object-e architecture

Fields part II: Morpher/BlendShapes

2012-01-28T18:05:00.003+02:00

Morphing, is the technique where a transition between two images is achieved seamlessly. The technique was (of course) developed initially for cinematographic purposes. As we read on filmsite.org, the first time it was used extensively was in the movie the willow, in 1988. One of the most impressive early movie examples was in Terminator 2: the judgment day. There the T-1000 cyborg terminator was equipped with the ability to morph into any kind of object (it was actually supposed to be made out of a morphing metal); the running time of the morphing scenes are counting up to 16mins (again according to filmsite.org). A very interestin example in the arts is the work of Daniel Lee and more specifically his 1993 manimal series (from these series Ben van Berkel and Caroline Bos are using the "year of the ox" in order to explain their 'hybrid building' concept). Of course, 3D motion effects could not stay out of the game in such a case. Most 3D packages today include tools able to transform seamlessly one piece of geometry into another (morphing or blend shapes). 3D morphing is based on the position of vertices of the objects. There is a base object (the one being animated) and one or several targets. The vertices of the base object are interpolated on paths created between the initial position of the vertices in the base object and the position of the vertices in the target objects.

The base concept behind 3D morphing however, while applied extensively in computer animation, is not that new. In ~1480, painter Piero della Francesca publishes his third book De Prospectiva Pingendi where he deals with the 3-dimentional representation of objects. As we read on this article, the book is composed out of three chapters: The first deals with the projection of 2-dimentional shapes and the second extends that to the projection of 3-dimentional shapes. The third chapter however appears to be the most interesting: there he describes what he calls 'The other method'. This 'other method' (meaning 'not Alberti's perspective method') is illustrated through drawings that are explaining how it can be used in order to represent a human head: First he draws cross-sections from top to bottom and then axial sections from the center of the head. The intersection of the two sets of sections, gave him 128 points positioned around the human head. All this process is already amazing considering the time that it was made, but the really amazing part comes next: Piero della Francesca was able to use those points and their relations in order to rearrange them and subsequently in order to be able to draw any other posture of the human head, in essence achieving auxiliary projection some hundreds of years before that was actually invented by Gaspard Monge. On a first note this is a great example of how one can shift from a representational method to a generative one. The representation of the intersection points of the two sets of sections, becomes a generative tool that allows the creation of any other position of the head.

Images of human head with orthographic projections & Head rotated from Piero della Francesca's, De prospectiva pingendi, Book 3, figures lxiv & lxvii. (Casa Editrice Le Lettere, source: http://www.thelancet.com)

Considering the relation with morphing, while Piero della Francesca's 'other method' is not exactly the same as contemporary morphing techniques, the similarities are nevertheless still striking: both methods are using points (the intersection points in the first case, the vertices in the second) strategically positioned on a surface that through their relative positions can be used in order to represent several other 'incarnations' of the surface.

When coming to initial contemporary practices in 'digital' architecture, morphing had a critical role. One of the main reasons was that morphing made possible explorations of the topological transformations of an object. Now, topology is a rather over - and extensively mis - used term in architectural cycles. It was used heavily in order to denote any kind of computer generated, curved form, the same way 'blobs' were used before that and 'parametric' is used now. We all have heard more than enough times how topology is an alternative to Euclidian geometry, meaning in essence curved forms vs rectilinear forms. For better or for worst though, topology has nothing against Euclidian geometry, since topology is not a different geometry at all (at least not in the sense that Riemannian geometry for example is); on the contrary, most topological studies remain within the Euclidian 'field'. Euclidian - or for that matter any kind of - geometry is studying the state of an object. Topology however is concerned with the transformations of an object. In other words, there is no such thing as a topological surface or object. The only thing that can be topological is a transformation. If we were to over-simplify, geometry is quantitative - the sizes of an object is what matters - topology is qualitative - it is connectivity, continuity and convergence that matters -. In short, the topology of an object is preserved when that object goes through continuous deformations. On the other hand the topology of an object changes if for example a new hole is introduced to it. Therefore, morphing is concerned exactly with that aspect: the way an object is transformed continually, moving from one geometrical shape to another while keeping its topology the same.

