All Plane-filling Curves (using edge-replacement)
by Jeffrey Ventrella







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 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