, 3, 1, 2}, {2, 2, 4, 5, 7, 6, 8}}]

The PlotStyle option lets you specify the style for each set of data:
ListLinePlot[{{1, 3, 4, 3, 1, 2}, {2, 2, 4, 5, 7, 6, 8}}, PlotStyle -> {Red, Dotted}]

The Mesh option lets you show the actual data points too:
ListLinePlot[{{1, 3, 4, 3, 1, 2}, {2, 2, 4, 5, 7, 6, 8}}, Mesh -> All, MeshStyle -> Red]

As well as looking at the sequence of values in a list, it’s also very common to want to see how often different values occur. You can do this with Histogram.
Here are the lengths of the first 30 common English words:
StringLength[Take[WordList[ ], 30]]

Histogram[StringLength[Take[WordList[ ], 200]]]

Including all the words gives a smoother result:
Histogram[StringLength[WordList[ ]]]

Find an array of height values around Mount Everest, and plot it in 3D:
ListPlot3D[ GeoElevationData[ GeoDisk[ Entity["Mountain", "MountEverest"] , Quantity[2, "Miles"]]]]

Show it without a mesh:
ListPlot3D[ GeoElevationData[ GeoDisk[ Entity["Mountain", "MountEverest"] , Quantity[2, "Miles"]]], MeshStyle -> None]

Make a contour plot, in which successive ranges of heights are separated by contour lines:
ListContourPlot[ GeoElevationData[ GeoDisk[ Entity["Mountain", "MountEverest"] , Quantity[2, "Miles"]]]]

When one’s dealing with large amounts of data, it’s often better to use a simpler visualization, such as a relief plot, that essentially just colors according to height.
Make a relief plot of the topography 100 miles around Mount Everest:
ReliefPlot[ GeoElevationData[ GeoDisk[ Entity["Mountain", "MountEverest"] , Quantity[100, "Miles"]]]]

24.1Make a plot with lines joining the squares, the cubes and the 4th powers of integers up to 10. »
Expected output:
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24.2Make a plot of the first 20 primes, joined by a line, filled to the axis and with a red dot at each prime. »
Expected output:
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24.3Make a 3D plot of the topography for 20 miles around Mount Fuji. »
Expected output:
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24.4Make a relief plot of the topography for 100 miles around Mount Fuji. »
Expected output:
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24.5Make a 3D plot of heights generated from Mod[i, j] with i and j going up to 100. »
Expected output:
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24.6Make a histogram of the differences between successive primes for the first 10000 primes. »
Expected output:
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24.7Make a histogram of the first digits of squares of integers up to 10000 (illustrating Benford’s law). »
Expected output:
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24.8Make a histogram of the length of Roman numerals up to 1000. »
Expected output:
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24.9Make a histogram of sentence lengths in the Wikipedia article on computers. »
Sample expected output:
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24.10Make a list of histograms of 10000 instances of totals of n random reals up to 100, with n going from 1 to 5 (illustrating the central limit theorem). »
Sample expected output:
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24.11Generate a 3D list plot using the image data from a binarized size-200 letter “W” as heights. »
Expected output:
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+24.1Make a histogram of word lengths in the Wikipedia article on computers. »
Sample expected output:
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What other kinds of visualizations are there?
How do I combine plots I’ve generated separately?
Use Show to combine them on common axes. Use GraphicsGrid, etc. (see Section 37) to put them side by side.
How can I specify the bins to use in a histogram?
Histogram[list, n] uses n bins. Histogram[list, {xmin, xmax, dx}] uses bins from xmin to xmax in steps dx.
What’s the difference between a bar chart and a histogram?
A bar chart is a direct representation of data; a histogram represents the frequency with which data occurs. In a bar chart, the height of each bar gives the value of a single piece of data. In a histogram, the height of each bar gives the total number of pieces of data that occur within the x range of the bar.
How can I draw contour lines on a 3D topography plot?
Use . The (#3&) is a pure function (see Section 26) that uses the third (z) coordinate to make a mesh.
How do I label heights in a contour plot?