Name of this "cut 'n slide" fractal? 
Can you identify this fractal--if in fact is has a name--based either upon its look or on the method of its generation? It's created in this short video.
It looks similar to a dragon fractal, but I don't think they are the same. Help, please?

That is the twindragon.  It is a two-dimensional self-similar set.  That is it is composed of two smaller copies of itself scaled by the factor $\sqrt{2}$ as shown here:

Using this self-similarity, one can construct a tiling of the plane with fractal boundary.  Analysis of the fractal dimension of the boundary is also possible, but it's a bit harder.
It's all truly great fun!
