Applications of Fractals
Most plants show some form of branching. This happens when the main stem (of trunk) splits into a number of branches. Each of those branches splits into smaller branches, and this kind of splitting continues until the smallest branches. You have probably noticed that a tree branch looks similar to the entire tree and a fern leaf looks almost identical to the entire fern. This property, called self-similarity is one of the most important properties of fractals. Because of numerous ways branching can be achieved geometrically, there are several ways of creating models of plants as well.
One classic way of creating fractal plants is by means of l-systems. Lindenmayer, who is the founder of l-systems, introduced them in a book called The Algorithmic Beauty of Plants, where he first used them to create models of plants. Some of the fractal plants he created became classic examples. Here are some of them in addition to several other ones:
Another way of creating fractal plants is using fractal canopies or Pythagoras trees. Fractal canopies are formed by splitting lines, which is very similar to branching. Pythagoras trees, such as the one below do the same more realistically by using squares and triangles instead of lines:
One of the properties of fractal canopies is the endpoints being interconnected. This is especially interesting in its similarity to broccoli, where the branches’ endpoints form an interconnected surface:
The final way of creating plant models is by using IFS fractals such as the Barnsley Fern below, which resemble plant shapes:
|Fractal Trees Applet - this applet randomly creates very realistic fractal trees. Beautifully demonstrates fractals in nature.|
Algorithmic Beauty of Plants
Przemyslaw Prusinkiewicz, A. Lindenmayer
Written by the founders of l-systems, this books is great for that topic.It mostly focuses on using l-systems to model plants and contains a lot of beautiful pictures. It is not very hard to read, especially because the topic is very visual.
Geometry in Biological Systems : An Analytical Approach
Philip M. Iannaccone(Editor), Mustafa Khokha (Editor)
Although extremely hard to read, this book is an excellent collection of the most exotic applications of fractals. The topics touched come from practically all areas of biology, from DNA structure to the heart rhythm.