(CNN) Police say Redmond James O'Neal, the son of actors Ryan O'Neal and the late Farrah Fawcett, is responsible for a "violent crime spree" last month that left several people injured in Los Angeles.

The 33-year-old is accused of "randomly" attacking five men between May 2 and 5, in the Venice Beach and Palms neighborhoods. Police say the attacks were unprovoked and some victims were seriously hurt.

Redmond O'Neal was charged Friday with attempted murder, two counts of assault with a deadly weapon, brandishing a knife, battery and criminal threats, police said.

O'Neal, who has had a history of drug and legal troubles, has been held without bail by the Los Angeles County sheriff since his arrest on May 8, for the alleged armed robbery of a 7-Eleven store , according to police and CNN affiliate KABC

CNN could not immediately reach O'Neal's attorney.

White man with red hair, distinct tattoos

The alleged incidents that led to the new charges "all seem to be random," Los Angeles Police Department Sgt. Scotty Steven told KABC

"It appears, though, based on what we know now, that it just started as an argument between unknown persons and quickly escalated with the violent acts," he said.

The motives are unknown.

All five alleged attacks involve a suspect whose description, at least partially, matches that of O'Neal, including being white, with red hair and distinct tattoos. All the victims described by police were white males.

Redmond O'Neal

• On May 2, a suspect punched another man and tried to hit him with a broken glass bottle in the Palms neighborhood, police said. The victim made the suspect angry when he "appeared to look at him," they said.

• Hours later, a man reportedly punched another man repeatedly in the head and threw him to the ground outside a convenience store, police said.

• On May 4, a suspect stabbed a man who had looked at him as he walked near the Venice Beach boardwalk, police said, adding that the wound was "serious."

• About three hours later, people found another man lying "in a pool of blood with obvious stab wounds to his face and upper body." Surveillance video showed the suspect walking away shortly after the victim was found, police said.

• The following afternoon, a suspect was spotted at a coffee shop. When an employee confronted him, the suspect "became belligerent" and pulled out a folding knife, police said. He "lunged, jabbed and threatened to harm the employee with the knife" before fleeing, police said.

After O'Neal's arrest three days later in connection with the 7-Eleven robbery, detectives linked him to the series of alleged attacks, police said.

"After O'Neal's arrest, the violent crime spree ended," police said in a statement, "and Pacific Area robbery detectives found O'Neal to strongly match the description of the suspect in these crimes."