A three.js app to visualize vector fields.
Live here! You can check out the 3D version here!
Set equations for the x and y components of the vector field using variables x and y, representing the location of the point in the coordinate system, along with t representing elapsed time. You can also use any JavaScript math function, such as Math.sin.
There's also an option to plot a shape as it deforms in the vector field over time. x/y length control the length of that shape. You can set the amount of cross-sections to deform (more cross sections = more CPU intensive). The rest of the settings are self explanatory.
I don't visualize the magnitudes of the vectors because it would get real ugly real quick.