And this is the point where topology becomes a very useful concept in architecture today, and morphing a very useful tool that helps to study that concept. Because, if we were to abstract the principles of topological thinking, we could see that is not the state of an object that matters but the transformations that it goes through. Or, if we were to take that in a more philosophical level, we don't care so much about the being of an object, or whatever it is that we are studying, but we focus instead on the becoming of an object. If we consider the classic example of a cube morphed into a sphere, it is not really the sphere or the cube that we care about; it is the cube becoming a sphere - or the sphere becoming a cube - that is of interest (as in Terminator 2: it is not T-1000 as a human or T-1000 as a small lake of liquid metal that has an impact on us; it is the small lake of metal in a state of becoming human that is the most frightening). Consequently, identity is defined through difference: it is not what something is, but what something is in the process of becoming that matters, and therefore the differences between the stages of the transformation are the ones that are helping us identify it as the same object. On a different level, topology can help us understand a little better - or see from a different view - the difference between constants and variables; what are the things that have to remain the same and what are the things that can change values, in order for something to keep its identity.

During the last six years I have been working quite a lot with blend shapes and morphers, as a useful tool to study the above, and therefore developed several simple tools to help me deal with morphing. My main aim was to have tools that would allow me to use the different (but topologically equal) version of an object all at the same time, in the context of a field (see this post for more on fields). The concept for all of them is simple: an array of one object that gets locally differentiated according to specific factors. As a side note, all of them are more like a base to expand upon than fully developed tools.

1. surfaceBlendShapeField.ghx: this is a grasshopper definition that takes the idea of a blend shape and distributes it in a field. The local differentiation is based on the distance of each element from point or/and curve attractors. Quite primitive in relation to the next ones, but it can be easily expanded.

2. morphField_v1.ms: This is the same idea implemented in maxscript and it is much more robust than the rest. It is installing expressions that are controlling the value of a morphed target in all the objects of the field.

3. blendShapeFieldWithAttractors_v1.mel: this is the exactly the same as the above, only that it is implemented in mel for maya. Also, it is a little bit less user-friendly than the maxscript version - as is always the case with maxscript vs mel for me.

4. fluidsToBlendShapes.mel: This is a similar idea, implemented in mel, only that it is not using points to drive the blendShapes, but the density of maya fluids, which can give some very interesting results. Both mel scripts were initially written for the SKG in flux workshop that took place in 2009 with some minor updates added to them later. This an animation produced with the last script during the workshop:

SOPA Black Out.

2012-01-18T18:50:00.000+02:00

The internet is based on protocols. Protocols are the means to control. SOPA/PIPA bills are taking control from the users transfering it over to centralized places of power. Therefore, they are threatening the very existence of the net as we know it.

Learn more.

Madren 5340: opening today

2012-01-13T19:48:00.002+02:00

The new infrared installation will be on display on January 13,14 and 15 at the Art|House gallery-bar, as part of the event platforma 1. The opening is on Friday Jan 13th, at 20:00.

Merry Christmas

2011-12-24T22:49:00.002+02:00

It was a strange year the last one, but not without its moments. I hope 2012 will prove to be better. Merry Christmas and a happy new year to everybody!

Hilbert Snowflake was designed and fabricated last Christmas.

infrared @ SYMBIOSIS

2011-10-06T19:46:00.000+03:00

A new infrared project, under the title 313/315 is part of the SYMBIOSIS exhibition at the hotel Ariston, in the context of the XV Biennale de la Mediterranee.

The exhibition is opening on Friday, October 7th, at Hotel Ariston, Dioikitiriou (Karaoli & Dimitriou) 5. Starting at 21:00 and onwards.

Of patents, trolls and differential geometries.

2011-09-05T14:44:00.000+03:00

image: File:Patent, Mechanical Fan, 1830.png (wikipedia.org)

There is a debate going on the last days in relation to the idea of patenting geometric forms or the means used to produce them. The discussion started with this post on the Digital Morphogenesis blog. The post was triggered by a small note on the latest Kangaroo release:

"note : regarding the planarization functions – I have been asked to draw your attention to the patents held by Evolute, Helmut Pottmann and RFR: http://www.evolute.at/technology/patents.html"

As is turns out, there are actually two patents owned by evolute, Helmut Pottmann and RFR regarding (in simple words) the panelization of free-form surfaces with flat panels. To be more precise: they are not patenting the algorithm, they are not patenting the geometry per se, but "the physical architectural building solution". In other words, you can re-invent the algorithm, you can create a different algorithm that offers the same solution and you can play as much as you want with such forms in your computer. But if you decide to build the form, then you have to pay 1% of the construction cost. Really?

