Abstract
The paper deals with homogeneous random planar tessellations stable under
iteration (random STIT tessellations). The length dis- tribution of the
typical I-segment is already known in the isotropic case [7]. In the present
paper, the anisotropic case is treated. Then also the direction of the
typical I-segment is of interest. It comes out that the joint distribution
of direction and length of the typical I-segment in a random STIT
tessellation is equal to the joint distribution of direction and length of
the typical edge in a certain mixture of homogeneous Poisson line
tessellations.