Fields have been an issue in architectural discourse, at least for the last 25 years. Stan Allen in his – now classic – text “from object to field” specifies some of the properties of a field. One is multiplicity. Fields are always multiple, since they are made out of a large number of individual elements, but most importantly because they allow multiple connections/relations between those elements. Then, they have a non-hierarchical character. Each element of the field is equal to all others, and gets differentiated from them due to local conditions. Also fields are inherently expandable (Allen uses the example of the Cordoba Mosque to illustrate that): A field can be expanded, virtually to infinity, without changing its inherent rules and syntax.

Computation added the tools necessary in order to study such field conditions. The element of a field is in its essence – no matter what its visual representation is – a vector. A vector has – at least in Euclidean space – a length (or magnitude) and a direction. Therefore a field of vectors becomes the ideal tool to represent, to study or to create flows (of energy, of matter, of information). And it is as such that the field has been used most successfully in computational experiments in architecture. Object-e has been involved in several such experiments during the last 5 years, which resulted in several (projects) but also in several tools created in order to extend the functionality of existing software in such directions. So this post is one of a series that will present some of those (simple but sometimes useful) tools and make them available for download (provided that I find the time to sort and clean those scripts a little bit…)

Orientation_field.ms is a script of this kind that does what the name implies: alters the orientation of a field of objects based on the distance of each object from several attractor points. Therefore focuses on one of the properties of the vector (direction) and it does so quite literally. The script is simple enough, but it serves as a good base in order to expand it more and enrich it with more functionality (and meaning). An earlier and even more primitive version of that script was used for Axi:Omes’ Digital Fabrication Lab project, 3 years ago. Of course the really fun part was actually (and manually) building that nice and clean digital model, which meant cutting, bending, sanding, drilling, threading and putting in place hundreds of steel bars, each one of different size and rotation. I think that it was all that work that gave meaning to the project. I miss those days…

"The element of a field is in its essence – no matter what its visual representation is – a vector"

What about scalar or tensor fields ?

I think the connections between these are also very interesting architecturally - for example taking the gradient of a scalar field to get a vector field, contouring a scalar field to get an isosurface, or splitting a vector field into 2 scalar fields, etc.

The term 'attractor points' seems to be thrown around a lot in generative design discourse, but mathematics provides us with much more precise terminology for talking about these things.

I am not talking so much about vector fields in a strict mathematical sense. I am trying to think of what a field could mean in an architectural context where it looks like thinking of fields as if they are made out of vectors is an abstraction that can be helpful. (and still, a scalar field can be a vector field where we focus just on the magnitude of the vector, and a tensor field a vector field in higher dimensions). Things are getting interesting when you start leaving mathematics behind and you begin imagining what new meaning concepts (like vectors) can acquire in their new context (architecture). Here is a very interesting attempt from Lebbeus Woods.

Same thing for attractors: I am sure that there is more precise terminology in physics or mathematics, but I don't really care about mathematical precision; I am looking for a word that will make sense in architecture, and I think that 'attractor' is such a word (see for eg. how Betsky uses the word in 'architecture must burn')