Download 1.9.6 Contour and Density Plots

1. A Practical Introduction to Mathematica
176
1.9.6 Contour and Density Plots
ContourPlot f, {x, xmin, xmax}, {y, ymin, ymax}]
make a contour plot of f as a function of x and y
DensityPlot f, {x, xmin, xmax}, {y, ymin, ymax}]
make a density plot of f
Contour and density plots.
This gives a contour plot of the function
sin(x) sin(y).
In 1]:= ContourPlot Sin x] Sin y], {x, -2, 2}, {y, -2, 2}]
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A contour plot gives you essentially a “topographic map” of a function. The contours join points on
the surface that have the same height. The default is to have contours corresponding to a sequence of
equally spaced z values. Contour plots produced by Mathematica are by default shaded, in such a way
that regions with higher z values are lighter.
Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected];
http://www.wolfram.com/; 1-800-441-6284.
 1991 Wolfram Research, Inc.
Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited.
1.9 Graphics and Sound
177
option name
default value
ColorFunction
Automatic
what colors to use for shading; Hue uses a sequence of
hues
Contours
10
the total number of contours, or the list of z values for
contours
PlotRange
Automatic
the range of values to be included; you can specify
{zmin, zmax}, All or Automatic
ContourShading
True
whether to use shading
ContourSmoothing
None
what smoothing to use for contour lines
PlotPoints
15
number of evaluation points in each direction
Compiled
True
whether to compile the function being plotted
Some options for ContourPlot. The first set can also be used in Show.
Particularly if you use a display or
printer that does not handle gray levels
well, you may find it better to switch off
shading in contour plots.
In 2]:= Show %, ContourShading -> False]
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Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected];
http://www.wolfram.com/; 1-800-441-6284.
 1991 Wolfram Research, Inc.
Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited.
1. A Practical Introduction to Mathematica
178
This increases the density of contours,
and tells Mathematica to apply a
smoothing algorithm to each contour.
In 3]:= Show %, Contours -> 30, ContourSmoothing -> Automatic]
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You should realize that if you do not evaluate your function on a fine enough grid, there may be inaccuracies in your contour plot. One point to notice is that whereas a curve generated by Plot may be
inaccurate if your function varies too quickly in a particular region, the shape of contours can be inaccurate if your function varies too slowly. A rapidly varying function gives a regular pattern of contours,
but a function that is almost flat can give irregular contours. You can often use the ContourSmoothing
option to ContourPlot to reduce the visual impact of these irregularities.
Density plots show the values of your
function at a regular array of points.
Lighter regions are higher.
In 4]:= DensityPlot Sin x] Sin y], {x, -2, 2}, {y, -2, 2}]
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Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected];
http://www.wolfram.com/; 1-800-441-6284.
 1991 Wolfram Research, Inc.
Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited.
1.9 Graphics and Sound
179
You can get rid of the mesh like this.
But unless you have a very large
number of regions, plots usually look
better when you include the mesh.
In 5]:= Show %, Mesh -> False]
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option name
default value
ColorFunction
Automatic
what colors to use for shading; Hue uses a sequence of
hues
Mesh
True
whether to draw a mesh
PlotPoints
15
number of evaluation points in each direction
Compiled
True
whether to compile the function being plotted
Some options for DensityPlot. The first set can also be used in Show.
Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected];
http://www.wolfram.com/; 1-800-441-6284.
 1991 Wolfram Research, Inc.
Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited.