The son of film stars Farrah Fawcett and Ryan O'Neal has been charged with attempted murder following what police said were a series of violent attacks on strangers.

Redmond O'Neal, 33, allegedly stabbed one victim just for looking at him in Venice Beach, Los Angeles.

Three hours later he left another alleged victim lying in a pool of blood after stabbing him in the face, neck and upper body, it is claimed.

He is said to have carried out a total of five random attacks between 2 and 5 May this year.

Police said he was linked to the crimes after he was arrested on suspicion of robbing a 7-11 store in Santa Monica at knifepoint on 8 May.

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

On Friday the Los Angeles District Attorney's Office filed one count of attempted murder, two counts of assault with a deadly weapon, one count of criminal threats, one count of brandishing a Knife and one count of battery.

Mr O'Neal remains in the custody of the Los Angeles County Sheriff's Department.

He has a previous conviction for possession of of drugs in 2009 and possession of a firearm in 2015, according to the Los Angeles District Attorney's Office.

He is the only child of the late Ms Fawcett, who died of cancer in 2009 and was best for her role in TV's Charlie's Angels.

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His father, who received an Academy Award nomination for Love Story and has three other children from previous relationships, was diagnosed with stage IV prostate cancer in 2012.

Mr O'Neal's crime spree is said to have started on 2 May when the first victim was punched by a "male white suspect with red hair and distinct tattoos" in the Palms neighbourhood of Los Angeles.

The next day a man was repeatedly punched in the head after trying to start a conversation outside a convenience store.

At around 5pm on 4 May near the Venice Beach Boardwalk, "a male White victim looked at the suspect, at which time, the suspect stabbed him with a knife", according to a statement from the LAPD.

"Initially, the victim thought that the suspect had merely punched him in the back," the LAPD said. "However, once paramedics arrived, the paramedics discovered that the victim had sustained a serious stab wound to the left side of his body."

Another man was attacked nearby as he walked to his car at around 8.30pm.

"At 8.45pm, several people found the victim laying in a pool of blood with obvious stab wounds to his face and upper body," said the LAPD.

The fifth victim was threatened with a folding knife after the suspect "became belligerent inside a coffee shop" near Venice Beach on 5 May.

Mr O'Neal has already been charged with robbery, assault with a deadly weapon and possession of drugs in relation to the robbery of the convenience store on 8 May.