This paper is about the autonomous acquisition of detailed 3D maps of a-priori unknown environments using a stereo camera – it is about choosing where to go. Our approach hinges upon a boundary value constrained partial differential equation (PDE) – the solution of which provides a scalar field guaranteed to have no local minima. This scalar field is trivially transformed into a vector field in which following lines of max flow causes provably complete exploration of the environment in full 6 degrees of freedom (6-DOF). We use a SLAM system to infer the position of a stereo pair in real time and fused stereo depth maps to generate the boundary conditions which drive exploration. Our exploration algorithm is parameter free, is as applicable to 3D laser data as it is to stereo, is real time and is guaranteed to deliver complete exploration. We show empirically that it performs better than oft-used frontier based approaches and demonstrate our system working with real and simulated data.