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


The boundary of the area filled by a plane-filling curve (its "skin") can be classified into one of several groups. The properties of a skin are not directly associated with the gross anatomy (overall shape) of a plane-filling curve. Rather, every unique skin has a countour that is a fractal boundary with fractal dimension ranging between 1 and 2, and which exhibits scaling self-similarity. Its true nature is revealed upon progressive zooming.

In other words, as you zoom in to remote regions of the skin, the nature of the countour remains the same. Many families share the same skin type. Thus, there are fewer skin types than there are families.

These skins are listed below. Refer to the collection of plane-filling curves to see the flesh within the skin.

The straight skin is common to several families

skins unique to the 2G family
2G1 (Dragon skin)

skins unique to the 3E family
3E1 (Ter Dragon skin)

skins unique to the 4E family
4G1 (Dragon of Eve)
4G2 (Cityscape)

The First Nine Families