When the minions of the self-anointed caliph in the self-declared Islamic State that now straddles Iraq and Syria blow up a mosque supposed to contain the remains of the prophet Jonah, or offer punctilious details about the kind of purdah to be imposed on women, the world takes brief notice. But the group’s military campaigns have made less news in recent weeks because they seemed to have stalled.

Now, according to Western military analysts, it’s time to start worrying again. Those studying the attacks by the group formerly known as ISIS see critical changes in the bombings and skirmishing by the caliph’s troops and their allies in and around Baghdad. Some experts warn that a blitzkrieg—a lightning attack—is imminent, and it will be one the beleaguered and squabbling politicians in the Iraqi capital are ill equipped to combat. But it is more likely to be a guerrilla and terrorist offensive than an all-out push along conventional military lines.

Until recently, Islamic militant action around Baghdad appeared sporadic, uncoordinated, and lacking a clear strategic purpose. But analysts at the U.S.-based think tank the Institute for the Study of War, who have been plotting the locations and types of attacks in the recent flurry of blasts buffeting the Iraqi capital, have noted a clear pattern developing. They say it suggests the Islamic State is building up to something big and is no longer just focused on consolidating its grip and developing governance in the lands it now controls. […]