Determining the image of some singular function

The problem is as follows: How to describe graphically the set $T(1)(\Gamma)$ where $T(1)(z)=\int_\Gamma\frac{d\mu(\zeta)}{\zeta-z}$ and $\Gamma=\Gamma_\theta$ is the Von Koch curve, $\theta\in(0,\pi/4)$. In this paper we give some expression permitting us to compute $T-\theta(1)(z)$ for each $z\in\Gamma$ to within an arbitrary $\epsilon>0$. Also we provide an estimate for the error.