Specify the density of seed points for the streamlines:

Specify specific seed points for the streamlines:

Plot streamlines over a specified region:

Streamlines are drawn as lines by default:

Use 3D tubes for the streamlines:

Use flat ribbons:

Use "arrow" versions of the stream markers to indicate the direction of flow along the streamlines:

Arrows on tubes:

Ribbons are turned into arrows by tapering the heads and notching the tails of the streamlines:

Use a single color for the streamlines:

Use a named color gradient for the streamlines:

Include a legend for the field magnitude:

Use StreamScale to split streamlines into multiple shorter line segments:

Increase the number of points in each segment and increase the marker aspect ratio:

Use a theme:

Use a log scale for the x axis:

Reverse the y scale so it increases toward the bottom:

By default, Axes are drawn:

Use Axes False to turn off axes:

Turn each axis on individually:

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

By default, BoxRatios is set to Automatic :

Make the box twice as long in the x direction:

Use named sizes, such as Tiny , Small , Medium and Large :

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatio Full will fill the available space:

Use maximum sizes for the width and height:

Use ImageSize Full to fill the available space in an object:

Specify the image size as a fraction of the available space:

No legends are included by default:

Include a legend that indicates the vector field norm:

Specify the location of the legend:

Specify a theme:

Show the region defined by a RegionFunction :

Use None to avoid showing the boundary:

Specify the color of the region boundary:

The boundaries of full rectangular regions are not shown:

Plot streamlines in a ball:

Plot streams only where the field magnitude exceeds a given threshold:

Region functions depend, in general, on seven arguments:

Use RegionBoundaryStyle None to avoid showing the boundary:

Use a log scale for the x axis:

Reverse the y scale so it increases toward the bottom:

Color the streams by their norm:

Use any named color gradient from ColorData :

Color the streamlines according to their x value:

Use StreamColorFunctionScaling False to get unscaled values:

By default, scaled values are used:

Use StreamColorFunctionScaling False to get unscaled values:

By default, lines are used:

Draw the streamlines as tubes:

Draw them as flat ribbons:

"Arrow" stream markers automatically break the streamlines into shorter segments:

Use 3D arrowheads on tubes:

Use directional ribbons:

Make segmented markers continuous:

Break continuous markers into segments:

Use automatically determined stream points to seed the curves:

Specify a maximum number of streamlines:

Give specific seed points for the streams:

Use coarsely spaced streamlines:

Use more finely spaced streamlines:

Segmented markers have default lengths, numbers of points and aspect ratios:

Modify the lengths of the segments:

Specify the number of sample points in each segment:

Modify the aspect ratios for the stream markers:

Make segmented markers continuous:

Break continuous markers into segments:

The aspect ratio controls the thickness of ribbons and tubes:

Increase the width of the ribbons and tubes:

The aspect ratio controls the sizes of arrowheads:

Control the number of points in each segment:

Change the appearance of the streamlines:

StreamColorFunction takes precedence over StreamStyle :

Use StreamColorFunction None to specify a streamline color with StreamStyle :

Ticks are placed automatically in each plot:

Use Ticks None to not draw any tick marks:

Place tick marks at specific positions:

Draw tick marks at the specified positions with the specified labels:

Specify tick marks with scaled lengths:

Customize each tick with position, length, labeling and styling:

By default, the ticks and tick labels use the same styles as the axis:

Specify overall tick style, including the tick labels:

Specify tick style for each of the axes:

Consider a vector differential equation where f(x)=If[TemplateBox[{x}, Norm]<=1,x,{1,0,0}] is defined piecewise.

Visualize solutions of using seed points for the streamlines that are inside the unit sphere:

Consider Stokes flow for a point force of the form , where is a constant vector and is a Dirac delta function. For example, a force pointing down:

Define the fluid velocity vector , the pressure and the viscosity :

Confirm that the equations for Stokes flow are satisfied so that and :

Plot streamlines for the flow:

Visualize Stokes flow around a unit sphere. Define the fluid velocity vector , the pressure , the viscosity and the far-field fluid speed :

Confirm that the equations for Stokes flow are satisfied so that and :

Plot streamlines for the flow:

Plot the pressure for the flow:

Specify the Navier–Stokes equations for a fluid through a pipe with a bulge:

Specify the geometry for the flow:

Specify the boundary conditions for flow from left to right:

Solve for the flow velocities and pressure:

Specify seed points for the streamlines:

Plot the streamlines for the flow:

Visualize electric field lines for a dipole:

The streamlines appear to have uniform color because of the extremely rapid change in the vector field norm near the point charges at . Bounding the magnitude of the vector field norm with a region function makes the colors visible:

Add spheres to indicate the positive (red) and negative (black) point charges:

Arrows can be used to provide more information, but the colors change because arrow markers are colored by the field magnitude at the tip of the arrow:

Use a custom StreamColorFunction to exert more control over the colors:

Lorenz attractor:

Use ribbons or arrow ribbons to visualize the torsion of a twisted cubic:

Visualize solutions of differential equations on manifolds:

Visualize streamlines for Poiseuille flow. The fluid speed is fastest along the central axis:

Visualize solutions of Euler's equations for a rotating rigid body: