Trees
Tree structures are some of the most common fractal structures, and they are also some of the simplest to construct. We saw an abstract forest in section 1.2. Now we will construct trees from simple vertical line segments.
The simplest way to construct a tree is to start with a segment:
and add two "branches" at the top, like so:
This is one iteration of our IFS. Another iteration will give us this:
This is an overly simpistic example. Now we will create a more interesting one. We start with our srgment, as before:
This time, however, we will add a few more branches. We wind up with this:
This is not much more complicated than the first tree. But if we continue to iterate this, the results are quite astounding:
By the time we get to the fourth iteration, it is almost impossible to tell that this is not an actual plant! And this was created using only a few simple functions. The Mathematica code for these functions can be found here.
The fact that such realistic images can be created with relatively little effort using fractals is something very useful. In fact, one of the more common real-world applications of fractals is in simulation of nature. Such simulation is not limited to plant life, however, as we will see next.