The twindragon is a planar self-similar fractal that can be dissected into two congruent
smaller copies of itself. It is therefore a rep-tile
of order 2 (Ngai et al. 2000). Taking 
, a normalization in the complex
plane is
 |
The binary digits are unrestricted, so grouping the expansions by their first digit gives the iterated function system
 |
Both maps have scale factor 
. The figure shows a finite
approximation, with the two first-level pieces colored separately.
The twindragon has nonempty interior, equals the closure of its interior, and tiles the plane by translations (Bandt 1991, Ngai et al. 2000). The tame twindragon uses a different quadratic equation to specify its complex base and is not similar to the twindragon (Ngai et al. 2000).
."
Proc. Amer. Math. Soc. 112, 549-562, 1991.