Japanese architect Takato Tamagami used the golden spiral of the Fibonacci mathematical sequence to plan the twisted proportions of this house in Hokkaido, Japan (+ slideshow).

The house is named Northern Nautilus as a reference to this spiral shape and is positioned on the side of a hill overlooking a park to the north.

"We imagined that if we made the house high enough, they will have a nice view towards the park and the panorama of the town on the hill," said Takato Tamagami.

The volume of the house comprises two overlapping blocks, with one running parallel to the street and the other rotated through 30 degrees. Floor levels are different in each block and create a series of split levels.

"We created a dynamic spiral flow of circulation and form," added the architect. "Light and view transform in multiple ways as you move up and down the space."

A dining room and kitchen are located at the very top of the house and feature a double-height window with a view out over the park.

Two staircases lead down from this room to a mezzanine floor in the middle of the house. One winds down into a living room, while the other descends into a private, window-less study that is used by the client's wife.

One bedroom is slotted into the corner of this storey, plus two more are located on the ground floor below.

The split levels of the house create a large storage area between the floors in the centre of the house. A parking garage is also integrated into the volume, with a shelf above for storing a canoe.

Tokyo-based architect Takato Tamagami launched his studio in 2002. Past projects include N-House, which comprises two homes tangled around each other, and a showroom with a curving chasm for an entrance.

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Here's a project description from Takato Tamagami:

Northern Nautilus

This house for a young couple stands on a lot in a readjusted land on a hill. The site faces a street on the north, and is surrounded by neighboring houses on the other three sides. It seemed like a rather commonplace urban condition at first, but we were excited to discover a good view of a park below, located across the street towards northeast direction. We imagined that if we made the house high enough, they will have a nice view towards the park and the panorama of the town on the hill, and enjoy seasonal changes of trees from there. So our design started from providing a large window towards the park view on top floor.

The building consists of interlocking volumes of cuboid located parallel to the site and cube rotated by 30 degrees to face the park. Plan of the cuboid is based on golden proportion and spatial division is determined by logarithmic spiral. By giving order to spatial proportion and composition, one can provide a sense of stability and comfort in living environment. This is a classical design method that had been adapted by many architects in the past.

We added a new step to this method that is extracting the square and rotating it. As a result we created a dynamic spiral flow of circulation and form. Light and view transform in multiple ways as you move up and down the space.

Each volume has floor on different level and each floor is allocated for specific use, and the floors step up continually and extend outwards. The gap between mezzanine ceiling and top floor is used as storage space.

Garage is placed in a part of rotated cube and the ceiling is made high enough to accommodate a canoe, as the client loves outdoor sports. And we made storage space above the garage so that they can load and unload outdoor sport goods directly from the car.

Each space has different ceiling height. Entrance hall has a 6.6 meter-high void space and as you go up ceiling height of each living space gets lower. Living room on the mezzanine level is 3.9 meters high and dining room on the second floor is compressed to 2.2 meters high. Here the sense of horizontality is emphasized to enhance visual experience. As you approach the full-width window a bright panoramic view of trees and surrounding townscape opens up dramatically.

Study/book storage is located in that middle on the mezzanine level, which is used as private room of the client's wife. It is visually inaccessible from the rest of the house, except that it is visually connected to the double-height bedroom so the couple can feel each other's presence while maintaining some privacy. She can go down there from the second floor using stairs located behind the kitchen, so it is easy take a break from housekeeping and enjoy her free time.

By splitting floor levels we were able to separate living spaces while maintaining a sense of togetherness at the same time.

Above: concept diagram

The couple stands by the dining room window and sees neighborhood children playing cheerfully in the park. When they have a child on their own he/she will eventually join there. From this window they will keep an eye on growth of all children and their hometown.

Above: ground floor plan

Above: middle floor plan

Above: top floor plan

Above: section