A Gaussian white noise implies a normal distribution of e t and a normal distribution is completely defined by the first 2 moments. So in this case: White noise process = Iid white noise.
Generating white noise and colored noise signal in matlab. To generate white noise one can use rand function from matlab library or awgn (additive white Gaussian noise) function can be used. To know more on AWGN refer page on channel model. To generate colored noise data generated using rand to be filtered (either low pass, high pass etc.) to

Burst noise is a type of electronic noise that occurs in semiconductors and ultra-thin gate oxide films. [1] It is also called random telegraph noise ( RTN ), popcorn noise, impulse noise, bi-stable noise, or random telegraph signal ( RTS) noise. It consists of sudden step-like transitions between two or more discrete voltage or current levels

However, the noise reduction for white noise is less in each successive smooth. For example, three passes of a and the noise in line 9. A typical result for a Gaussian peak with white noise smoothed with a pseudo-Gaussian smooth is shown on the left. Here, as it is for most peak shapes, the optimal signal-to-noise ratio occurs at a smooth
\n\n \n white noise vs gaussian noise
2. I would answer the question bluntly I would say it is because Perlin noise is super simple to get your head around. Simplex noise on the other hand is very much a more complex and hairer beast. Getting a Perlin implementation up and running is much easier than simplex and thus gets more usage.
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white noise vs gaussian noise