  A key goal of the Event Horizon Telescope is to observe the shadow cast by a
black hole. Recent simulations have shown that binary black holes, the
progenitors of gravitational waves, present shadows with fractal structure.
Here we study the binary shadow structure using techniques from nonlinear
dynamics, recognising shadows as exit basins of open Hamiltonian dynamical
systems. We apply a recently developed numerical algorithm to demonstrate that
parts of the Majumdar-Papapetrou binary black hole shadow exhibit the Wada
property: any point of the boundary of one basin is also on the boundary of at
least two additional basins. We show that the algorithm successfully
distinguishes between the fractal and regular (i.e., non-fractal) parts of the
binary shadow.
