Do Dyck Words or Dyck Paths Have Manifestations in Nature?

Question

Working with the Dyck language of well-balanced strings of parentheses, I am led to wonder what, if any, phenomena the concept relates to in the natural world - in the same sense that Fibonacci numbers, for example, have manifestations as patterns in sunflower floret spirals.

Since Dyck words have equivalent Dyck paths, I also included the latter in my question.

I hope this is an appropriate board to ask such a question; if you can suggest a better place, I'll be happy to go there.

Answer 1

From a page in the presentation of the Vancouver (B.C., Canada) science museum Science World:

A fractal is a kind of pattern that we observe often in nature and in art. As Ben Weiss explains, “whenever you observe a series of patterns repeating over and over again, at many different scales, and where any small part resembles the whole, that’s a fractal.”

Not only is it a fractal. It's also a Dyck language, since a Dyck language is an abstraction of precisely the recursive structure described in that paragraph.