The following writing is a collection of historical observations that emerged during our travels and studies of the nine-square grid, which eventually led to the creation of studio substrata in 2018. Rather than presenting complete arguments in essay format, we decided to present this discussion on Palladian principles in correlation with our practical studies on heterogeneous space. It is everything but complete as we embrace the yet unnavigated future of our findings and operations. Ghost in the Shell was published in Act Two: The Riga Project as part of the reissued edition of John Hejduk: The Riga Project through which we’d like to seek new spatial possibilities.

Palladian villas visited during our Veneto expedition, autumn 2018, studio substrata, Reinis Salins, Igors Malovickis

Palladian villas visited during our Veneto expedition, autumn 2018


Ghost in the Shell

When Andrea Palladio designed villas for the sixteenth-century Venetian patricians, he employed a precise logic to create not only monumental but also economically and spatially sensible country houses. This logic, which was documented in The Four Books on Architecture (I Quattro Libri dell'Architettura, 1570), inspired generations of architects and historians to study his methodology in hopes of unveiling the rules that produced it. As the age-old problem of necessity and possibility has persisted through time, we too attempt to make sense of rules that can effectively counter it. Our study of the nine-square grid is a journey towards a lasting design strategy and an attempt to systematically respond to the complexities of the physical world.

By establishing a system of relationships between spaces, Palladio created a responsive structural framework that allowed him to shuffle and arrange architectural elements. He reinforced a general logic in which mathematical composition was the principal design strategy. In Principles of Palladio’s Architecture – Palladio’s Geometry: The Villas (1944), Rudolf Wittkower, a scholar of Palladio’s work, argues that a similar geometric formula underlies all of his villas – a nine-square grid. “Once he [Palladio] had found the basic geometric pattern for the problem ‘villa,’ he adapted it as clearly and as simply as possible to the special requirements of each commission,” writes Wittkower, adding that “he demanded a hall in the central axis and absolute symmetry of the lesser rooms at both sides.”

Influenced by his teacher in Munich Heinrich Wölfflin and his seminal work Principles of Art History: The Problem of the Development of Style in Later Art (Kunstgeschichtliche Grundbegriffe: Das Problem der Stilentwicklung in der neueren Kunst, 1915), Wittkower and later his own student at the Warburg Institute Colin Rowe practiced a methodology in which the subject matter of the work was removed from the overall context to focus entirely on the compositional strategy. In Mathematics of the Ideal Villa (1947), Rowe formally investigated the nine-square grid in Palladio’s Villa Foscari and Le Corbusier’s Villa Garches. Both architectural works were removed from their respective contexts and reduced to simple plan diagrams, which allowed Rowe to study rhythm, proportions, structure, and internal logic of form while sparing the delicacy of the surrounding environment completely.

The technique, in which the plan diagram acts as a conceptual foundation for architectural work, was an important point of study for Rowe’s fellow Texas Ranger – John Hejduk. Hejduk – an avid scholar of architectural language – used a kit of various architectural elements to develop a nine-square grid exercise in his University of Texas studio in the mid-1950s. Students were given a pre-existing nine-square frame and a set of architectural elements to explore the impact of design operations on the transformation of space. The task, whereby the design process was detached from challenges imposed by the physical world and the client, outlined an open framework in which architectural ideas, relations and elements can be developed. Hejduk used these principles to define a vocabulary of narrative structures and spatial relations between elements, which he perfected in the Texas Houses.

