VISUALIZING VECTOR FIELDS

An introduction to using the Java Microscope developed by Shannon Holland and Matthias Kawski.
(The above site is a local mirror of the original site, which can be accessed here.)

Quick Start:

• Think of a vector field F = Mi+Nj.
• Enter the components M, N of your vector field in the boxes labeled M, N.
• Click on the button labeled Draw Vector Field.
• Click anywhere in the picture to bring up a magnified image.

• Enter a vector field as above.
• Click on the tab labeled Lens.
• Select a type of lens (see below) from the pulldown menu.
• Click anywhere in the picture to bring up a magnified image.

• Contin: Shows the vector field as seen from rest.
• Deriv: Shows the vector field as seen from comoving observer.

  (This is the derivative of the vector field!)

• Radial: Shows the radial component as seen from comoving observer.

  (Integrate this around a loop to get the divergence!)

• Circ: Shows the tangential component as seen from comoving observer.

  (Integrate this around a loop to get the curl!)

• Div: The pure divergence part of the vector field (for sufficiently high magnification).
• Curl: The pure curl part of the vector field (for sufficiently high magnification).
• Comm: Combines the divergence and curl.
• The other lenses show the shear, which does not contribute to either the curl or the divergence.
• Use the sliders to adjust the magnification.

• Click on the tab labeled Flow.
• Click and drag anywhere in the picture to create a rectangle.

  When you let go, the rectangle will be distorted along the flow lines!

• Use the slider to adjust the speed.
• Use the top buttons to look at different parts of the flow
• Use the bottom buttons to look at different shapes.

This page written by Tevian Dray in May 2001.