The blog post mentioned before points out the insanity of the situation. You can read evolution's answer here, and the answer of the creator of Kangaroo here. Better read for yourselves so you can draw conclusions, but here is how I see it:

Patenting of algorithms, geometrical forms, their constructed version or whatever else you can think of in this line, is fundamentally against any idea of intellectual or creative freedom. I don't really care if someone is a patent troll or not, the problem begins with the patent itself. If someone wants to capitalize on the research he is doing on architectural geometry, he can very well do so by selling the software (which is very much true for evolute), or by selling his services as an expert. Now, if he thinks that this is not enough there is a simple answer: do not conduct the research. Somebody else will. I am afraid that it is a rather important issue, and it is in the hands of all the people that are part of this community to give a strong answer: by voicing our opinion, by not supporting in any way those that follow such practices, by creating open source, freely available software and (equally important) by appropriately crediting the work of others that has helped us in our work. Let's just use the power of bottom-up processes.

update Sep 07: A new blog post from evolute on the subject here.
Looks like they are trying to make sure that we understand that they do have the patent. And no, by adding a little bit of torsion, you can not escape, they are going to get you!

August 2011: Chania

2011-09-02T20:46:00.000+03:00

I just return from an intensive 10-days-stay at Chania, where first the Sens[e-Res]ponsive Architecture workshop and then the "Rethinking the Human in Technology-Driven Architecture" conference took place. The results of both were really satisfying. The 3 student teams of the workshop worked intensively for seven days and produced some great ideas and 3 interactive installation (currently on exhibition in the Mediterranean Center of Architecture). I have to thank everyone involved in the workshop, and especially Kostis Oungrinis, Marianthi Liapi and Socratis Yiannoudes for being amazing hosts, and Maria Voyatzaki for the invitation and all the help. Hopefully the students will start uploading their projects on the workshops' blog soon, but here are some random photos:

The conference on the other hand had some great presentations and a lot of interesting ideas. Manuel DeLanda's presentation/performance was an ideal closing! My presentation was in the morning session of the second day, under the title "Network Protocols / Architectural Protocols. Encoded Design Processes in the Age of Control" The full schedule of the conference is here.

Sens[e-Res]ponsive Architecture Workshop

2011-05-27T20:29:00.000+03:00

This August I will be part of the Sens[e-Res]ponsive Architecture Workshop. The workshop will take place during 22-29.08.2011 at the Department of Architecture at the Technical University of Crete in Chania, Greece.

The overall discourse of the workshop revolves around the contextual and material frameworks of mediums, tools and techniques to create sensponsive environments that extend from useful to collaborative, developing a "sense" of their own. This year’s theme involves the design of an intriguing space for children with responsive partitions, utilizing rhino3D grasshopper with firefly and arduino. A detailed description of the theme can be found here.

The workshop will be taught by an interdisciplinary team of designers and theorists from Harvard, MIT, TU Delft, University of East London (UEL), Aristotle University of Thessaloniki (AUTh) and the Technical University of Crete (TUC). More information can be found here.

The Sens[e-Res]ponsive Architecture Workshop is now open to applications. Anyone interested in participating can fill-in an application form and submit the necessary material here.

Protocol Architecture / Beyond Representation @ UPatras

2011-05-24T00:35:00.000+03:00

On Wednesday (14:00) I will be at the School of Architecture of the University of Patras, where I will be giving a lecture under the title "Protocol Architecture / Beyond Representation". The subject is somewhere between encoded architectural protocols and the architectural drawing as a generative tool. The lecture will be part of the course 'Architectural Design and Digital Media'. Many thanks to Yannis Zavoleas for the invitation.

New Infrared project installed today

2011-03-24T20:10:00.000+02:00

The new infrared project was installed today in Aristotle Square, Thessaloniki. More info here.

Thess Bic Seat EEE?

2011-03-13T23:41:00.000+02:00

A new infrared project is almost ready to launch. Meanwhile, this a video of the previous one. More info on the previous project here, and for the new one will follow...

Digital Representations Final Review

2011-02-04T00:25:00.000+02:00

This year's class of Digital Representations has just ended. Here are some images of the projects.

Fields part I: Orientation

2010-12-01T03:27:00.000+02:00

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…

OEK-SIKA 2010 Competition: Honorable Mention

2010-11-15T17:24:00.000+02:00

The results for the OEK-SIKA 2010 Competition have just been announced, where we are awarded with a honorable mention. The competition concerns the design of a housing project at the outskirts of Thessaloniki. Congratulations to our hardworking team: Theodora Christoforidou, Sebastian Duque, Dimitris Gourdoukis, Roumbini Makridou, Vasilis Ntovros, Spyros Papadimitriou, Katerina Tryfonidou, Fotis Vasilakis.

