Now, we are finally getting to the application of this "psrdnoise" noise function to create the turbulent, swirling patterns shown by Ken Perlin and Fabrice Neyret in their Siggraph sketch "Flow Noise" from 2001.
To make the kind of visuals they showed in their examples, we make a sum of several noise octaves, starting from the one with largest features, and use the combined gradient of all previous terms to warp the texture coordinates for the next term. The warping influence from each of the gradients should decrease as we get to the later terms with lower weight in the fractal sum.
This first demo shows the influence of such warping, using only two terms for clarity. At the top of the image, both terms of the sum are plain noise, without warping. Moving towards the bottom, the warping increases, and at the bottom the gradient from the first noise term changes the texture coordinates quite a lot for the second noise term. This makes the second noise component become "crinkled", as it varies more rapidly along the gradient direction where the gradient is strong and, vice versa, gets stretched out in both directions where the gradient is weak. In a manner of speaking, we are "pushing the features of the second term along the slopes of the first term"
Yes, this is difficult to grasp, so let's do this again, but with a grid overlay on the final texture, to see more clearly how the texture domain is warped.
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