Field theory describes the relations between these sheep when herded.

Architectural Myths #12: Field Space


Field space is the (heh heh) cornerstone of Parametricism so let’s find out what it’s all about. First thing – how did fields suddenly become so cool?

Classical fields are functions defined over some region of space and time. There’s gravity – described by a Newtonian gravitational field, and electromagnetism –described by electrical and magnetic fields. Here’s that magnetic field we all remember from school.

magnetic field

Your teacher hopefully explained that the iron filings aren’t the field – they only allow us to observe it.

Quantum fields are the same as classical fields but also take account of real things such as photons and electrons, inside them.

Quantum objects have the bizarre but useful property of being able to exist in multiple states at once, a phenomenon called superposition. Physicist Erwin Schrödinger illustrated the strange implications of superposition by imagining a cat in a box whose fate depends on a radioactive atom. Because the atom’s decay is governed by quantum mechanics – and so only takes a definite value when it is measured – the cat is, somehow, both dead and alive until the box is opened.

catteeScientists have now succeeded in measuring a quantum state without looking at it directly. i.e. The cat’s alive, but not happy.
quantum cat

This means we can get on with making quantum computers since it’s now possible to know when a quantum state is a zero or a one. It’s a start, OKAY.

Fields are useful in mathematics but they’re also useful in cricket so let’s just agree that field theory describes many and diverse phenomena. New ones are being found all the time. Field theory describes how these sheep behave when herded.

Field theory describes the relations between these sheep when herded.Or cows, when scared by a helicopter.


Field theory describes the movement of starlings within murmurations. (See also “swarm theory”)

Actually, these fields aren’t very diverse at all, are they?

Craig Reynold’s 1987 paper “Flocks, Herds, and Schools: A Distributed Behavioral Model” is the go-to classic. Here’s the introduction. [My emphases.]

The motion of a flock of birds is one of nature’s delights. Flocks and related synchronized group behaviors such as schools of fish or herds of land animals are both beautiful to watch and intriguing to contemplate. A flock exhibits many contrasts. It is made up of discrete birds yet overall motion seems fluid; it is simple in concept yet is so visually complex, it seems randomly arrayed and yet is magnificently synchronized. Perhaps most puzzling is the strong impression of intentional, centralized control. Yet all evidence indicates that flock motion must be merely the aggregate result of the actions of individual animals, each acting solely on the basis of its own local perception of the world.

One area of interest within computer animation is the description and control of all types of motion. Computer animators seek both to invent wholly new types of abstract motion and to duplicate (or make variations on) the motions found in the real world. At first glance, producing an animated, computer graphic portrayal of a flock of birds presents significant difficulties. Scripting the path of a large number of individual objects using traditional computer animation techniques would be tedious. Given the complex paths that birds follow, it is doubtful this specification could be made without error. Even if a reasonable number of suitable paths could be described, it is unlikely that the constraints of flock motion could be maintained (for example, preventing collisions between all birds at each frame). Finally, a flock scripted in this manner would be hard to edit (for example, to alter the course of all birds for a portion of the animation). It is not impossible to script flock motion, but a better approach is needed for efficient, robust, and believable animation of flocks and related group motions.

This paper describes one such approach. This approach assumes a flock is simply the result of the interaction between the behaviors of individual birds. To simulate a flock we simulate the behavior of an individual bird (or at least that portion of the bird’s behavior that allows it to participate in a flock). To support this behavioral “control structure,” we must also simulate portions of the bird’s perceptual mechanisms and aspects of the physics of aerodynamic flight. If this simulated bird model has the correct flock-member behavior, all that should be required to create a simulated flock is to create some instances of the simulated bird model and allow them to interact.

With only three simple rules governing the interactions of his “boids”, Reynolds was able to create a flock. None of the rules was ‘make a shape’.

Here’s some nature for you. Don’t be amazed by the pretty shapes. The birds are just going about their daily business following some simple rules and trying to survive. Not unlike us.

When the natural world produces such pretty shapes and patterns, it was a matter of time before architects would begin to think of ways to monetize it as the thinking person’s Art Nouveau – a new way to represent Nature (for whatever reason: biophilic predeliction, delayed onset of Industrialisation trauma, God-complex, desire for the illusion of immortality, because it’s pretty, because it sells ….) In other words, it has the potential to become an architectural style. With this precondition satisfied, we’ll need some academic analysis. First up was Princeton professor Stan Allen‘s 1996 “From Object to Field: Field Conditions in Architecture and Urbanism”. I quote.

To generalise, a field condition would be any formal or spatial matrix capable of unifying diverse elements while respecting the identity of each. Field conditions are loosely bounded aggregates characterised by porosity and local interconnectivity. Overall shape and extent are highly fluid and less important than the internal relationship of parts, which determine the behaviour of the field. Fields work neither through regulating grids nor conventional relationships of axiality, symmetry or hierarchy.

To his credit, Allen says his description of the properties and potentials of what he’s calling field conditions won’t necessarily produce a systematic theory of architectural form or composition, but he’s putting thoughts in people’s minds all the same.

