WHAT ARE THEY?

Consider a long strip of paper. We will represent it by a line. Fold this strip in half and unfold it so that the angle between the two halves is 90 degrees:

Now consider folding the paper twice and then three times:

As you can see the picture gets more and more complicated after every fold. Wouldn’t it be interesting to know what happens after an infinite number of folds? What we get is the famous Dragon Fractal:

In this fractal, we folded the paper the same direction all of the time and made the angle 90 degrees. However, by using different angles and folding in different directions, we can get a great variety of paper-folding fractals:

THINGS TO NOTE

By looking at the paper-folding fractals you can see that they occupy some area. This means that all of them can be considered to be Peano curves. Paper-folding fractals can be generated using generator iteration. However, this poses a problem because the motif in all of them is not placed the same way throughout iteration. If you read about it already, you probably realize that all paper-folding fractals are also sweeps.