Police mounted a reconstruction of Ms Muller's murder
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Police say a man who may have attacked two female joggers did so for "self gratification".
They also warned women against running alone in north east London parks after a knife attack on a 39-year-old which may be linked to the killing of jogger Margaret Muller.
The latest victim was repeatedly stabbed on Friday evening in Clissold Park, Stoke Newington, north London.
Detectives say her life was saved only because a doctor happened to be passing by and gave her first aid.
They think the attacker may be the same man who stabbed American-born artist Ms Muller to death in a nearby park 10 months ago.
As a result, Detective Chief Superintendent Jon Shatford warned female joggers to be "alert and aware".
The latest victim is now recovering in hospital, where she is under police guard, after undergoing emergency surgery to stop the bleeding from a severed artery.
Speaking outside Clissold Park, Mr Shatford said he was "very, very concerned" about similarities between Friday's attack and the murder of 27-year-old Ms Muller.
Margaret Muller was stabbed 49 times
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She was stabbed 49 times on 3 February, in Victoria Park, Tower Hamlets, east London, which is less than two miles away from Clissold Park.
Both women were small, had dark hair, were jogging in parks that are similar, and the attacks seem to be motiveless as there was no indication of robbery or sexual assault.
Mr Shatford said: "We are working on the assumption that the same person for this attack is the same person responsible for killing Margaret Muller.
"We are left with the conclusion that the sole reason for both these attacks is for the self-gratification of whoever committed these nasty crimes."
Murder prevented
He said he believes the attacker chose the latest victim because she was slightly built so that he could have "power over her".
The Clissold Park victim managed to escape from her attacker after a scuffle and ran away but collapsed because of her injuries.
But the female doctor who was in the park with her children at the time treated her.
Mr Shatford said her help had "probably stopped this being a murder investigation".
He advised women jogging alone to be more vigilant.
"While we don't wish to be alarmist in any way, I would ask women using parks in the area to be alert and aware of their surroundings.
"Let someone know where you are going, keep in the company of other people and report anything suspicious to the police."
Appealing for information, he wanted to hear from anyone who may have noticed a change in a male relative or who may have been approached in the park by a man "who made them feel uncomfortable".
Appeal to medics
He extended the appeal to medical professionals, who may be treating someone they suspect.
The attacker is described as white, in his early 20s or possibly a bit younger and wearing a hooded top.
Five people were arrested by police investigating Ms Muller's murder but they were later released.
Anyone with information is asked to contact Shoreditch police 020 7275 3404 or Crimestoppers anonymously 0800 555 111.