f* Voronoi

October 28th, 2010, essays

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[1]. 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[2], 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”[3].

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[4]. 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[5]. 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[6].

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


[1] 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.

[2] 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.

[3] 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/

[4] 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).

[5] 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/

[6] 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.

22 Comments. Wow. What do you think? Add your voice to the conversation below. Should be fun! Click to show the comments.



Thank you for this. I tell a story at the beginning of the year explaining this very issue…its a personal story, full of deception, coming of age, etc. In due time, I will tell it to you too, but I very much appreciate you taking the time to express this in such an eloquent way…

Quite a nice reflection, and one which could easily be transferred to other patterns/structures as well. To some extent, it would be refreshing to see more architects have the courage to say “I do X because I like it” instead of clouding their design decisions into pseudo-scientific, and often misunderstood, theories, often justified by irrelevant or heavily biased data.


Hey Louis, I knew you would somehow like this. ’tis you who coined the “voronoi porn” idiom in the first place. Can’t wait to hear the story – Delft is waiting. Thanks again for the kind words.

Hello _li, I can’t agree with you more. The “symbolical” from the subtitle is quite relevant, and you’re absolutely right – voronoi just got picked on because, well, it’s probably the most common example. The problem goes much deeper, as you very well said it – there is a clear trend running speculatively wild with different theories/algorithms/pseudo-science which are blindly applied to architecture – and usually, if you go behind the nice renderings, you find a quite strained and unfunctional product.

I think you make some really good points and voronoi fatigue has definitely set in to the computational architecture crowd. My experience with it was a trial by fire, doing a voronoi project at the DRL after so many before me. But if you work at it and use it properly, it can be a useful tool. Our project ended up being successful, though in part by burying the voronoi under many other layers of computation. In my research I also found structural engineers can it as an actual tool of optimization (wish i could still find that article)

I like to think of the voronoi as the equivalent of the Nine Square Grid project that every student of Modernism in the middle of the 20th century had to do. Give some students a voronoi project, and you’ll be able to tell who really understands computational architecture and who just wants to make some pretty shapes.

There are plenty of other systems that fall into this same category: L-systems, Cellular Automata, the Diagrid. But as a designer I don’t think it is a bad idea to try each of these systems out, and learn from them. Even if the initial results may be superficial.

But I think the most important thing you point out is that voronoi is not architecture, it is a tool, and it can be used well or poorly. I think what we showed in our DRL project is that if you use the voronoi as just part of a larger concept which focuses on architectural issue not biomimicry the project can be successful despite the voronoi.

Hello Matei,

You do make several very interesting points. First off, I’m not accusing every single aspect of voronoi-usage (or any other algorithm/geometrical system – the association is not fixed in regards with already proven items, rather I see it as freely encompassing variations, modifications and new “concoctions” of computational processes with a, more or less, geometrical output), and I freely admit that there are quite a few applications in architecture which are truly meaningful (the article you mention sounds quite enticing). For sure this is a weak point of the text and I should accord more space to this matter.

I have mixed feeling on the pedagogical aspect of a voronoi exercise, and an experiment like this can turn out good or bad, depending on many unquantifiable factors (tutor’s skill, student’s skill, student’s motivation to research more, etc.). You might be able to discern who’s in or who’s out – but there’s lot of room for error and I don’t think fixed standards are a way to judge people’s skills straight away. I’ve had some experience with tutoring at workshops, and usually people used to jump on an easy recipe (and voronoi for sure is one amongst many) not thinking much why, just because it was there and it was easy to reach only to end up with sensual, “shallow” geometries and a highly well-sustained discourse and rhetoric attached to them (i hesitate to call it theory). Depends on what your goal is, pushing parametric modelling and scripting skills via nice exercises or providing a rational and self-critical attitude towards all the wonders of computational architecture (like Neil Leach already argued for back in ~2000 in his essay Forget Heidegger – i think sometimes we ignore these aspects just because of the “flow”).

