  Society faces a fundamental global problem of understanding which individuals
are currently developing strong support for some extremist entity such as ISIS
(Islamic State) -- even if they never end up doing anything in the real world.
The importance of online connectivity in developing intent has been confirmed
by recent case-studies of already convicted terrorists. Here we identify
dynamical patterns in the online trajectories that individuals take toward
developing a high level of extremist support -- specifically, for ISIS. Strong
memory effects emerge among individuals whose transition is fastest, and hence
may become 'out of the blue' threats in the real world. A generalization of
diagrammatic expansion theory helps quantify these characteristics, including
the impact of changes in geographical location, and can facilitate prediction
of future risks. By quantifying the trajectories that individuals follow on
their journey toward expressing high levels of pro-ISIS support -- irrespective
of whether they then carry out a real-world attack or not -- our findings can
help move safety debates beyond reliance on static watch-list identifiers such
as ethnic background or immigration status, and/or post-fact interviews with
already-convicted individuals. Given the broad commonality of social media
platforms, our results likely apply quite generally: for example, even on
Telegram where (like Twitter) there is no built-in group feature as in our
study, individuals tend to collectively build and pass through so-called
super-group accounts.
