There are only two planefilling curves in this family. They are both based on a common generator shape (two unit segments joined at a right angle), but the segments have different flippings. This family corresponds to a Gaussian integer with norm 2. Since it is a prime, all segments have length 1. The resulting contrast in phenotypes (a complex dragon vs. a right triangle) is a common occurance in several families. 
name:
Dragon Curve
Skin: 2G1 (Dragon Skin) attribution: John Heighway, Bruce Banks, William Harter reference: Wikipedia comment: Also called 'Jurassic Park Dragon' 
name:
Polya Sweep
Skin: straight attribution: George Polya reference: The Fractal Geometry of Nature comment: fractal dimension of boundary = 1 
The First Nine Families 



fractalcurves.com 