Nick Waterlow, 68, and his daughter, cookery book author Chloe Waterlow, 37, were found stabbed alongside an injured toddler at a house in an affluent Sydney suburb on Monday.
The victim's son Antony Waterlow is the prime suspect in the investigation into both murders, though police have declined to name him officially.
Both Mr Waterlow and his daughter suffered multiple stab wounds and the young girl, believed to be Ms Waterlow's two-year-old daughter, was treated for a wound to her throat, police said.
Today a former girlfriend of Antony Waterlow, who did not want to be named, told the Sydney Morning Herald he had suffered from "delusions" in the past.
"He had delusions which he believed to be real," she said.
"Mixed with this was also a truth to him... a truth that he cared for me, cared for people and that he didn't want harm to come to me, or anyone, and he wanted the best for me."
New South Wales police issued a photograph of a man seen leaving the property which police sources confirmed showed Mr Waterlow, 42.
Acting Chief Superintendent Geoff Beresford renewed the appeal for public help and added: "We believe that he's in the Sydney city area.
"We don't have any reason at this point in time to suspect that he's gone very far but the truth is we haven't been able to locate him."
Mr Beresford warned the public not to approach the suspect but to call police if they spotted him.
The injured girl's two brothers, aged four and eight months, were also understood to be at the house at the time of the attack, but were unharmed.
Mr Beresford said: "The children's father did arrive back this morning at around about 8am. (9pm GMT)
"He was reunited with his family at another location.
"He is with his family now and they're safe and well under the particularly harrowing and traumatic circumstances."
Local reports named Ms Waterlow's husband as digital technology consultant Ben Heuston who had been on a business trip to London when he received the tragic news.
The bodies were discovered in the semi-detached house in Clovelly Road, Randwick, in the Eastern Beaches suburb of Sydney, shortly before 6pm local time on Monday (5am GMT).
Mr Waterlow, who was awarded a Medal of the Order of Australia for his contribution to the arts, was described as "visionary" by critics when he was appointed director of the 1979 Sydney Biennale festival, the first to incorporate Aborigine art.
The University of New South Wales' College of Fine Arts (Cofa) said he was the director of its Ivan Dougherty Gallery and "a much loved and respected member of staff".
A Cofa spokesman said: "Nick will be greatly missed by generations of students to whom he was a powerful mentor, by his colleagues at Cofa and many friends and supporters in the arts community.
"We extend our deepest sympathy to his partner and other members of his family."
He said Mr Waterlow was a leading member of the arts community.
Mr Waterlow's sister-in-law, Anne O'Brien, told the Sydney Morning Herald newspaper Ms Waterlow was "a vivacious young mother who adored her littlies".
One neighbour, who wished to be known only as John, said he had heard a dispute at the house on Monday.
"I heard someone screaming, a man, but that was only for a few seconds," he said. "I thought it was a fight or something. I didn't hear a woman's voice."
A former neighbour, who asked to remain anonymous, told the newspaper Antony Waterlow "seemed like a really normal, average young man" when they chatted a few years ago.
He said they talked about sport, girls, computers and Mr Waterlow's attempts to become a writer.
Mr Waterlow admitted he had suffered from a problem with alcohol in the past but said he had given up drinking, the man said.
A Foreign Office spokesman said: "We can confirm the death of a British national in Sydney on 9 November.
"New South Wales police are investigating.
"Consular staff are liaising with local authorities and have offered consular assistance to the families."
Mr Beresford said the family had asked for privacy and would not be making a statement at the moment.
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