For sure, experimentation with different algorithms and processes can’t hurt anyone – the problem relies in the superficial results, which are not happening just “at the beginning”. We’ve been experimenting for quite some time, and it’s probably a right moment to stop and think about what we are doing exactly, lest we keep on experimenting for the experiment’s sake – and, what’s worse, impose our results as some sort of universal path architecture should follow (we should learn from history, not?).

Your final point is indeed most valid, and I couldn’t agree more. Like Neil Leach said, computers can be seen as prosthetics of the human body – without our input they’re inert. So the “responsibility” of how these tools are used falls on the user – how will this end for architects? I will end this over-long comment before i bore the shit out of everybody…

Hi Dimitrie,

nice article (I understand the feeling that drove your tone), also the comments exchange here with Matei raises interesting points of view and issues.

I totally agree on many points, and if I might add something to the discussion is that too often I have noticed (as an educator and also in many Archistar declarations and/or writings) a huge misunderstanding between a process and the descriptive mathematical algorithm. Many processes can be described in terms of more than one mathematical algorithm, yet none of those is comprehensive in rendering the complexity of a phenomenon.

I think the literal interpretation of this necessary starting semplification (that is, when the cathegories you define as orienting point in a dynamic field become a trascendental “grid” of discrete states thus excluding the initial complexity) is one of the main cause of the production of such poor production.

I see no wrong in experimenting for the experiment’s sake, and the attempt to universalize a trascendental taxonomy is the huge mistake behind many manifestos in architectural history. Truth is, in my opinion, that there is no recipe for “good” architecture. Despite the evolution of tools, theory and practice, talent counts. Wether it is an individual or a collective, diversified and articulated one.



Hey Allesio,

Thanks for your most insightful comment! Can’t really add too much to it. To maybe explain better, I am a bit distressed that many architecture students/graduates/teachers/etc., just meeting up with computational techniques (…) are either instantly converted to it or are quickly dismissing it because of its too experimental nature. The reality isn’t that black&white, of course, but I think that this sometimes is the case. So that’s why I am a bit biased against experimenting for the experiment’s sake – I do think an increased focus in applying these techniques to real-life, present-bound problems would represent a better investment of time. On the other hand, experimenting for sure is the best way to properly grasp and understand the philosophical and theoretical constructs behind a lot of contemporary architectural theory (emergence, self-organization, fractals, symmetry, flows, ecosystems, the non-linearity of it all, chaos, etc. etc.).

My main reason for writing this article, was, first of all, to provoke some discussion – which seems to happen, as well as to attract attention to the computational “traps” which might distance architecture from its goals, and, maybe better formulated by Andrew Humman in the comment above (or below), the “fetishization of algorithms”.

Looking back, the comments on this article are worth as much as the article itself. Wonderful to see the internet working!

Hi Dimitrie,

Just wanted to add a couple of points that seem relevant from a discussion between Sanford Kwinter and Jason Payne at the end of the From Control to Design book that I just finished reading.

First Kwinter talks about the move from process based projects to product based projects. This is something that I think is very good and I think emphasizes your point about moving beyond experimenting for experiments sake. Until these tools are put to use in actual settings we will not be able to see there true value, and if they can stand up to the rigors that buildings demand, from gravity to bathrooms.

This leads into the second point that Jason Payne makes that computational techniques are not design tools but production tools. I think that he is right in the sense that we as architects have to put them to work in terms of architecture, whether to create space or affect or just dealing with very specific parameters of a projects. In the end we have to solve architectural problems which demand architectural solutions.

In any case this is a discussion that is part of the larger debate going on about computations place in architecture, and I’m glad that you were able to stimulate such a lively one here. And I look forward to more.

Hey Matei,

Thanks for your input! It surely makes me want to re-write the whole article, to take into consideration all the points made in the comments here. Indeed it is/was a lively and most welcome discussion, thanks a bunch for making it happen! I have to get back to some readings.

It definitively makes sense, the transition to process-based products to product-based projects – it surely enforces a more architectural way of thinking, which, of course, i welcome!

thanks again, d.

