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Is this news? I don't know about anyone else, but ever since my undergrad days, I see repeating patterns in nature and I just say to myself "oh, there's another partial differential equation"

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I guess most of nature is described by differential equations, starting with fundamental physics. So in the end, that statement does not add much. It is the kind of differential equation that actually matters. In this case it is a non-linear DE, which means that it is probably not really a fundamental process, but a more complicated, derived process.

Besides, there are also non-repeating patterns in nature that are governed by differential equations. Very basic examples are the temperature across a heated room, and the voltage across a resistor.

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