The tame twindragon is a planar self-similar fractal obtained from expansions using binary
digits in the complex base 
, a root of 
(Ngai et al. 2000).
A normalization in the complex plane is the compact
set
 |
It satisfies the iterated function system
 |
Since 
,
the two pieces are congruent copies with scale
factor 
.
They have disjoint interiors,
making the tame twindragon a rep-tile of order 2. The
figure shows a finite approximation with the two first-level
pieces colored separately.
The tame twindragon has nonempty interior, equals the closure of its interior, and tiles the plane by translations (Bandt 1991, Ngai et al. 2000). Although it has the same two scale factors as the twindragon, the two fractals are not similar (Ngai et al. 2000).
."
Proc. Amer. Math. Soc. 112, 549-562, 1991.