The 27-year-old American artist was stabbed to death while jogging in Victoria Park, Hackney, a month ago. More than 100 people who were in the park at the time of the killing returned to retrace their steps.
Witnesses were told to wear the same clothing that they had been on the day of the killing, and to bring dogs if they had been walking them on the day.
They were accompanied by 100 police officers to help them mark their positions, with 100 support staff logging any crucial findings or developments.
Detectives believe that the murderer may have returned to the park to take part in the reconstruction. Detective chief superintendent Jon Shatford said that he thought the killer would attend to avoid drawing attention to himself by his absence.
"It may be that the killer has to place himself in the park, albeit in a slightly different position than on the day in question. If he does not, and if he is known in this park, he will be very obvious by his absence," he said.
He added that, if the killer was not in the park, he could be around the periphery or watching events on television. Mr Shatford said that detectives were looking for anyone showing an "unhealthy interest" in the investigation.
Ms Muller, a student at the Slade School of Fine Art, in London, was stabbed to death on a path in the park on February 3. Born in Virginia, where her parents still live, she came to the UK in 1998 and had also worked as a teaching assistant.
Her body was found by joggers and cyclists who heard her screams. Witnesses were today asked to stand in the exact positions they had been in at the time of the murder.
"We are trying to create two or three snapshots in time, where all the people there on that day will be asked to assume the positions they were in immediately before, at the time of and after the murder, so they can say who they passed in the park and who they spoke to," Mr Shatford said.
"We are looking for gaps, people who should be here who are not here today. I will hold accountable anybody who is not here today."
An actress who of similar height to Ms Muller, who was less than 5ft tall, jogged through the park wearing the same clothes: white trainers, black leggings, a baggy green jumper and a purple and white hat.
Overhead, two helicopters monitored the reconstruction as detectives accompanied witnesses and noted down any details they had remembered.
Among the witnesses retracing their steps were a 68-year-old woman who found Ms Muller after being alerted by her screams, a park warden who also ran to the scene and a cyclist who went to get help.
Mr Shatford described the killer as someone "who gets self-gratification from stabbing" but who may not be obviously mentally ill.
"He may have approached other women in this park, and may have been building up to this for some time," he said. "The killer was a stranger to Margaret Muller, not a stranger to the area or the park."