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Driving through areas of the American Southwest such as Utah and Arizona, you notice stratified rock formations everywhere. The grand canyon is the best known example. One striking thing is that the thickness (or height) of individual layers of rock seems to be roughly constant, within an order of magnitude. (Perhaps 20 feet tall? Hard to tell from the road.) This is true even for very tall cliffs which have dozens of layers. Does this imply some kind of very long-term periodicity in climate over geologic time scales? If so, what is it? If not, why is there a dominant length scale in these features? What sets this scale?

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The layers in the Grand Canyon may superficially appear constant, but they aren't. See and lots of other articles on the stratigraphy of the Grand Canyon.

Layers may be laid down in all sorts of unrelated ways. Speaking as a strictly amateur geologist I don't think there are any long term periodicities. I suspect the pattern recognition bits of the human brain may be excessively active in this case :-)

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