Fock and Goncharov showed that positive geometry can be a powerful tool for studying higher Teichmuller spaces. One consequence of the positive geometry of higher Teichmuller space is that one can tropicalize higher Teichmuller space to get an analog of measured laminations that one could call higher laminations. I will explain how to realize higher laminations via configurations in the affine building. I will also explain how tropical geometry reflects the piecewise-linear metric geometry of the affine building. I will focus on the case of higher Teichmuller spaces for SL_n/PGL_n.