Credits: Left-hand image and right-hand image

Bifurcation: A division into two forks or branches; the point of such division; either or both of two such forks or branches

Perforation: A hole made by boring, punching, or piercing; an aperture passing through or into anything.

Perturbation: The deviation of a system, process, etc., from its regular or normal state or path, caused by an outside influence;

Learning from his design for the unfinished Colònia Güell chapel (1898-1914) Antoni Gaudí wanted the structure for the Sagrada Família Basilica (1882 – ongoing) to be ‘equilibrated’, and calculated accordingly. By equilibrated, we mean that the gravity forces for the whole basilica are directed axially through the columns: each column, for instance, is therefore aligned to meet these forces as efficiently as possible through their axes. As a calculated optimised solution, every column is positioned slanted rather than vertically, which is atypical compared with what we are used to seeing in most buildings. Therefore, the Sagrada Família Basilica is a visual representation of the accommodation of gravity loading at work.

Columns alone will not efficiently accommodate all the forces being grounded unless they are subdivided through branching up to meet the masses they are required to support. The lyricism of Gaudí’s expression of worship beneath the canopy of a petrified forest is therefore matched by a lyrical structural solution.

Poetic in its simplicity, such a solution nevertheless introduces formal complexity: how do we make branching columns, and what is the nature of the joint between trunks and branches?  And what of the surfaces to the ceiling mass the columns support, and the perforations made to them as windows and rooflights?  

Architect Antoni Gaudí understood that freeform is extraordinarily difficult to scale up from sculpture to basilica and requires a degree of explicability.  But to make your intentions practically explicable to the builders, can surfaces still be more than planes, and columns more than cylinders, yet neither necessarily freeform, ungovernable by any algorithm? 

In his final work for the Sagrada Família Basilica, Gaudí introduced the hyperboloid of revolution (of one sheet) as his principal crafting tool to sculpt all the basilica’s window and ceiling vault openings along with many of the column capital intersections with the ceiling vaults. Columns are doubly rotated helixes that bifurcate into treelike structures to support the ceiling vaults.  Each ceiling and window opening is composed of hyperboloid geometry, each surface describable using nine parametric variables that can be configured infinitely of themselves, with each hyperboloid a unique instance with regard to its spatial relationship with its neighbours.  They combine using hyperbolic paraboloids in the spaces between to form the characteristic perturbations and perforations we see today.  Tweaking just a single variable can have a profound effect on the sculpted outcome; tweaking all nine offers unprecedented possibilities for the creative designer motivated by the beauty of light being guided to illuminate the interior while seeking optimal environmental performance. The world has been slow to take up Gaudí’s lessons, and this seminar aims to pick up where Gaudí left off.

Credits: Mark Burry

This workshop will look at the following challenge: Gaudí bequeathed a fascinating paramorph – an infinitely parametric archetype for all the towers that sit atop and surround the basilica void below.  This is his 1:10 model for the sacristies, one of which has been built today.  How might he have designed this archetype differently had he had full access to contemporary digital design and fabrication tools?  In the seminar, we will explore alternative options using hyperboloid perforations and helical columns and perturbating their assembly using hyperbolic paraboloids.  The description and representation of columns, creating a potentially underlying geometrical guide to how we branch columns and join them elegantly to the trunk. We will also seek alternative strategies for perforating the ceiling and walls to optimise heat and light gain with extraordinary aesthetic sensitivity. To do so, our journey will focus on generating and putting into practice a workflow that goes from design computation to composition and composition to fabrication, all based on parametric design software and a blend of analogue and digital fabrication tools.

Credits: After Gaudí Seminar, Perforating Light, MAA01 2021/22

Throughout this course, participants will be introduced to the subtleties of Gaudi’s parametric design and reveal the richness of his use of hyperbolic geometry. Using the provided digital workbench, participants will develop tools for sculpting a building façade, roof and ceiling, and supporting columns for a hypothetical development of Gaudí’s design for the sacristy. We will do this while simultaneously adapting hands-on techniques to experiment with intersecting hyperboloids, hyperbolic paraboloids, and helicoids (and planes when required). Furthermore, an additional layer of optimisation will be introduced and adapted to craft the facade parametrically with maximum environmental performance criteria. The aim is to develop a system that provides sufficient light to the interior while illuminating it with the beauty and subtlety of the Sagrada Família Basilica itself to which they are attached.

Credits: After Gaudí Seminar, Perforating Light, MAA01 2021/22

Finally, with the aid of analogue and digital fabrication and 3D printing, participants will produce a series of scale facade modules to test the effectiveness of the simulation software with respect to the environmental performance and aesthetic outcome.

Credits: After Gaudí Seminar, MAA01 2021/22

Learning Objectives

At course completion the student will:

• Understand lesser known but crucially innovative aspects of Gaudí’s design approach applicable to our time.
• Explore the architect’s role in adopting design strategies that are more familiar to the sculptor.
• Compare and contrast physical and digital representations of design intentions, especially concerning planned-for environmental performance.
• Introduce participants to the subtleties of Gaudí’s parametric design.
• Critically engage with Gaudí’s design philosophy by revisiting his project for the basilica sacristies.
• Experience working with geometries with nine degrees of freedom (parametric variables) to establish how less can lead to more.
• Adopt optimisation tools to craft the façade parametrically with maximum environmental performance criteria.
• Learn robotic fabrication strategies to produce large and small-scale models.