Allen’s paper contrasts geometric and algebraic systems of design. Alberti’s famous axiom that “Beauty is the consonance of the parts such that nothing can be added or taken away…” is an example of an ideal organic geometric unity. “Parts form ensembles which in turn form larger wholes.”

alberti design additive

He then offers the example of the mosque at Córdoba in Spain as an example of a field on the basis that successive extensions have not altered the fundamental relationships between the parts as there is no overriding geometry making it all hang together.


However, his illustration of a plan minus the Gothic church inserted into it post-1236 suggests field relationships aren’t as indestructible as he suggests.


Allen’s second example is Le Corbusier’s unbuilt Venice Hospital.

There is no single focus, no unifying geometric scheme. As in the mosque at Córdoba, the overall form is an elaboration of conditions established locally.

venice332That’s two strong examples – both historical and of considerable, FWIW, repute. So we’re now more than halfway towards a new architecture! A little something from the world of art won’t go amiss. Enter post-war American painters and sculptors “attempting to move beyond the limits of Cubist compositional syntax.” Donald Judd, for one.

donald judd

Allen says post-minimalist Barry Le Va is the artist who moves most decisively in the direction of what he is calling field conditions. It’s all starting to get quite architectural.

Minimalist work of the 1960s and 1970s sought to empty the artwork of its figurative or decorative character in order to foreground its architectural condition. The construction of meaning was displaced from the object itself to the spatial field between the viewer and the object: a fluid zone of perceptual interference, populated by moving bodies.

Did somebody say fluid? Before we take that word and run with it, I’d like to thank Stan Allen for this paragraph and bringing Eladio Dieste (future Architecture Misfit #14) to my attention.

eladio dieste

eladio dieste brick

Did somebody say computer? All we need now is to add some technology to show how modern we are, and our theory is complete.

Parametric field space

Allen’s 1996 paper is fifth in the bibliography of Patrik Schumacher’s The Autopoiesis of Architecture Volume 1.

UntitledUntitled 2

Parametricism is about (and these are not my words – p293 TAoA Vol.1)

“finding associative logics that allow for the formal inter-articulation of a rich array of functional scenarios. […] instead of working with rigid forms, set up all architectural elements as parametrically malleable; instead of repeating elements, set up systems that continuously differentiate its elements; instead of leaving systems unrelated, always forge lawful correlations between the various systems that enter into a composition.” [emphasis mine].

Two points:

  1. In the natural world, the shapes of flocks and herds form because of certain parameters but none of those parameters says “form a shape” or rather, “form an infinite variety of them and pick one.” Architectural parametric design is an oxymoron. 
  2. The pretty, natural phenomena field theory describes are all in motion. They’re dynamic, not “dynamic”. No single frame of that dynamic phenomena is better or worse than any other. Choosing one single frame from infinite possibilities is a design decision of the old-skool kind.


Untitled 3

Let’s see where this next statement takes us.

Every form in architecture is susceptible to the formulation in terms of continuously varying parameters.


When one is on a ski jump or, for that matter, in an elevator to get to it, there isn’t much scope for functional variation. If we’re talking composition, then the elevator shaft and the ski slope are not resolved.  By Parametricism’s own definitions, the double code of function and beauty has not been achieved.


Football tends to be played on rectangular courts. Here, the roof does “intensify the relationship” between the roof and action that tends to be concentrated at the ends of the courts where the goals are. We need to remember that one can play football perfectly well without a roof over one’s head (although, to be fair, perhaps not in Qatar in summer).


Olympic swimming is also a function that resists parametricization. Swimmers dive in at one end, swim up and down a bit, and leave the pool. People generally watch from the sides. The ZHA Olympic Pool is an example of a building being protheticised in a very non-parametric manner to accommodate a function. It’s also possible to swim very well without a roof over one’s head.


With tall buildings, there aren’t many functions that can be parametricized without messing up structure, vertical circulation and maxxed-out floor plates.

zaha hadid_section

Auditoriums have similarly stringent functional requirements that can’t be messed with.


However within those parameters is scope for endless variation.


Stairs also resist reduction to the parametric variables of field space. The height of steps is generally constant, steps happen one after the other, and generally have a destination up and/or down. The only things that can be messed with a handrails (do you or don’t you?), the walls, and the roof.

zaha hadid boat

Finally, I’ll wager this boat has a symmetrical keel and central axis of propulsion.

It must be a continual battle to draw attention away from the functional bits that expose the limitations of Parametricism.

[Parametricism] and thus the advantages it can confer, is being validated by the style’s aesthetic values. 

Patrik Schumacher, 2011


The motion of a flock of birds is one of nature’s delights.

Craig Reynolds, 1986
Starling murmurations are simple field phenomena. (also see "swarms"

* * *

I don’t think ‘the advantages Parametricism can confer are being validated by the style’s aesthetic values.’ 

I think an aesthetic end result contrived to mimic nature’s delights is responsible for this interest in functional space as field space. Arse about face, as they say.

I doubt field theory would appear so attractive to architects if it usefully modelled unpicturesque things such as climate change, stock market volatility, the behaviour of people in mobs, the growth of cancer cells …

2 thoughts on “Architectural Myths #12: Field Space

    1. Graham McKay Post author

      I’m bound to get back there eventually Jonathan. These days, I tend to think ducks are really just decorative sheds. This gives us a choice between decorative sheds, decorated sheds or just plain ol’ sheds.


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