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I'm trying to use an animated ramp in the geometry opacity channel and would like to use the noise function that C4D has in their native ramps. Is there a way to add an animated noise function like the one in C4D, or recreate it within Arnold? I'm using it to both be a texture to emit particles and to make the emitter object invisible.
You can't use the Gradient directly in Arnold. You can use the C4D Noise shaders, custom Arnold noise shaders, read the U or V coordinate with a state_float shader, etc. I don't know the exact math behind that noise function in the Gradient, so I'm not sure you can replicate it (probably not).