Antonio Gaudi’s La Sagrada Famiglia in Barcelona is a fascinating structure. Not only has it been under construction since 1882, but it can arguably be considered as one of the earliest examples of the application of parametric design.

Gaudi used models as design tools, especially ones using chains hung from ceilings, or strings with small weights attached.

It has been known for centuries that a chain suspended from its ends results in a curve that naturally distributes the tension load evenly between the links of the chain. This is a called a catenary (think the Golden Gate Bridge). When this shape is flipped vertically, the now compressive load is similarly evenly distributed, resulting in an optimally efficient arch.

Gaudí applied this tension-compression analogy to chains hanging from other chains, in turn hanging from ceilings and made models of his buildings upside-down. Then, using mirrors on the floor, he visualised his designs downside-up.

Parametric design allows alternatives to be studied and compared in the search of an optimal design. Gaudí’s hanging chains do exactly that. If a chain end-point is moved, then the shape of the entire hanging chain model shifts and settles into a newly optimised catenary geometry.

Compare this to the traditional design process.

What may be considered the traditional design process involves selecting certain properties of the element being designed, applying the relevant laws of the universe to the selected properties, and then seeing what you get at the end of the process.

As a very simple example, a structural engineer may select a concrete beam depth and width, the concrete strength and the amount and distribution of steel reinforcement for a beam of a given span and a given applied load, apply the laws of solid mechanics, and so predict the strength of the beam in bending and shear.

If the strength is inadequate, different combinations of these properties can be selected and the process can be repeated until an adequate solution is obtained.

Note that this process results in an adequate solution, not necessarily the optimum or most efficient solution. We don’t know if a slightly different combination of these properties would result in a solution that uses less material unless we carry out numerous iterations of various alternatives.

Computers today can carry out these iterations very quickly. However, in many cases our design tools are basically responding to the “what if?” question of the designer. What if my beam is X by Y deep, for example.

Essentially, this design process, which admittedly is now done very quickly by computers, is modelled on the human limitation of only being able to do or think about one thing at a time in a linear, sequential process.

The parametric design process changes this.

Very simply, the parametric design process changes the “what if” question to an “I want” statement.

In the example above, instead of selecting the beam properties, we now say "I want a beam configuration for this span, to carry this load, and to have the most efficient combination of materials."

Provided we clearly define what we mean by ‘most efficient’ and provide the appropriate data and code, a parametric design package can answer this question.

At its most basic, it is simply the use of logic and rules to determine an efficient arrangement.

As an example, our London office was involved in the design of an exhibition building for the new headquarters of Abu Dhabi's Urban Planning Council. The building had a 70-metre by 70-metre two-way spanning expressed portal frame with "randomised" diagonal bracing elements. The overall aim was intended to create an architectural effect not dissimilar to the Beijing Bird's Nest stadium. Around and above this portal frame,a secondary structure created the roof and walls.

Initially the "randomised" diagonal elements were arranged simply for the aesthetic effect rather than any structural purpose. We tried using the diagonal elements to support the secondary roof structure, but trying to achieve this while also creating a "randomised" appearance lead to a highly inefficient design.

We decided to use parametric design to optimise the arrangement to suit our purposes, and so we started to compile our list of “I want” rules or parameters.

We realised that we would need to use the diagonal elements for bracing and reducing effective lengths. In consultation with the architect, we increased the number of bays within the portal frame to reduce the spans of the secondary roof and used the diagonal elements only for bracing and to reduce the effective lengths of the portal frame elements. This led to a number of rules for our parametric design, such as "limit the beam effective lengths to six metres."

We also consulted with steel fabricators to get advice on constructability. This led to more rules, such as "diagonal elements should not intersect at less than a five degree angle" and "diagonal elements should not cross primary frame elements at splice points."

Finally, we introduced rules to increase the "randomised" appearance of the arrangement.

This parametric approach resulted in a significant improvement in the efficiency and constructability of the diagonal elements and portal frame and resulted in a significant reduction in steelwork tonnage. Given the number of rules we had and the "randomised" nature of the geometry, it would have been nigh on impossible to come up with an efficient arrangement by hand or with traditional computer analysis.

There are numerous parametric design packages on the market, but I'm not looking to sell software. I hope to challenge the way we design today and urge designers of all products, be they industrial designers, furniture designers, architects or engineers, to consider their options.