See Image:White noise.ogg for details on generation and conversion.

Instead of rand(), this uses randn(), which generates normally distributed random values centered about 0. So to generate 10 seconds of noise sampled at 48 kHz:

gwn=randn(48000*10,1);

The wavwrite() function expects values in [-1.0, 1.0), so, for lack of a better idea, I just normalized the data to this range:

gwn=gwn/(max(abs(gwn)));
wavwrite(gwn,48000,16,'white noise normal.wav');

So the normally-distributed version is somewhat quieter than the uniformly-distributed version. (According to SoX, there is an 8.4 dB difference, but it sounds around 4.5 dB.) I can fix this later, but I'll wait until after I've done all the other noise colors to see if it's worth trying to make them all the same RMS amplitude, or if this will require them to be too quiet.