The Gosper curve is a recursive, space filling, fractal curve.

https://spacefillingcurves.wordpress.com/

https://kilin.clas.kitasato-u.ac.jp/museum/gosperex/343-024.pdf
Orders 0 through 3 were generated manually with MoI, fairly easily using rotations and scales and copies and more rotations.

A script is being attempted, which would allow for rounded edges.

EDIT: The command Orient, Line/Line performs the copy align and scale function desired!

It is necessary to deal with directed line segments, "arrows," not just a polyline. I was thinking of using something like:

genseg0.head, genseg0.tail? Or something like part of a half edge data structure?

Red is the "Initiator" arrow line segment, which is order 0.

Blue is the Generator curve, of order 1, with 7 arrow line segments.

Radiant Orchid is the order 2 curve, with arrow heads deleted, and has 7*7 = 49 segments.

Emerald is the order 3 curve, with arrow heads deleted, and has 7*7*7 = 343 segments.

White is the triangle lattice.

- Brian

There are also other Generalized Gosper curves.

I'd like to router the pattern on a slab of wood...