Well, no particular use case I can think of. The OP asked for anything that you find interesting so here we are. =)
I'm sure there is a use for it, that pattern may be representative of some other phenomenon in the universe that we haven't correlated it to as of yet.
Well there is this famous paper by Volovich [1] where he argues that space is basically pixelized and p-adic numbers might best describe their geometry. But of course this has no connection with the reality we have access to.
p-adic numbers are also used in various areas of number theory (not my expertise).
I see them like the lesser known sibling of real numbers.