Fractal substitution system

Question

It is known that substitution system

$$ A \to ABA, B \to BBB $$

produces approximations to Cantor set: $$ A, ABA, ABABBBABA, ABABBBABABBBBBBBBBABABBBABA, \ ABABBBABABBBBBBBBBABABBBABABBBBBBBBBBBBBBBBBBBBBBBBBBBABABBBABABBBBBB\ BBBABABBBABA $$

I numerically estimated its dimension using naive box-counting method and got the value $D=0.62\pm0.01$

There are many other sequences that have fractal properties:

• Simple kneading sequence: $A \to AB, B \to AA$

• Thue–Morse sequence

• A self-descriptive fractal sequence

I tried to estimate their dimensions by various suitable methods, but I always got about 1.

So first question is:

Is there an example of a substitution system leading to the appearance of a fractal different from Cantor set with a fractal dimension $0 < D < 1$ ?

Second question much more difficult:
Is there any example of a substitution system produces multifractal?