"If I unravel one pattern, there are 2000 variations," Tohi says.
Forms are highlighted in some of the drawings. These forms are then worked on with a computer drawing programme or turned into small wooden maquettes.
One such form, Aotea (White Cloud), was rendered in steel and placed on the forecourt of Auckland Art Gallery Toi o Tamaki during 2012's Home AKL survey of Pasifika artists. It forms the centrepiece of the Mangere show.
Tohi uses pins and yarn to explore the three-dimensionality of his patterns, building them off the surface. He paints fragments of them, and turns them into op-art prints.
Hanging from a ceiling are a couple of dozen cylinders wrapped in coloured wool, done 20 years ago while he was doing his stone sculptures, as a way to explore the patterns in another dimension.
For every pattern there is a different one on the reverse side that he wants to find and extend. On one side a point, on the other a hollow.
"The point is the intersection," he says.
Tohi came to Auckland from Ngele'ia in Nuku'alofa in 1978, when he was 18, eventually winding up in New Plymouth, where he taught Maori carving in the work schemes of the mid-1980s. That kindled his interest in traditional Tongan forms.
"In the islands as a young boy, you want to come here. You don't want to know about where you are coming from. You just want to enjoy everything new," he says. "When I worked with Maori, I saw what they do here was very similar to what we do back home."
In 1989, he received funding from Creative New Zealand Pacific to research in Tonga and Fiji, which consisted of interviewing traditional artists, many of them in their 70s and 80s. Often he wasn't sure what they were talking about - that would come from years of further study and reflection - but he knew it was important to capture their words.
On his return in 1990 he started applying some of those traditional forms to his work, which at the time had shifted into monumental stone carvings.
"There are certain patterns people come up and say, 'That is Tongan', but in fact there are thousands of them," he says.
For Tohi it raises questions about knowledge. "Where does mathematics come from, where does architecture come from, what is the core of everything?"
Buried in a weaving or lashing can be a story, a map, a military code, a prayer. There's also a sense of play that is universal. He points to a drawing recording the traditional bird pattern manuloa, and compares it with Dutch artist MC Escher's drawing of birds emerging from a triangle and flying away.
Parallels can be drawn from Tohi's work to the op-art of Victor Vasarely and the minimalism of Sol LeWitt, but he's careful to emphasise how his work is grounded in tradition, and he can't just place a point or line where he feels like.
"I have to go through in a traditional Tongan way to be able to understand it more logically, the logic of where to apply a point."
Working in so many media, what does he prefer?
"I thought I liked carving, then I thought I liked stone, then I moved into traditional painting and thought I liked it, then I moved to the computer and liked it. In the end I love all of them because you feel that you are holding the universe in the way you are touching three dimensions.
"In flat painting, you see one side of the pattern but you can't see that the other side is different. You can't see that until I build it, and then you can walk around it and see what it looks like."
Sculptors have storage problems, but Tohi now has a library of forms that could be built some day, if anyone wants to commission them. In New Plymouth, Tohi shared a studio with Don Driver, Tom Mutch and Michael Smither, working for years on his patterns and sparking interest not just in Aotearoa but internationally.
Eight years ago he packed up 20 tonnes of work and moved to Auckland.
"I hope Tongan people and Pacific people will see this show because they can relate to this kind of modern work. If you tell them about traditional things they don't want to hear because it's too old, and fair enough because they don't have time to make things. But when they see this, it takes them back to see some of the past and the traditions, because they were real in their time.
"This kind of work, I call it urban, this is about Aotearoa, because it is made in Aotearoa. It is about urban growing up."
Exhibition
Who: Tukutuku Kafa Mei Lotomoana by Filipe Tohi
Where and when: Mangere Arts Centre, Nga Tohu o Uenuku, to November 2
