Transition between Rauzy fractals

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What is drawn ?

The picture above, drawn using WegGL, shows Rauzy fractals between the two following :

a -> ab

b -> c

c -> a

and

a -> ab

b -> ac

c -> a

But the coloration isn't correct except for the Tribonnacci fractal.
More precisely, the fractal drawn with parameter t correspond to the automaton :
with β_t root of X³ - X² - tX - 1.
The corresponding Rauzy fractal R_t is the union of smallest non-empty compact set R_t^l satisfying
R_t^l = ∪_{L →^x l ∈ A} β_t R_t^L + x