A homeless woman was doused in a flammable liquid and set ablaze in Van Nuys on Thursday in what police called a random "horrific" attack.

She was whisked to a hospital, where she remains in critical condition. The seemingly random attack even shocked LAPD veterans, who said they were trying to make sense of it.

LAPD Deputy Chief Kirk Albanese said it was unclear whether the suspect, Dennis Petillo, 24, even talked to the woman before he allegedly set her ablaze.

“There was no incident or dispute or clear motivation for this horrific attack. He did not know his victim. It defies explanation,” Albanese said. “He is not of sound mind.... The motive is mental illness. There is really no logical basis for this terrible action.”

Police have not released her name, which residents said was Flo Parker. She was also known as Violet: a 5-foot-tall woman with dirty blond hair and a time-worn face that made her look older than her 67 years.

But for much of Thursday, her identity was secondary. Violet had become a symbol to some residents  of both the dangers that face the homeless and the depths of human cruelty.

“This is a hate crime as far as I’m concerned. All this woman did was try to sit out here and get warm,” said Barbara Weiss, 57, who works for a company that provides transportation to the handicapped.

Had she seen Violet before?

“I probably have,” she said. “I just don't know.”

In Thursday’s wee hours, witness Erickson Ipina told reporters, he watched in horror as the attack unfolded. A man walked out of the Walgreens with what appeared to be rubbing alcohol, he said.

“He just poured it all over the old lady,” Ipina said. “Then he threw the match on her and started running.”

Ipina said he gave chase. “Hey, stop right there!” he said he yelled. “Stop right there!” But the man kept running.