WASHINGTON — As the uprising closed in around him, the Libyan dictator Col. Muammar el-Qaddafi warned that if he fell, chaos and holy war would overtake North Africa. “Bin Laden’s people would come to impose ransoms by land and sea,” he told reporters. “We will go back to the time of Redbeard, of pirates, of Ottomans imposing ransoms on boats.”

In recent days, that unhinged prophecy has acquired a grim new currency. In Mali, French paratroopers arrived this month to battle an advancing force of jihadi fighters who already control an area twice the size of Germany. In Algeria, a one-eyed Islamist bandit organized the brazen takeover of an international gas facility, taking hostages that included more than 40 Americans and Europeans.

Coming just four months after an American ambassador was killed by jihadists in Libya, those assaults have contributed to a sense that North Africa — long a dormant backwater for Al Qaeda — is turning into another zone of dangerous instability, much like Syria, site of an increasingly bloody civil war. The mayhem in this vast desert region has many roots, but it is also a sobering reminder that the euphoric toppling of dictators in Libya, Tunisia and Egypt has come at a price.

“It’s one of the darker sides of the Arab uprisings,” said Robert Malley, the Middle East and North Africa director at the International Crisis Group. “Their peaceful nature may have damaged Al Qaeda and its allies ideologically, but logistically, in terms of the new porousness of borders, the expansion of ungoverned areas, the proliferation of weapons, the disorganization of police and security services in all these countries — it’s been a real boon to jihadists.”