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Parametric Design as Contemporary Expression

Matt Fineout

Parametrics as a technique has recently gained a critical position in the discourse of architecture. It is considered to offer a new paradigm for architecture with its said capacity to generate an endless array of original and unique forms. Parametrics, it is important to note, represents a method that is based within a framework of constraints or parameters that through their individual variations can generate a seemingly endless variety of forms: an infinite matrix of sorts. But parametrics has also developed into a type of thinking: a thinking and approach that engenders a particular type of architecture. Proponents of this thinking consider parametrics the most significant development in architecture since the module. It is true that the apparent fluid mutability of parametrics stands in stark contrast to the hard and fixed increments of the module, but is parametrics and the thinking it represents something that is really new to architecture? I would suggest that today’s expression of this technique and thinking is only the current manifestation of a long lineage that finds its origins deep in the history of architecture, and that the tools we use today, namely tools of digital application, are primarily responsible for the foregrounding of this approach as an accessible means to generate architecture. In order to pose this argument, this paper will examine two projects from different time periods, one contemporary and the other historic.

S. Carlo alle Quattro Fontane by Francesco Borromini, designed and built in the early seventeenth century, can be considered in terms of parametric design within the context of contemporary architectural discourse. Of particular interest are the dome and its surface articulation, the sequential deformation of self-same figures in response to an external geometry. To begin with it is first important to understand the underlying geometry that constitutes the form of the dome. The dome is based on an oval described through the arrangement of primary geometrical figures, the circle and the triangle. Two equilateral triangles are arranged so that they share a common side. Circles are then inscribed within the triangles so that their circumference lays tangent to each side of the triangle. Lastly, the end points of the common side of the triangles serve as the center points of arcs that tangentially join both circles together. These are the constituent elements that form the oval, each primary and symmetrical in their base geometrical form.

From the oval springs the dome of which the surface articulation is a progression of geometrical figures, the Greek cross, an octagon and a hexagon. The surface articulation of the dome represents a sequential deformation of these base figures until they reach a diminutive form at the lantern. The base geometrical figure is a Greek cross. Octagons and hexagons are secondary geometrical figures that lie at the boundary of the cross. Octagons are located axially between the legs of consecutive crosses and hexagons are formed by the intersection of the legs between diagonally adjacent crosses. As these figures map along the elliptical surface of the dome their shapes must change in response to the diminishing circumference of the dome. The figures located at the base of the dome represent the primary figures that are the least distorted and nearly symmetrical. As the figures travel up the dome, their shapes and sizes distort to accommodate the changing geometry of the dome. Here the successive permutations of a figure are evidenced as a primary feature of the design in which one can witness the evolution of the form. This is an example of parametric design where one element progressively changes in response to the constraint of an external variant in this case the geometry of the elliptical dome.

Now let us turn to the Soumaya Museum by Fernando Romero in Mexico City, Mexico completed in April 2011. The Soumaya Museum can be considered to employ similar techniques as found in Borromini’s S. Carlo alle Quattro Fontane in terms of parametric design, but in the case of Soumaya they are turned inside out, quite literally. The Soumaya Museum is a freestanding structure that stands at the axial terminus of F. f. C. c. Cuernavaca Boulevard, rising to a height of 150 feet. The exterior form of the Soumaya Museum springs from two general movements: one is the seemingly twisting action of the skin while the other is the contraction of the form at mid-height producing a concave envelope. The twisting action is the result of the rotation of plan-figures located at the base and top of the building. The plan of the exterior skin at the building base is a five-sided irregular polygon with a radius corner between straight segments while at the top it is a four-sided irregular polygon again with a radius corner between straight segments. These polygons are similar in shape and size but are rotated against one another, the long axis of the base polygon is rotated approximately 45 19 Fineout degrees in relation to the top polygon. This rotation between the two figures produces the twisting action of the skin. What further complicates the skin is the concavity of the form; at mid-height, the circumference of the building is at its smallest, expanding to its greatest at the base and top of the building. The twisting action coupled with the concavity of the form generates an extremely complex and irregular geometry. This approach significantly departs from the underlying geometries that constitute S. Carlo. Whereas S. Carlo employs primary geometrical figures as a method to generate form, Soumaya discards primitive geometries in favor of the nuanced and manifold conditions of the site and program as a means to generate form.

The patterning of the skin for Soumaya also follows a similar strategy as that employed in S. Carlo but, due to the complexity of the form, reaches completely different ends. As in S. Carlo the Soumaya Museum employs a primary geometrical figure as a basis in which to pattern the skin; an equal sided symmetrical hexagon. The base hexagonal figure is located at the mid–height of the building at which point a row of hexagons extends around the building forming a horizontal ring. From this ring the hexagons extend upwards and downwards progressively distorting in shape and increasing in size as they reach the base and top edge of the building. But, unlike S. Carlo, where successive figures maintain symmetry for Soumaya each successive figure increases in asymmetry. This is due to the complexity and irregularity of the form and the need for an asymmetrical deformation of each successive figure to accommodate that form. It is interesting to note that, in Soumaya, the base figure is the smallest at the center of the building and extends in two directions, upwards and downwards increasing in complexity and size whereas in S. Carlo the base figure is the largest found at the base of the dome extending in only one direction, upwards diminishing in size until reaching the lantern.

In terms of parametric design, Soumaya is the other side to the S. Carlo coin; while one is symmetrical, the other is asymmetrical, one is interior the other exterior, one based on geometrical figures the other based on nuanced phenomena. In this sense parametric design has not changed but the approach has become more sophisticated. One 20 enabling factor that has contributed to a reemergence of parametric design can be found in the digital tools that are now ubiquitous throughout the profession. For the Soumaya Museum complex mathematical logarithms were developed to pattern the skin. Of greater significance is the massive amount of data that was processed by these logarithms in order to develop the patterning of the skin. The manual processing of this data would require teams of people working over a significant period of time to reach the same conclusions. The processing of massive amounts of data is similar to modeling complex phenomena such as computer models of various weather systems. It is not that mathematics has changed since the seventeenth century but processing power has certainly changed. There are incredible examples of stereometric drawings by Guarino Guarini and Philibert De l’Orme, as well as others that describe complex forms through individual masonry units – I would suggest this was another form of parametric design, though the ability to process large and complex irregular forms was limited at that time. In this new-found capacity, parametric design has found a reemergence: it is not new but being tested in new ways. Parametric design as a technique is not embedded in the tools: it always been about the thinking.