## Kolakoski-(3,1) symmmetric variant, dual

### Info

The substitution $a \rightarrow aca, b \rightarrow a, c \rightarrow b$
has palindromic and thus mirror symmetric variant of the
Kolakoski-(3,1) substitution,
which is in the same MLD class, along with the further variants
A (mirror symmetric) and
B
(with its mirror image). The scaling factor $\lambda \approx $ 2.20557
is the largest root of $x^3-2x^2-1=0$.

This substitution has a simple dual,
with three mildly fractal tiles, which are all similar to each other.
The dual substitution scales by about 1.485, and rotates clockwise by
about 81.22°.

### Dual Substitution Rule

### Dual Patch