Then I added the Anything Grows modifier to the grid. I used a low strand count (500) so that it would be easier to see what the individual strands were doing (I also turned off shadows for the grid to aid viewing). I used a width of .1, a length of 3, two segments per strand and a Stiffness of zero.

I changed the Gravity Direction Z to 0%. X and Y were already at 0%, and I left them there.