Types of Fractals

Fractal Canopies

WHAT ARE THEY?

Fractal canopies are one of the easiest-to-create types of fractals. All you have to do is take a line segment and "split" it into two smaller segments at the end. Then you take the two smaller segments and split them as well. To create a fractal canopie, this process has to be continued infinitely (see iteration).

PROPERTIES

A fractal canopie has to have the following three properties:

1. The angle between any two neighboring line segments has to be the same throughout the fractal.
2. The ratio of lengths of any two consecutive line segments has to be constant as well.
3. Points all the way at the end of the smallest line segments should be interconnected.

The diagram below shows all of these properties:

 1. A = B 2. a/b = b/c 3. Interconnection shown in red

TYPES OF CANOPIES

There are several different ways a fractal canopie can look depending on the angle between the segments. With the angle less than 180 degrees you get fractals such as these:

If the angle is acute, it is also called a fractal umbrella. Does the picture on the bottom remind you of a broccoli? In fact, fractal canopies are very useful in creating models of plants. The splitting of fractal canopies is also very similar to the splitting of bronchial tubes in the human body:

If the angle is 180 degrees, you get the H-fractal:

If the angle is greater than 180 degrees, you get fractal canopies such as this:

If we try to give canopies a width instead of using lines, we can create fractals which are called Pythagoras trees.