The discrete dragon curve of level n can be formed as follows: Take a strip of paper, repeatedly fold the right side over the left side n times, and unfold it to get a strip of paper with 2n+1-1 creases. Then lay out the paper horizontally with a turn of 90 degrees at each crease.
The discrete versions of different levels line up if you rotate them a bit, so we can combine all the levels to form a two dimensional surface where the z dimension is the level of the curve. Here is a simple python program dragon.py to generate this surface, an example output mesh, and some screenshots: