The Kondo effect is a classic paradigm in condensed matter theory, 
which describes the dynamic screening of a quantum impurity 
embedded in a metallic host. The underlying renormalization group 
(RG) description of such problems is by now very well understood. 
But comparatively little is known in real-space: while a 
length-scale associated with the screening process has been proposed 
theoretically, its physical interpretation remains controversial. 
We demonstrate that as one moves away from the impurity, physical 
quantities evolve in a characteristic way, reproducing fully the 
RG flow between fixed points. Behaviour typical of each fixed point
 can thus be identified in distinct regions of space. The 
implications of these results are discussed in relation to the popular 
'Kondo screening cloud' picture.