So here is a render using a UV-driven shader that shrinks the tile, repeates it vertically, but not horizontally. In addition, it makes the strip follow a curve. The actual curve is randomly generated by a FractalSum node.  In final version, we would use a specific curve to force the strip to follow a specific path. We can work that out later.

This shot is with the camera at 20mm so we can see the entire UV space on a one-sided square. The tile you see above has been shrunk to cover 1/80th of the original size.

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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)