Taxonomy of plane-filling curves

The Family Tree of Fractal Curves
(a taxonomy of plane-filling curves using complex integer lattices)

G(1,1) norm 2 family

There are only two plane-filling 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 transforms. 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
reference: Wikipedia
comment: Also called 'Jurassic Park Dragon'

name: Polya Sweep
reference: The Fractal Geometry of Nature
comment: George Polya