Kolakoski-(3,1) symmmetric variant, dual
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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
