The order of chaos

At dinner a few nights ago someone brought out a dancing flame. It consists of a base which holds some highly flammable fluid, and four glass panes that serve to enclose it. The fuel is lit and sustains the flame for an hour or so, and for the entirety of that hour the flame flickers and moves and shifts. As is my want, I got to looking at it. In the few minutes that I watched it it never took the same form twice—from what I can tell. Which got me thinking about the nature of chaos and order.

There had to be a finite number of shapes, a definite number of ways in which the flame could manifest itself. The size of its base was fixed and the surface area of exposed fuel was determined, after all. So there was an order, a pattern to its burning, but one that I suspect it would be hard to map. Is this not how we consider chaos?

Specifically, aren’t many things that we think of as chaotic actually conforming to an order which we have neither the capacity nor the tools to comprehend?