There is this variation of the dragon curve:

  order: 10
  axiom: FX
  angle: 90
  
  X -> X+FYF-
  Y -> +FXF-Y

This avoids the self-intersections (like a similar depiction of the Hilbert and Gosper curves), yet it remains relatively simple, and reveals more of the structure inside the bulk of the curve.

It's especially pretty when completed into a twin-dragon with the axiom: FX+F+FX+F+ and same rules as above.