It can be constructed iteratively by starting with a 90° corner and replacing iteratively its sides by 90° corners rescaled by sqrt(2), as follows:
It self intersects at points, but this can be avoided by rounding it slightly.
Another way to round it...
One can also vary the angle of the corner to obtain different dragon curves. Some are not space-filling anymore, while other unavoidably self-intersect. Here are the curves for corners with angles 45°, 60°, 70°, 80°, 83°, 86°, 89°, 90°, 91°, 94° and 97°.
The twin dragon curve is closed, formed by two copies of the dragon curve.
And here are a few more twin dragon curves obtained by varying the corner angle to 45°, 60°, 70°, 75°, 78°, 80°, 83°, 86°, 89°, 90°, 91°, 94° and 97°.
