From the documentation, it is clear that

LineIntegralConvolutionPlot[{Subscript[v, x],Subscript[v, y]},{x,Subscript[x, min],Subscript[x, max]},{y,Subscript[y, min],Subscript[y, max]}]

can be used to generate plots for square geometries with geometry specified by

{x,Subscript[x, min],Subscript[x, max]},{y,Subscript[y, min],Subscript[y, max]}

How can we generate the corresponding non-square plots, for example, specified by reg (Region function)? What I mean is, how to generate these plots if the geometry is non-rectangular?
Also, what does the "white noise" mentioned on the function page represent? What does it signify? Thanks in advance!