Meaning and regularity
If one considers something to show regularity one may or may not consider it meaningful. But if one considers something random then usually one will also consider it meaningless. For to say that something is meaningful normally implies that one somehow comes to a conclusion from it. And this typically implies that one can find some summary of some aspect of it—and thus some regularity. Yet there are still cases where things that are presumably quite random are considered meaningful—prices in financial markets being one example.