While most efforts to curb terrorism concentrated on neutralizing terrorist nets, very little is known about the social space which is open to terrorist moves. Introducing the notion of social permeability to terrorism, we study the role of passive supporters to a terrorist cause using the physical theory of percolation. A passive supporter is a normal citizen who identifies with the terrorist cause but without any direct involvement with either the terrorist group or its activities. It is an individual dormant attitude associated with a personal opinion which characterizes passive support. It does not need to be explicitly claimed. Passive supporters just do not oppose a terrorist act in case they could. Unnoticeable, most of them reject the violent aspects of terrorist acts. They only partly share the terrorist cause. The question of the range of a terrorism threat is then analyzed in terms of a percolation phenomenon within a multi-dimensional social space. Traditional terrorism is found to correspond to non-percolating situations while international terrorism is associated to worldwide percolation. Using only military means to eradicate terrorism is shown to be inefficient. Hints are given on how to diminish the terrorism threat without military destruction.