Math Insight

Applet: Example three-dimensional vector field

Applet: Example three-dimensional vector field

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The structure of the vector field is difficult to visualize, but rotating the graph with the mouse helps a little. This vector field has both nonzero divergence and curl.

The vector field is $\dlvf = (-y, xy,z)$. Its divergence is $\div \dlvf(x,y,z) = x+1$, and its curl is $\curl \dlvf = (0,0,y+1)$

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The applet was made using three.js and requires Javascript as well as a browser that supports WebGL. For most three.js applets, you can drag with the mouse to rotate the view, drag with the right button to pan, and zoom in/out with the mouse wheel. Many applets contain points that you can drag to change values of variables.