Magnetic topology and connectivity in the model. In panel (a) the background image at the bottom shows the vertical component of the magnetic field in the photosphere (black and white indicate opposite polarities). Blue lines represent closed field lines, while purple lines indicate open field lines, i.e. field lines that reach the top of the computational domain and might close back out in the outer solar atmosphere or in the heliosphere. Panel (b) displays the fraction of area in a horizontal slice covered by open magnetic fields as a function of height for the snapshot shown in panel (a). The panels (c) show the magnetic connectivity at heights of 3, 5, 9, and 16 Mm. Blue and purple regions correspond to closed and open magnetic fields, respectively.