A symbolically critical pamphlet
For the hip architectural public, there surely isn’t any need of introducing the (in)famous Voronoi diagram. If there is, then you probably shouldn’t be reading this text and you’re better off doing something else. Nevertheless, I find myself under increasing pressure to express my thoughts regarding what I find to be a shallow, often completely mis-interpreted and un-justified use of what started out to be a mathematical “toy”. The practical applications of the Voronoi diagram are quite numerous highly fascinating. However, they are beyond the scope of this article – I want to focus mainly on the (mis)use of the aforementioned algorithm in architecture and urbanism.
I think it is quite safe to state that voronoi diagrams have now probably become the “golden mean” of computational architecture. However, I am quite surprised that it took this long for people to notice this – and, what’s even more surprising, there seems to be a severe lack of constructive criticism regarding this quite common and recurrent space-partitioning algorithm. Before moving forward, I would like to clarify the fact that I am not against using voronoi in architecture or urbanism whatsoever – there are clearly numerous meaningful uses, both in generating actual geometry and, probably more, in analyzing and visualizing data on an urban scale. What I am trying to criticize and draw attention to is the mental lock that this catchy algorithm has imposed, and, even worse, the common and frequent misconceptions induced by its strong affiliation with natural phenomena.
There are many reasons for the constant abuse of Voronoi cells (be they two-dimensional or three-dimensional) in architectural and urbanistic projects (the majority of which, by a lucky turn of events, are yet to be built). Crucial to this point is the association of voronoi patterns with organic structures found throughout Nature (living and non-living as well). The unmistakable silhouette can be found in numerous instances: you can see it under a microscope in almost any compact tissue like skin, you can see it in the way cells are distributed in a tree trunk, you can see it in the wings of a dragonfly; the list can carry on for quite a bit more. Taking into account the respective system’s constraints, voronoi cells can provide the most efficient structure or spatial routing paths for matter to organize itself into. This frequent recurrence in nature elevated the voronoi algorithm to the same status as that of the Fibonacci series and the golden mean was enjoying before. On top of this, its organic and apparently random appearance made it the perfect candidate for a wide range of good-looking geometric experiments. Furthermore, its close ties with nature somehow transcend the barriers of reason and magically attach organic, eco-friendly, pro-environment qualities to any product designed by using this technique.
For example, one common misconception is the fact that generating structure via a three dimensional voronoi diagram would automatically create a super-efficient, really optimized and, on top of this, organic looking structural system. This quite big confusion is probably caused by the numerous natural structures that resemble the output of a voronoi algorithm. There is however a quite obvious missing link in the association which should pop up instantly to any attentive observer. The structures generated by the voronoi algorithm are to be found at microscopic scales, starting off from somewhere near 1*10-5 m and continuing to decrease. Let’s say, for the sake of argument, that architecture begins somewhere around 101 m. There’s quite a big difference in scale, and due to symmetry breaking, physical laws (which, as any scientist worth his pay would tell you, are not universal truths, but the best approximations humankind has found for the way things work) rarely transcend through big scale jumps. In the present case it’s quite obvious – the predominant force in a living tissue at 10-5 m is a uniform pressure exerted on a cell by surrounding cells – and nature’s elegant response is a complex three dimensional voronoi structure which can be said is roughly indifferent to the main constraint which has shaped structural systems in architecture – namely Gravity. If you do a simple FEA analysis on a voronoi cell grid, you will see you’ll probably need more steel than a simple orthogonal grid to support the same loads, you will double production and building costs, besides getting less flexibility in terms of interior organization (spaces restricted to unique, bulky but flexible-looking cells). On the other hand, when used in straight-forward metaphorical approaches, and when this status is recognized and clearly expressed and not masked by a multitude of seemingly objective attributes, the approach can be considered to be “fair use”.
Another type of misuse of the Voronoi algorithm can be found throughout large scale urban projects – masterplans, local developments, etc. Cities are not composed of living “cells” in the literal sense – that’s where voronoi works. Cities are living organisms, but the rules behind the dynamics of city growth and crystallization are something completely different from a two-dimensional petri dish. You can use the voronoi diagram to compute the shortest possible paths around a set of point-like obstacles, but this argument is insufficient for justifying its direct transformation in a street network. Actually, street networks never had anything to do with the forces found generating voronoi cells. What you can often see is actually the same dangerous attitude and way of thinking behind modern urbanism clothed and presented as the exact opposite – naturally grown, organic urban lattices etc. – while in the end, if you start to rationally question and compare both approaches you can find dangerous similarities: both are lacking the same links with reality and are somehow strictly imposing their vision. This discrepancy noted here is actually, I believe, part of a bigger and much more comprehensive issue relating to digital and computational architecture.
What I find most distressing is the fact that there is a lot of cover-up work being done – voronoi diagrams, be they in three dimensions or two, always stand for some deep underlying natural phenomena whose efficiency and environmental-friendly qualities are automatically transferred to the respective project through a few rhetorical loops empowered by sophisticated jargon. The Voronoi algorithm does generate beautiful patterns and structures – which, when carefully used in the right places, are completely justifiable, sometimes even by aesthetic principles only. To conclude, I strongly believe that a certain level of sincerity should be (self)enforced when employing voronoi diagrams in architecture. While the manner in which this article is written might seem to some to be a bit too vehement, I am deeply concerned about the ease and nonchalance with which the voronoi algorithm is used – in the manner of an architectural recipe which can be applied anytime and anywhere, regardless of any other considerations. That’s why I have tried to raise awareness about the creative abuse taking place and its philosophical idiosyncrasies which, on a broader scale, do not restrict themselves to just this algorithm.
Dimitrie Stefanescu, 28 Oct 2010, Delft
 The most straightforward example of this is probably the duality of gravity and quantum forces. While at a large enough scale, space is dominated by gravitational fields. The smaller the space gets, gravity loses influence in the favor of electrostatic forces, in the end becoming a negligible factor. The analogy is quite relevant – voronoi-like patterns are found mainly at microscopic scales, whilst architecture operates on a completely different level which can be said to be under the strong influence of gravity.
 I am acutely aware of the advances in fabrication technologies and related sciences which might render this argument useless in the possible future. I am trying to argue that, given the sensible ecological context of our current world, we should look for more sensible uses and applications for the tools and techniques that science makes available.
 As any ego-centric person would do, I can’t help not to throw in a reference to one of my early projects: http://dimitrie.wordpress.com/2007/12/03/77/
 For more in-depth knowledge of this, I strongly recommend both Manuel DeLanda’s much praised A Thousand Years of Non-Linear History, as well as his interview with Neil Leach in the Digital Cities issue of AD (June 2009, p.50).
 I am not afraid to admit that I know this from personal, first-hand experience of the mentioned trap: http://improved.ro/blog/2010/01/urban-developement-proposal/
 To be more specific, an overall observed trend is that of employing computational geometry algorithms, often with spectacular visual results followed up by an active effort of fitting architectural qualities in the resultant shapes which usually ends in projects which are, for lack of a better word, fake.