Plotting and Visualization

Graphics are expressions like any other, so you can store, combine, and transform them. This lesson describes each plot rather than showing it.

More kinds of plots

Plot3D[Sin[x] Cos[y], {x, -3, 3}, {y, -3, 3}]
ContourPlot[x^2 + y^2, {x, -2, 2}, {y, -2, 2}, Contours -> 5]
ParametricPlot[{Cos[t], Sin[2 t]}, {t, 0, 2 Pi}]
PolarPlot[1 + Cos[t], {t, 0, 2 Pi}]
DensityPlot[Sin[x y], {x, 0, 3}, {y, 0, 3}]

• Plot3D draws a surface you can rotate with the mouse.
• ContourPlot shows level curves — here five circles. It also plots equations: ContourPlot[x^2 + y^2 == 1, ...] draws a circle.
• ParametricPlot and PolarPlot draw curves given by formulas in t.

Styling

Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi},
  PlotStyle -> {Blue, {Red, Dashed}},
  PlotRange -> {-1.5, 1.5},
  Frame -> True,
  FrameLabel -> {"x", "value"},
  PlotTheme -> "Scientific"]

Every plotting function takes options; look them up on the function's documentation page. PlotTheme sets many at once.

Combining graphics

p1 = Plot[x^2, {x, -2, 2}];
p2 = ListPlot[{{-1, 1}, {0, 0}, {1, 1}}, PlotStyle -> Red];
Show[p1, p2]
GraphicsGrid[{{p1, p2}}]

• Show overlays graphics on the same axes.
• GraphicsGrid, GraphicsRow, and GraphicsColumn place them side by side.

Drawing with primitives

Graphics[{Blue, Disk[{0, 0}, 1], Red, Rectangle[{1, 1}, {2, 2}],
  Black, Line[{{-1, -1}, {2, 2}}], Text["origin", {0, -1.2}]}]

A graphic is a list of primitives (Point, Line, Circle, Disk, Rectangle, Polygon, Text) and directives (colors, Thick, Dashed, Opacity) that apply to what follows.

Interactivity and animation

Manipulate[
  Plot[a Sin[b x + c], {x, 0, 2 Pi}, PlotRange -> {-3, 3}],
  {a, 1, 3}, {b, 1, 5, 1}, {{c, 0, "phase"}, 0, 2 Pi}]

Three sliders: {b, 1, 5, 1} moves in steps of 1, and {{c, 0, "phase"}, 0, 2 Pi} sets an initial value and a label. Animate works the same way but plays automatically. ListAnimate turns a list of frames into an animation.

Exporting

Export["surface.png", Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}], ImageResolution -> 200]
Export["wave.gif", Table[Plot[Sin[x + t], {x, 0, 2 Pi}], {t, 0, 2 Pi, Pi/8}]]

surface.png
wave.gif

A list of graphics exported to GIF becomes an animation. Vector formats (PDF, SVG) are best for papers and slides.