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.

In[1]:= |

Out[1]= |

In[2]:= |

Out[2]= |

The Mesh option lets you show the actual data points too:

In[3]:= |

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 Histogram.

In[4]:= |

Out[4]= |

The histogram shows how often each length occurs among the first 200 words:

In[5]:= |

Out[5]= |

In[6]:= |

Out[6]= |

Sometimes you’ll have data you want to visualize in 3D. For example, GeoElevationData can give an array of height values. ListPlot3D makes a 3D plot.

In[7]:= |

Out[7]= |

Show it without a mesh:

In[8]:= |

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]:= |

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]:= |

Out[10]= |

ListLinePlot[{list_{1},list_{2},...}] | plot several lists together | |

Histogram[list] | make a histogram | |

ListPlot3D[array] | plot an array of heights in 3D | |

ListContourPlot[array] | plot contours for an array of heights | |

ReliefPlot[array] | make a relief plot | |

GeoElevationData[region] | array of geo elevations for a region | |

PlotStyle | option for styling each set of data | |

Mesh | whether to have a mesh of points or lines | |

MeshStyle | option for styling a mesh |

24.1Make a plot with lines joining the squares, the cubes and the 4th powers of integers up to 10. »

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. »

24.4Make a relief plot of the topography for 100 miles around Mount Fuji. »

24.6Make a histogram of the differences between successive primes for the first 10000 primes. »

24.7Make a histogram of the first digits of squares of integers up to 10000 (illustrating

*Benford’s law*). »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). »

24.11Generate a 3D list plot using the image data from a binarized size-200 letter “W” as heights. »

+24.1Make a histogram of word lengths in the Wikipedia article on computers. »

What other kinds of visualizations are there?

Lots. Like ListStepPlot and ListStreamPlot, or BubbleChart and BarChart3D, or SmoothHistogram and BoxWhiskerChart, or AngularGauge and VerticalGauge.

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?

How can I draw contour lines on a 3D topography plot?

Use MeshFunctions(#3&). The (#3&) is a

*pure function*(see Section 26) that uses the third (*z*) coordinate to make a mesh.- The Wolfram Language makes many automatic choices for visualization functions. You can override these choices using options.
- An alternative to using PlotStyle is to insert Style directly into the data given to functions like ListLinePlot.
- At least over much of the Earth, GeoElevationData has data measurements down to a resolution of about 40 meters.