Simulations of large-scale magnetic field with uniformly random longitudes. Left: Vector sum magnitude. Right: Equatorial component of the vector sum. The blue line shows the median dipole strength from 10⁴ simulations. The orange line shows the result from the original simulation. Shaded regions show the 1σ–3σ ranges from the simulations. The black line in the left panel shows the strength of the axial component.