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How you generate the initial snow (Particles)
I am trying to generate the initial snow (with particles) in Blender, but the result is bad, so I wonder what algorithm you use to generate the snow particles in Houdini? I want the result from your video.

Here is my result in Blender:

Do you have any suggestions? Thank you for taking your time to read my issue.
I randomly fill a volume with particles, it is a built-in Houdini op. The algorithm used is probably equivalent to Blender's volume emission particle system.
Oh, I did the same, but randomly fill with particles, and render them with white color by using OpenGL shaders. Maybe I can randomly change the particle color's alpha channel ranged from 0.0 to 1.0, and see the result.
You are probably referring to the coloring/texturing/shading of the snow block. That is actually separate from the physics system all together. You can look up some tutorials on how to make a snow shader, looks like there are some for Blender; but you could adapt tutorials for other software as well. Snow in 3d graphics has got a lot more popular since I first was working on this, so looks like some people have come up with more realistic techniques for snow shaders since then.
For rendering, you will likely need to convert your particle system to either a volume or mesh, and often times to convert to a mesh you first have to convert to a volume. Blender has a volume to mesh modifier, but I'm not sure off hand whether there is a way to convert a particle system to volume. If you are planning on writing a simulator for blender, I suspect you could generate a volume alongside the particle updates if there isn't a builtin conversion or plugin already.
Sorry... hit "close with comment" accidentally
No problem, I will check for some snow shaders as you mentioned above. thank you very much for the time.