When I look at a tree, I see a lot of things. I see fractals. I see grass. I see an alien life form. I see computer data structures. I see primitive houses on the hoof. I see entropy in action.
Fractals are, strictly speaking, self-similar curves. A more general interpretation of the word is any self-similar structure, where self-similar means that the structure is composed of smaller copies of itself. A tree is fractal in the sense that the whole tree resembles on a larger scale a branch, which itself resembles a twig, which itself resembles the veins on a leaf. (My friends with a botanical bent will no doubt correct me on the specifics of the terms I've used, but you get the general idea.) Lots of stuff in nature is fractal, but trees are one of the most obvious examples.
The computer data structure called a "tree" comprises one or more records linked to form an acyclic graph, in which there is exactly one path from a distinguished record called the "root" to every other record. A more understandable definition that reveals the fractal-like qualities of the software version of a tree is that a tree is a record that points to zero or more smaller trees. A traditional family tree is an example of this kind of tree - each record contains two parents, and points to the children, who in turn point to their children, and so on.
The grass aspect of the tree again is related to its fractal nature. From a distance or a great height, a forest resembles a lawn to a certain extent. If I concentrate, when I walk through a forest I can imagine that I am very small and that each tree is an individual blade of (admittedly woody) grass. I enjoy shifting my perspective in this way on occasion - it makes me mindful of my place in the universe.
In a similar vein, I sometimes try to view trees as an alien would. Suppose that you landed on another world, and all you saw from horizon to horizon were lacy constructs of bluish crystal - some tall, some short, no two alike, none exactly symmetrical, but all exhibiting some self-similarities. It is not that far of a stretch to then look at our own landscape and substitute cellulose and chlorophyll for crystal, and to wonder at the large variety of shapes growing like mold over every exposed surface of the planet.
Finally, the specter of entropy rears its ugly head. No one that has ever raked leaves in the fall could argue that order increases with time. I was going to write about how trees disturb all of the nice orderly photons coming from the Sun and the nice simple compounds in the soil, but frankly, I can't remember how that argument goes. You can find it in The Emperor's New Mind, by Roger Penrose, if you are interested - but it's not an easy read.
And that roughly exhausts my thoughts on trees for today. I'll leave all of the sappy beauty, nostalgia, and circle-of-life thoughts to others. Both puns intended.
You can respond to my ranting here.
I think that I shall never see a rant lovely as a tree.