Nature and Complexity

Clouds are not spheres, mountains are not cones, and the bark of a tree is not smooth. In one word, nature is complex. By complex I mean that the level of detail does not decrease as we take a closer look.

Take a wristwatch, for example. If you look at it from a couple of meters away, you will only notice its general shape. But as you move closer, details will appear. Notice, however, that details seem to stop at a certain scale. There is no single feature smaller than a few millimeters. If you were to view it through a microscope, you would see that the surface is not really smooth but full of ridges due to manufacturing. However, at least in apparent terms, there is a discontinuity in detail.

Now, compare a wristwatch to a leaf of a tree. The closer you look, the more details you see, even at the microscopic level. There's a continuous increase in detail as we increase the scale. It's an interesting property of natural elements that is shared by all animals, plants, water, clouds, and even terrain. This continuity manifests itself in two apparently different but similar scenarios: geometry and appearance. Using the example of a leaf again, you notice as you move closer the nerves, wrinkles, and so on but also tiny texturing patterns, subtle color changes, and more.

So, the first conclusion of this analysis implies that all methods devoted to nature rendering will have a level-of-detail (LOD) component, allowing us to approximate the varying level of detail found in the real world.