... For my own game I think it would be nice to have
wind blowing over the sand.
I think it would be appropriate to generate noise and displace it each frame.
Do you have any idea of what type of patterns I should look into (noise generation)?
I think in general something looking similar to how light is refracted on the ocean sand would feel nice, if it's also translated constantly.
Aka something like this
Or any other suggestions how the windy desert should look like? thanks.
May sound a little bit over the top, and I think there are much cheaper
solution, but given that the caustics are in part due to the elevation of
the water's/waves height, why not try to use the Shallow Water equation with
some randomization for simulating the movements of sand/dunes? The Shallow
Water equation, despite being a rude approximation to the Navier-Stokes equation,
shares some similarity to the Korteweg–de Vries equation from which one can
compute pattern/texture formation (see the formation of a Leopard's texture as
he grows). It basically comes down, if I remember correctly, to compute the
so-called solitons (wave patterns etc.) which can combine with others yet
won't be altered in the process such that they can separate again without
any distortions in shape. The thing is that the Korteweg–de Vries equation,
and for that matter the Shallow water equation, are of advective/hyperbolic
type, which share some similarity to the wave equation, and hence, these
equations will transport the forming patterns/waves around.
The Shallow Water equations was studied and used a lot for gaming etc. to
approximate cool looking waves/ripples as seen in many games. So there should
be some documentation using it for games. And I think it can be recast into
a sand/dune setting.
Here is a solution of the Shallow Water equation
Wiki
Don't know if these things will fit your game or are way to complex whatever,
but depending on the game it may also lead to other interesting stuff in the
process, i.e. gameplay-wise etc. Who knows.