Hmm. I didn't read all you wrote, because you're on the wrong track from the start.

The curve input, to replace the Fractal_Sum, must be a gradient in the V direction, with no change in the the U direction.  The idea is for each row, there is U_Offset that should be used to move that row into position on the figure.

You don't want the offset to vary within a row. So in any given row, every pixel should have the same gray value. We really only want to represent a 1-dimensional array of numbers, laid out vertically.

When you used the black-and-white pattern, you were doing all or nothing, and it was changing within the row. You want to use an image that has a gray value between 0 and 1 that defines the offset within that row, period.

For example, let's say that at some point you desire the U_Offset to be .675. You should put Gray level 255 * .675 = 172.125 in that row all the way across. Of course you cannot do fractions, so you would use 172.

This may cause some noticeable jumps - we'll see. You may have to encode the data in a 16-bit tiff instead.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)