CA Landscapes pt. I

2010-11-05T13:12:00.000+02:00

Two abstract landscapes, exploring the notion of vertical algorithmic growth. A CA is the basic algorithm, and it then gets interpreted into geometry. Those two images are actually early sketches. Hopefully more will follow in that direction.
Also, I am afraid that I drove my pc to its limits with this model counting 7.870.016 polygons. Somehow you always seem to need more computational power...

Algorithmic Body & Urban Performance @ Model

2010-10-08T13:20:00.000+03:00

Algorithmic Body and Urban Performance are featured on the latest damdi special Issue publication, "Architectural Models Lead to Design" that is focusing on physical modeling and its relation to the design process. Here is a link to the book webpage.

algorithmic body:

urban_performance:

Flying Info Collectors

2010-09-30T12:01:00.000+03:00

F(lying).I(nfo).C(ollectors) is a proposal for the Piraeus Tower 2010 competition that was asking for the ‘reformation’ of the facades of an existing tower in Piraeus, Greece. Our proposal is a swarm of mechanical 'birds' that covers the facades of the building (when the 'birds' are nesting) while it visually communicates information (when the 'birds' are flying). More information for the project here.

object-e @ 'portfolio' by damdi

2010-09-29T14:35:00.000+03:00

Damdi Publications just released 'portfolio', a collection of 5 books featuring work from 107 offices from around the world. Among them object-e. Features What if NYC Competition, Para*site, MAP, Algorithmic Body, Space Sound and the KU School of Architecture. Here is a link to the book page at the damdi website.

eCAADe 2010

2010-09-20T00:08:00.000+03:00

I just returned form the eCAADe 2010 conference in Zurich where I presented Protocol Growth. Several interesting presentations (full program here). Most of them in the direction of performance/optimization (and some sustainability as well). However I was a little disappointed to see that there were very few exploring experimental design, that is new approaches to the design process... Lets see how things will be developed...

Aggregate! on the 6th Biennale for Young Greek Architects

2010-09-14T14:42:00.000+03:00

Aggregate! is featured in the 6th Biennale for Young Greek Architects, at the Benaki Museum in Athens. Opening of the exhibition in on Wednesday, Sep. 15th, at 8:00pm.
More for the project here.

The Bankruptcy of Architecture

2010-08-30T15:58:00.000+03:00

The 2010 KAM workshop at Chania focused this year on the concept of Bankruptcy, literary or metaphorically, and included several interesting lectures along with the 9 projects that were developed by the students. A lot of material on:
Flickr
Blogger and
Twitter
many thanks to Stavros Vergopoulos and Aristide Antonas for the invitation.

KAM Workshops 2010: The Bankruptcy of Architecture

2010-08-10T01:19:00.000+03:00

This August I will be part of the 2010 KAM workshop entitled "The Bankruptcy of Architecture", which will take place from August 18th to August 27th, at Chania, Greece. Applications are still open (you can find the application form here) More information at http://www.kamworkshops.com/

Glowing Cloud - Parametric Model

2010-07-03T16:52:00.000+03:00

Glowing Cloud

2010-07-02T12:53:00.000+03:00

Glowing Cloud is a proposal for the open space between the existing building of the Hellenic World Foundation, in Athens, Greece. The canopy structure has been generated through an attractor field that encodes information regarding lighting conditions and possible movements. More information for the project here.

Urban_Performance @ DesignNet

2010-06-30T20:59:00.000+03:00

The results of the Urban_Performance workshop have been published on the July issue of the Korean design magazine designnet, v.154. More for the workshop here.

Urban Performance Exhibition

2010-06-29T16:20:00.000+03:00

more @ Urban_Performance

Urban Performance @ Thessaloniki Center of Contemporary Art

2010-06-08T18:34:00.000+03:00

The results of the Urban_Performance workshop will be presented at the Thessaloniki Center of Contemporary Art from June 8th to June 13th. The opening of the exhibition is on Tuesday, June 8th, at 20:00

Thess Bic Seat? in action

2010-06-07T01:25:00.000+03:00

more info @ infrared

Thess Bic Seat?

