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More Forms of Visualization
We’ve seen how to plot lists of data with and . 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:
In[1]:=
ListLinePlot[{{1,3,4,3,1,2},{2,2,4,5,7,6,8}}]
Out[1]=
The option lets you specify the style for each set of data:
In[2]:=
ListLinePlot[{{1,3,4,3,1,2},{2,2,4,5,7,6,8}},PlotStyle{Red,Dotted}]
Out[2]=
The option lets you show the actual data points too:
In[3]:=
ListLinePlot[{{1,3,4,3,1,2},{2,2,4,5,7,6,8}},MeshAll,MeshStyleRed]
Out[3]=
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 .
Here are the lengths of the first 30 common English words:
In[4]:=
StringLength[Take[WordList[],30]]
Out[4]=
{1,3,8,5,6,5,7,7,9,11,5,9,5,7,9,5,9,8,4,6,5,5,10,11,12,8,10,7,9,6}
The histogram shows how often each length occurs among the first 200 words:
In[5]:=
Histogram[StringLength[Take[WordList[],200]]]
Out[5]=
Including all the words gives a smoother result:
In[6]:=
Histogram[StringLength[WordList[]]]
Out[6]=
Sometimes you’ll have data you want to visualize in 3D. For example, can give an array of height values. makes a 3D plot.
Find an array of height values around Mount Everest, and plot it in 3D:
In[7]:=
ListPlot3D[GeoElevationData[GeoDisk[,]]]
Out[7]=
Show it without a mesh:
In[8]:=
ListPlot3D[GeoElevationData[GeoDisk[,]],MeshStyleNone]
Out[8]=
An alternative visualization is a contour plot, in which one’s effectively looking from above, and drawing contour lines at evenly spaced heights.
Make a contour plot, in which successive ranges of heights are separated by contour lines:
In[9]:=
ListContourPlot[GeoElevationData[GeoDisk[,]]]
Out[9]=
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:
In[10]:=
ReliefPlot[GeoElevationData[GeoDisk[,]]]
Out[10]=
Vocabulary
list 1 list 2 | plot several lists together | |
make a histogram | ||
plot an array of heights in 3D | ||
plot contours for an array of heights | ||
make a relief plot | ||
array of geo elevations for a region | ||
option for styling each set of data | ||
whether to have a mesh of points or lines | ||
option for styling a mesh |
Exercises |
Q&A
What other kinds of visualizations are there?
How do I combine plots I’ve generated separately?
How can I specify the bins to use in a histogram?
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?
How do I label heights in a contour plot?
Tech Notes
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The Wolfram Language makes many automatic choices for visualization functions. You can override these choices using options.
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