The tower’s parametric surface description or diagram is constructed upon a number of variables that increase the spectrum of differentiation and at the same time make it more specific to site and programme conditions. In this way, one never quite settles on whether the ‘rising masses’ are pragmatic or surreal. This initial diagram was based on an equation originally developed by Myung Min Son, Claude Ballini and George L Legendre for the first Rising Masses studio at the Architectural Association (AA) in London. It was made available in 2008 with a tender package that included the provision of space for commercial, office and residential uses and which specified the project brief: a building structure capable of operating within the tight margins set by developers while aiming to maximise the efficiency of the building’s performance ratios. A matrix processes the constraints given by the tendering package (such as plot size, floor height, number of floors, plot coverage, floor-to-ceiling height and floor area ratio) to determine dimensions of maximum efficiency. Overview of the site within Singapore’s office district. Starting with this premise, the project constitutes an attempt to challenge the ubiquitous skyscraper, in which the form is achieved by a process of mere extrusion and stacking of floors. Depending on the angle of view, the structure appears either solid or transparent, exposing the inner cores. Max Kahlen, Rising Masses, Singapore, 2008

Physical model of the tower slabs and podium. The articulation of the proposal challenges the phenomenon of thinness, the main desire at work here. 1

Text © 2011 John Wiley & Sons Ltd. The application of fast Fourier transforms (FFTs) reduces discontinuous, complex three-dimensional geometries to simple/developable surfaces. Along the same lines, the goodness of a square plan is acknowledged for its programmatic efficiency and simplicity; in fact, the mathematical notation of the square is equivalent to a ‘coarse’ circle plotted with only four points. The interlocking areas of the ‘towers’ within the tower form the critical moments of the production of spatial diversity. The idea is not to scare the user, but to create a building of transparency, where minimum depth allows internal spaces to span from one facade to the other, opening up views on both sides. By providing a catalogue of distinctive spaces, qualitatively and quantitatively, through the simple repetition of the square plan, the diagram of the tower aims to generate new organisational potentialities capable of producing difference. External staircases are placed between the vaulted facade grid and the straight inner slab. ✓

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X. Formally, the Hinging Tower calls for a new ‘coarseness’ or ‘low-resolution curvature’. The folds run diagonally on both building faces and intersect in two points to provide stability to the excessively slender slabs as well as to link the circulation paths. Starting with an elemental square plan, a mechanism of repetition driven by the diagram or mathematical function produces a variety of distinctive spaces and great organisational potential. The second approach is based on a set of periodic functions that aggregate to define the gridded facades. Both slabs connect at two points throughout the overall height. The morphological configuration of the space determines the programmatic pattern of the tower that begins to take shape: every programme automatically locates itself in the most suitable spot. ‘low-resolution curvature’ to optimise construction. The conceptual leap occurs when, in contrast with other parametric trends, the formal agenda of the Hinging Tower embraces a new ‘coarseness’ or

Within the infinite morphological variation that the diagram offers, the form of the tower is shaped by local conditions and the specificities of the site. Right: Calculation template to automate the building mass. Offices and apartments occupy both slabs. The process implies some degree of uncertainty. The intertwining effect brings a double benefit: structural strength and circulation flexibility. What this struggle produces is a building structure appearing at times rigorously efficient and at others surprisingly excessive and redundant. Additional parameters, such as the number of buildings and their proportion, as well as a periodic function that gradually arranges floor-to-floor heights, contribute to shaping a building mass of extreme dimensions. The Hinging Tower exemplifies a speculative architectural practice, conscious of its position within history and aware of its potential as a creative reservoir, probing purposefully the unknown for new models and opportunities. The gridded texture is kept independent of the floor arrangement, gradually distributing the horizontal members with increasing intervals towards the top, in keeping with the structural stress patterns of the facades. The final proportions determine two 180-metre (590-foot) high slab buildings of 6 x 40 metres (20 x 130 feet) each, sharing a common podium. It is characterised by an extreme thinness that is intended to heighten the experience of working in such a dense urban context. The cavities between the vaulted facade grids and the straight building slabs are open and accommodate external staircases. Being inside this space should trigger a feeling of floating between the pixellated facades of the neighbouring office towers. The external facades reflect the monotony of the neighbouring buildings, while the discrete break between the two slabs offers a vertical territory that allows one to step out into an unresolved urban void. Two approaches of mathematical nature were deployed to give distinct form to this desire. Walking along these stairs feels like stepping outside the building into the in-between courtyard, looking through a cloud of structure that hovers beyond the building limits. They are staggered lengthwise to create an in-between space serving as a vertical courtyard of private nature, in contrast to the open views onto the adjoining neighbourhood from the opposite side. In this sense, the integration of multiple variables makes the final form (iteration) of the tower an organisation responsive to local conditions, as well as to site and programme specificities. ЛІ2

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The project began with a coiling diagram based on the combination of sinusoidal, continuous and periodic functions. The elevator cores are not clustered, but distributed equally throughout the length of each slab, providing direct access to the offices and flats, and external corridors alongside the courtyard connect to the external staircases to allow interim circulation and access of fresh air. ,01

The programme requirements feature the mixture of residential apartments, offices and hotels so common to the urban landscape of modern Asian cities. It is at this juncture that the architect’s imagination, understood as the mediation between intuition and understanding, comes into play as a critical tool, operating to identify new potentials. The displacement of the ‘towers’ within the tower reveals the coiling effect of the sinusoidal, continuous and periodic functions. The site for Rising Masses is located within the regimented grid of Singapore’s booming office district. 1

Text © 2011 John Wiley & Sons Ltd.