toneburst> I still don’t honestly see the point in moving across the noise field in anything other than a straight line, though.
The use-case I described was using two (or more) lines traversing the map. As have both concluded, if those two lines are parallel and in close proximity, the value series read by each line will be quite similar and highly cross-correlated, because they will be traverse similar, but not identical terrain. Move the lines further apart and the similarity (serial cross-correlation) between them drops off. OK, so how would you produce two channels in which the similarity between them varied in time? Well, one reading line could be straight, and the other could be a sinusoid (or other shape) curvy line that periodically comes close or crosses the straight line. If you look at the time-series of values read by a curve from a Perlin map, and the values read by a straight line, each in isolation, I agree, they will be indistinguishable. But if you look at the their mutual similarity with each other at each point in time, well, that’s a function of their distance from each other at that point, and if you want that distance between them to vary over time in a cyclical way, then one of the reading lines must not be straight.
toneburst> Your use of the term ‘degenerate’, implies to the lay reader a somewhat arbitrary value-judgement (though in sure it wasn’t intended that way).
Sorry, it was mathematical jargon - no disrespect or value-judgement intended. 1D Perlin noise is degenerate because, as Olivier pointed out, you don’t need to go through the whole Perlin algorithm to generate it - there are easier ways.