2010-06-04T11:41:00.001+03:00

Infrared are presenting Thess Bic Seat? as part of the event "I Thessaloniki Allios" organized by Parallaxi, on Saturday 5th and Sunday 6th. The installation suggests a new way of seating at the Nea paralia of Thessaloniki, combined with a space for bicycle stands. The geometry of the constructed object consists of a sequence of gradually differentiating planes thus creating a fluid, complex form. The shape offers many possibilities of ways of seating as well as playing and climbing for the children.

Urban Performance Workshop.

2010-05-24T03:44:00.000+03:00

Urban Performance is a workshop taking place until May 25th at the Aristotle University of Thessaloniki. Aim of the workshop is to explore how parameters concerning site conditions can guide the design process, while exploring at the same time the possibilities arrising from the use of industrially produced recycled materials. Here is the website of the workshop.
Visiting Professors for the workshop are Heather Woofter and Sung Ho Kim of Axi:Ome llc.

FLOW - Steedman Competition 2010. Honorable Mention

2010-05-09T00:11:00.000+03:00

FLOW, the entry for the 2010 Steedman Competition was awarded with a Honorable Mention. Subject of the competition was "the relationship between urban environment's and the river's edge, specifically the relationship of the City of St. Louis to the Mississippi River." Here more information on the project, and here the competition site.

P.I.U. – 09

2010-05-01T01:47:00.000+03:00

A proposal for a modular student housing project. More information here.

Aggregate! selected for the 6th Biennale of Young Greek Architects.

2010-03-15T20:51:00.001+02:00

Aggregate! has been selected to be exhibited at the 6th Biennale of Young Greek Architects. The biennale will take place in September 2010 at the Mpenaki museum in Athens. Here is a link to the biennale site and here more information for the project.

SKG in flux

2009-12-14T02:52:00.000+02:00

From December 11 to December 18 the SKG in_flux is taking place at the school of Architecture of the Aristotle University of Thessaloniki. The workshop is focusing on parametric urbanism, through generative and scripted techniques.
The final review will take place on December 19th, with guest critics Patrik Schumacher and Reiner Zettl.
A link to the blog of the workshop here.

Protocol Architecture: Public Presentation of PhD Proposal

2009-12-05T17:14:00.000+02:00

This coming Tuesday, December 8, 2009 I am presenting my PhD proposal, at the School of Architecture, A.U.Th. at 15:00. The title is:
Protocol Architecture. Complex Systems and Models of Self-Organization in Architectural Design.
The jury is: as.prof. S. Vergopoulos, prof. E. Tzekakis, as.prof D. Papalexopoulos.
The presentation is open to the public, so anyone interested is welcomed.

Sphere Packing vs Sphere Growth

2009-11-27T14:10:00.000+02:00

According to wikipedia, sphere packing “concerns arrangements of non-overlapping identical spheres which fill a space”. A classic problem in mathematics and computational geometry, sphere packing can be regular (where the centers of the spheres form a symmetrical lattice) or aperiodic. While regular packing can be of some interest, aperiodic configurations can yield some extremely complex and interesting results, that are worth studying…

You can find a simple sphere packing algorithm implemented in maxscript here. However, in my way to create the algorithm, I made a small mistake; I forgot the obvious: to check that the created sphere was actually inside the volume that I was trying to pack. Which gave some very interesting result, as seen in the second image, that resemble a ‘sphere growth process’. Mistakes in scripting are usually annoying (especially if you can not find them) but sometimes are the best way to discover new directions. This second version of the script is here. The two versions of the code are almost identical; one conditional less for the ‘growth’ option. The last two images show triangles created between the centers of the spheres.

Protocol Infrastructure

2009-10-23T19:50:00.001+03:00

Protocol Infrastructure attempts to approach the design of infrastructure in an alternative, bottom-up fashion, that is not based on master planning but instead on the development of a protocol that would allow infrastructure to ’self-organize’, adapting at the same time to the conditions that it encounters. The characteristics of such an approach are illustrated through the example of a structure, designed for the San Francisco Bay, which aims to the development of a system that would allow for a settlement to face the rising of the water level because of global warming. The model proposed, instead of following a ‘long term’ plan adapts itself to the situation that it encounters (water level, population needs) and grows in height following an algorithm designed for that reason. Machines are used from the system as the agents that would allow self organization to happen and the means to build the structure. More information here

object-e.net

2009-09-21T13:42:00.000+03:00

Object-e has a new home here. This blog will of course continue...

object-e.net

Fields of noise

2009-07-28T19:39:00.000+03:00

Noise is an unwanted random addition to a wanted signal [...] In Information Theory, however, noise is still considered to be information... (from wikipedia.org)

I would add, that sometime noise is the information. In these images an array/field of boxes is created, using the noise3, noise 4 and fractalNoise functions that MaxScript provides. The function is affecting each time the scale of the boxes.

