Aterrorist having no formal connect to or material support from a terrorist movement but having a psychological affinity with one is often descibed as (note: one-word answer).

lone wolf

Explanation:

Terrorism manifests itself in many ways. In most cases there is integration between terrorists who form cells and terrorist organizations like Al Qaeda. However, some people plan terrorist attacks without any help, these people are called lone wolves. Shooters who open fire on civilians are usually considered lone wolves. These cases are more difficult to predict by the public power intelligence system.