Abstract: "We study the structure of geodesics in the fractal random metric introduced by Aldous and Kendall, constructed from a self-similar Poisson process of roads (i.e, lines with speed limits) in $mathbb{R}^2$. In particular, we prove a conjecture of Kendall stating that geodesics do not pause en route, i.e, use roads of arbitrary small speed except at their endpoints. We also consider geodesic stars, and give a complete description of the local structure of geodesics around points in the geodesic frame. Based on ongoing work with G. Blanc and J. Kahn"