Flexagons and Fractals

Prof. McIntosh has studied this origami-like paper based mathematical area. There is a connection to Fractals. I take from his webpage the following:

"This understanding consists in regarding a flexagon as a geometric fractal, in the style of the dragon curves, and their predecessors such as Hilbert's space filling curve or Helga Koch's snowflake. Such figures result from replacing an arc, usually a line segment, by another figure, probably more complicated, some of whose internal arcs have been marked for further replacement. A true fractal replaces again and again without limit, but as a practical matter the fractal would only be carried through a few stages; interesting ways to partially fill up a plane region ensue. A construction for the classic dragon curve is reproduced in Figure 8."