Here are some examples of samples of gaussian process (seen as a function of the two dimensional space, time and color). In all cases the sampled GPs come from kernels following a Kronecker structure.
Brownian motion Kernels
Thresholded samples
The fact that there are only limited colors is that at some point I did a thresholding operation in each of RGB the channels, giving 8 colors.
Periodic Kernels
The moral here is that to obtain this periodic-like motion one can use a periodic Kernel