A dragon curve is a recursive nonintersecting curve (line) which gets its name from its resemblance to a dragon.
I thank http://orig14.deviantart.net/016e/f/2011/091/5/4/red_dragon_01_by_oberonsson-d3cy5f5.jpg for the thumbnail, and http://mathworld.wolfram.com/DragonCurve.html for the construction.