We know that any substitution can generate sequence, for example the Fibonacci substitution:

$\sigma(0)=01, \sigma(1)=0$, then we can define a Sturmian sequence $\omega$, i.e., the fixed point of $\sigma$. ($\sigma(\omega)=\omega$). We can define an orbit space which is based on the fixed point of the substitution, for example, the Fibonacci substitution, we can define $\Omega=\overline{\{T^{n}(\omega):n\in \mathbb{N}\}}$, here $T$ is the left shift. This system is very good as it has a uniquely ergodic measure, say $\mu$. By ergodic theorem we have that $\mu([0])=\mbox{frequency of }0 $, $\mu([1])=\mbox{frequency of }1 $, where $[0],[1]$ are cylinders in $\Omega$. Also we can calculate the measure of other cylinders, such as $\mu([01]),\mu([100])$ and so on. We can use the irrational rotation to find the formula of the measure of each block.

My question is that if given other substitution, for example, $\sigma(1)=110, \sigma(0)=11$, we can also define the orbit space according to the fixed point of this substitution. Let the orbit space be $X=\overline{\{T^{n}(\tau):n\in \mathbb{N}\}}$, where $\tau$ is the fixed point of the substitution mentioned above. We can always define an invariant measure, say $\nu$, on $X$. In fact it is the limit of $\nu_n=\dfrac{1}{n}\sum_{i=1}^{n-1}\delta_{T^{i}(\tau)}$ in the weak sense. Here $\delta_{x}$ is the Dirac measure. How can we calculate the measure of cylinders, for instance, $\nu([1])=?$ $\nu([11])=?$ Can we give a formula to find the measure of all the cylinders?