Octavian GheorghiuNovember 11th, 2010 at 9:32 pm

Hy Dimitrie,
It is really nice to see students mature. I never got to meet you in Bucharest though I wanted to.
A much deeper point to the voronoi topic is the usage of algorithms and other parametric processes to generate architecture. I would not blame any project that uses this kind of tools as a mean of exploration and as a way to learn and improve. To prove something true or wrong, with value or shallow you can theories, use past examples, axioms or you can just experiment and see the outcome. The true problem lies in the power people have or have not to be self-critics.
I think a bigger problem to the misuse of such approaches is the fact it gives a strong argument, and to be truth, a good argument, to the conservatives who do not understand or do not want to understand a new style or architecture, called in many ways, Patrik Schummacher called “Parametricism” , I for a long time called it “Digitalism” and so on. Some people used scripting as a “lazy” tool to get fast results. This is especially dangerous for students who can fell in a trap set by this tools, a trap where the tools become concepts and after graduation become just some form of shallow architects who have no ability to make real concepts.
MEL,Grasshopper and classes like Rhinoscript 101 made scripting available to majority and unleashed the power to create new tools when the software was not able to respond to the needs, which I think was a good turn around because you would not design using only the tools made available by the creators of software, but instead you could make your own tools, and use the maximum of your imagination. I hope that this trend of just making formalism design based on “cool” scripts, design that have no real concept to support them will not be encouraged. But I think as you, and honestly I, have discovered many others will see the potential bad and good of this.
I would not worry about shallow architecture that might appear as a effect of misusage of algorithms or parametric processes, mostly because the world of real buildings has a strong filter in witch if you can`t explain why, who, what for and other basic questions it will not go along with designs just for sake of design, though sometimes it does, but it is so rare (and there is an even bigger topic if this kind of architecture is as bad as the low quality architecture). I think the economic crisis brought with it the end of the “Bilbao Effect”, and this is where the new tools have so much potential. This new potential to design smart, made in my opinion architectural practices like BIG so hip, not because they made “cool” designs, but because they had strong concepts put into use by tools made in house. Think that all major offices have, or will have research teams (SMG – Foster, We work for her – Zaha), who just make tools so that they can build smarter, faster and cheaper.
I hope I made a good argument to your topic and I believe that in the near future we will have a major shift in the way we design and build. It was nice to write some thoughts that I had for a long time on this topic.
All the best 

Hello Octavian,
Thank you for your contribution! I agree with all what you are saying, except the part regarding the new “style” of architecture – Patrick Schumacher’s parametricism or digitalism etc. I really don’t think these approaches can mature into a style, or by artificially doing so they will limit themselves and the practice. More or less they are ways of looking or understanding the world and architecture, or approaches. This abrupt transformation into a style can prove to be a bit cumbersome or dangerous – in terms of promoting radical ways of doing architecture, and/or formal and theoretical limitations, etc.

But this an altogether different talk. Thanks again for your most insightful comment. I think the article has doubled in size and meaning by the discourse along it!

Hi Dimitrie.
I love this article. And agree with you.

Just one thing: You used to use the Voronoi diagram too, even in Urbanism, where it has very small sense of usage, not to say it is pointless to use it there.
But now your opinions about Voronoi`s digram changed?

Sorry for the delay with which I answer and publish your comment – it’s just that for every human there’s 100 spambots and i’ve hardly had the time to go into spam filtering mode until now…

It’s just a simple evolution process – or that’s how i like to see it as. I’ve been riding the computational wave quite a bit, but this doesn’t stop me from critically reflecting upon what i do and why i do it. I actually used my projects as negative examples in a few lectures when i presented this article and the relinquishing control piece.

This piece is a bit harsh. For example, now – after reading a few more books – I can argue that authored architecture’s relationship with nature has always been on a superficial metaphorical level, and therefore the voronoi diagram fits right in as a continuation of previous endeavors – not that i agree at all with this relationship in the first place, it’s just the way it was pushed through by the obvious needs of “grounding” society into its surrounding world (or, to be more specific, its interpretation or understanding – scientific, societal, religious, etc. – of the surrounding world).

C'mon, write your thoughts in the box below.