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.

• Zoom 0th kind: Shows the vector field as seen from rest.
• Zoom 1st kind: Shows the vector field as seen from comoving observer.
• Radial component: Shows the radial component as seen from comoving observer.
  (Integrate this around a loop to get the divergence!)

  Tangential component: Shows the tangential component as seen from comoving observer.

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

  Trace*identity: The pure divergence part of the vector field (for sufficiently high magnification).

  Skew symmetric: The pure curl part of the vector field (for sufficiently high magnification).

• Click on the tab labeled Flows.
• Click and drag anywhere in the picture to create a rectangle.
  When you let go, the rectangle will be distorted along the flow lines!