If you look at the leaves of a tree, they are seemingly randomly arranged. We call it chaos. If you take 100 pennies and arrange them on a flat surface in rows and columns of 10 it's called order. We assign the label chaos to something that occurs naturally and has done so for billions of years. Wouldn't that occurrence be considered order if it had been there a long, long time and the human species and our perceptions are very new in comparison?

I'm not sure that whether something occurs "naturally" nor whether it's been thus for a long time is the issue here. Nature gives us many examples of things that are very orderly and not "chaotic" or "random" at all. Crystal structure is an obvious example. So is the periodic table. And things with human origins can display a lot of randomness. Spin a roulette wheel a bunch of times and try to predict the outcomes.

A bit too simply, there are cases -- old and new, natural and human-made -- where we can make very accurate predictions about what comes next, so to speak, on the basis of what's come before. And there are other cases where our predictions will be (so to speak) no better than tossing a coin. I think that's what lies behind the distinction you're making, and there are branches of science and mathematics that have lots to say about the matter. (One particularly relevant field is information theory.)

Of course, there can be hidden order where there is apparent chaos, and there can be overall randomness in spite of local appearances to the contrary. But it's not clear that the natural/artifact distinction is really to the point, nor the ancient/recent distinction. It's a matter of the patterns and their structure or lack thereof.

The positions and numbers of branches and leaves of trees and plants are governed by Fibonacci series: 1,1,2,3,5,8.13 . . . . , so there is order in their arrangement. Whether this pattern exists seems to have little or nothing to do with how used to it we are.

Read another response by Allen Stairs, Jonathan Westphal
Read another response about Perception