D’arcy Thompson (1917) describes how simplified organic forms can be understood as mathematical formulas in order to discover the geometric relationships that lie behind them. The most powerful tool which Thompson uses to mathematically understand how one geometry can be transformed to another is the co-ordinate system. He calls this the Method of Coordinates upon which he applies a Theory of Transformations (pp. 1023).

Thompson discusses that the transformations geometries experience are in fact forces and that these geometries exist within a permanent field of forces. Trying to understand the cause of the forces is riddled with complexity but their effect can be understood as geometric transformations.

However, in order to define a 3D physical object as a 2D equation, there is substantial simplification needed. Thompson defends this assumption by stating that the method isn’t an attempt at defining the fish or the leaf itself. Instead, he is trying to show that by representing the outline of the leaf as a curve with clear values and parameters, one can potentially understand all the forms the curve can become. In essence, Thompson was discussing a parametric way of thinking in 1917.

Thompson’s clear descriptions and informative diagrams evoked a great deal of interest in me, as my design studio project is related precisely to the idea of geometric transformation through changing parameters. However, as an architecture student, I also want to create a 3D form at the end of the day. While Thompson was simplifying a 3D object into 2D geometry and transforming it, I am tasked with generating 3D form from these transformed/transforming geometries. An action which is much harder than I anticipated.

Continuing on the theme of simplification, I agree with Thompson’s assertion that it would be impossible to find similarities between complex organic shapes and specimens if they were not simplified first. However, I find value in the deviation from these geometries and potentially how these deviations could be applied to architectural form. With the growing use of technology in architecture and pervasive research in topics such as kinetic and responsive architecture, buildings are becoming increasingly local and responsive to specific site conditions.

The deviations Thompson spoke of, in my mind, are the responses to these local conditions. Although, to Thompson’s disappointment, I am still enthralled with the deviations, his work has very poetically opened my eyes to the logic and reason underscoring modern notions of parametric design. I look forward to exploring its possibilities in the coming semesters at IAAC.


Theory of Advanced Architecture is a topic of IaaC, Institute for Advanced Architecture of Catalonia developed at Master in Advanced Architecture in 2016 by:
Students: Connor Stevens
Faculty: Maite Bravo, Ricardo Devesa and Manuel Gausa