The possibilities of the nine-square grid were further investigated by Hejduk’s colleague at the New York Five – Peter Eisenman, who returned to spatial problematics in Palladio’s villas. After visiting Italy in 1961 with his mentor and colleague, Colin Rowe, and reading Transparency: Literal and Phenomenal (1955), Eisenman began to change his understanding of architectural perception and analysis. He writes in Lateness (2020) that “it was at this point that I realized that neither seeing nor representation was the basis of architecture, but rather, abstraction and the critical, which refers to the possible or the necessary commentary on a work. To be critical meant learning to see not only what was present, but also what was absent.” This led Eisenman to extensively study and experiment with the nine-square grid. Alongside building a series of Numbered Houses in the late 1960s and early 70s, he also wrote of Louis Kahn’s Trenton Bath House, Adler House and DeVore House in Ten Canonical Buildings (2008); Andrea Palladio’s villas in Palladio Virtuel (2015); and John Hejduk’s Texas Houses in Lateness (2020). In Virtuel, Eisenman analyzed Palladio’s use of the ‘kit-of-parts’ – portico, transition space and central space – and argued that in some cases they dislocate and overlay, creating different spatial conditions. Not necessarily “visible” in any one space, the characteristics of overlapping space cause it to be “other” and transition from supposed “ideal” towards “virtual” condition. By stating that Palladio’s space in some cases is heterogeneous, Eisenman opposed the homogeneity offered by Rowe and Wittkower.

Considering that researchers have mostly focused on certain geometric and spatial aspects within Palladio’s body of work, the full scope of his intelligence is yet to be grasped. Moved by the clarity of his villas, we set out on a journey to Veneto to create our own experience of the Palladian plan. As with Eisenman’s experience of standing in front of a Palladian façade in 1961 and describing what he could not see, we too felt a tremendous revelation when we saw countless layers of information and the sensitive reaction to the surrounding context, which Palladio so poetically described in the Quattro Libri. In Palladio, the Villa and the Landscape (2011), Gerrit Smienk and Johannes Niemeijer suggest that the only way to study Palladio’s villas is through an ecological perspective and in close relation to the peculiar environment they originated from. Amir Djalali offers further analysis of Palladian landscape in Prehistories of Common Space: Conflict and Abstraction in Renaissance Architecture (2013), arguing that in some cases Palladio reacts differently to context – at Villa Serego the land is organized through the rule of Brunelleschi’s perspective while Villa Almerico (la Rotonda) frames the landscape through the Albertian veil of colonnades.

Palladio’s ability to systematically organize spatial geometry and sensitively react to the surrounding landscape resonates with us deeply in our attempts to operate economy-driven rules and contextual nuances. The abandonment of strict symmetry and centrality has allowed us to effectively react to the complexities of small and dense land plots where natural daylight is often more valuable than the landscape. Similar to Palladio’s kit of three underlying spatial elements, we employ a system of three types of spaces as the basis for our algorithm, which allows us to generate seven hundred fifty-six (756) nine-square grid plan configurations, one hundred and eight (108) of which are spatially unique.

The input-based design methodology has become a vocabulary of possibilities, like the grammar of formal elements in Sol Lewitt’s Variations of Incomplete Open Cubes (1974). House for a Pastor (2018) was the very first physical prototype to which we deployed this algorithm. At first, it offered tens of probable configurations. Potential spatial curiosities, that could possibly complement the nature of the client, allowed us to narrow it down to a sufficiently suited nine-square grid composition. The plan of the chosen variation is organized around a central core – the baptistery – with a series of open, semi-open and private rooms. Each space is characterized by its own set of qualities – private rooms always retain their core character, semi-open rooms can merge with open spaces and retain their core functionality, while open spaces can combine with semi-open rooms or other open spaces to create new heterogeneous possibilities.

As we reflect on long-lasting design strategies, we frequently return to the ones used by Palladio. His ability to extract from historical context and offer new meaning for architectural elements is a profound inspiration, which accompanies our work today. By adopting and operating certain parts of the Palladian method, we are able to define a way of working in which place, time and the individual are at the heart of its meaning.

Algorithm for the nine-square grid, studio substrata, Reinis Salins, Igors Malovickis

Algorithm for the nine-square grid


Graphic representation of the algorithm, studio substrata, Reinis Salins, Igors Malovickis

Graphic representation of the algorithm


Compositional diagram for the house for a Pastor, studio substrata, Reinis Salins, Igors Malovickis

Compositional diagram for the house for a Pastor


The structure of the house for a Pastor, process image, 2019, studio substrata, Reinis Salins, Igors Malovickis

The structure of the house for a Pastor, process image, 2019


Interior view of the house for a Pastor, process image, 2020, studio substrata, Reinis Salins, Igors Malovickis

Interior view of the house for a Pastor, process image by Filips Smits, 2020