Time-dependent vector field
Warning: Online version is slow. Works better in your desktop.
Download the file so you can increase the number of particles, if you want.
You can draw something like the image below by activating the Trace box. Have fun.
Try this field:
F(t,x,y) = -π 0.5 sin(π (0.25sin(2π / 10 t) x² + (1 - 2 (0.25) sin(2π / 10 t)) x)) cos(π y)
G(t,x,y) = π 0.5 cos(π (0.25sin(2π / 10 t) x² + (1 - 2 (0.25) sin(2π / 10 t)) x)) sin(π y) (2 (0.25) sin(2π / 10 t) x + 1 - 2 (0.25) sin(2π / 10 t))
You will need to zoom in!