How to Draw Tropical Planes
  The tropical Grassmannian parameterizes tropicalizations of linear spaces, while the Dressian parameterizes all planes in $\TP^{n-1}$. We study these parameter spaces and we compute them explicitly for $n \leq 7$. Planes are identified with matroid subdivisions and with arrangements of trees. These representations are used to draw pictures. 
Sven Herrmann, Anders Jensen, Michael Joswig, Bernd Sturmfels