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.