Pattern Formation on Algorithmic Design

2009-07-19T15:34:00.000+03:00

Algorithmic Design is a new book published in Japan that focuses on the integration of algorithmic processes in architectural design. It features a reference on the Pattern Formation class that I was teaching last year at Washington University, in the last part of the book that discuses algorithmic design and education.

More CA...

2009-07-13T20:16:00.000+03:00

I was playing with MaxScript, trying to see how I can rewrite the .mel ca script and at the end I came up with a much more elaborate version for 3ds max, that implements 18 different sets of rules.
CA are quite critical for what I am researching right now (self-organization that is...). It is really impressive how different classes of rules produce different results, from quickly normalized ones to totally chaotic (rule 30).
The script is available for downloading at the tools section.

Folding the Suburbs / UIA 2005 proceedings

2009-06-03T00:05:00.000+03:00

This is a project, already quite old, that we presented at the 2005 UIA conference in Istanbul. It looks like it took some time but finally they published a selection from the presentations, including ours, under the title "Folding the Suburbs". I hope that it still makes some sense after five years... It was written and presented in collaboration with Vana Tentokali, Katerina Tryfonidou & Magdalena Pantazi.

Axi:Ome books

2009-05-23T15:48:00.000+03:00

Both Axi:Ome books are finally out! The first one (spacial practice) contains the earlier projects and the second one (damdi is.32 - between practice and education) the latest projects. It might sound strange coming from me, but I don't think that there are many practices with such quality and consistency of work, so these two books are really valuable!
You can find the first one here and the damdi here.

Cellular automata examples

2009-05-12T21:08:00.000+03:00

I finally found some time to wrap the ca mel scripts with a UI and to upload the at the /tools section of the blog. The following images are some examples where I used the ca in orders to generate geometry; surfaces in these cases.

Temporary Gallery Space

2009-04-29T18:11:00.000+03:00

The design for a temporary gallery space. Dimensions 10’X20’X10’. It explores the idea of having two ‘layers’ of transparency. One defined by the transparency/translucency of the material of the panels; the other defined by the size of the holes of the panels.

The grasshopper definition for the panels here.

KU project selected for the World Architecture Community Awards.

2009-02-28T18:01:00.000+02:00

The project for the New School of Architecture at Kansas University was awarded in the 2nd cycle of the World Architecture Community Awards. Here is a link to the project page and here a link to the posters. Thanks to those who voted for it!

foam brick

2008-12-17T13:50:00.000+02:00

“foam brick” is a proposal for a modular brick unit made out of foam that can be used in order to create soft partitions and walls. The bricks are held together with the help of cylindrical connectors that are also made out of foam.

Education in vacuo exhibition

2008-08-06T02:43:00.000+03:00

Education in Vacuo is an exhibition taking place at the Athens Byzantine Museum from 15th of June to 30th of August. It displays several diploma projects from the A.U.Th. from 1998 to 2006, all of which were developed with as. professor Vana Tentokali as advisor. Our participation comes under the name 'folding the suburbs' and goes back to 2004.
A lot of thanks to the organizing team for the great installation!

D. Areopagitou 2008 competition. 2nd price & mention.

2008-06-30T09:47:00.000+03:00

Our two entries for the D. Areopagitou 2008 competition. Theme of the competition was a design that will rethink the relation of Tschumi's New Museum, the Acropolis and the two historical building that are found between the two. Our first entry got a mention and the second one the second price. The competition site here.
(in collaboration with Katerina Tryfonidou, Theodora Christoforidou, Fotis Vassilakis, Vasilis Ntovros)

M.A.P. on ecoms magazine

2008-06-18T21:38:00.000+03:00

The competition entry for the 5th SUS aluminum competition has been published (along with the rest of the prices and mentions) on the 23rd issue of the Japanese magazine ecoms. Ecoms site here and details about the project here.

UIA 2008 infopoint competition

2008-06-17T23:19:00.000+03:00

This is the entry for the UIA 2008 competition. Two stochastic algorithms are used for the generation of the project. The first one is generating random boxes with the aim to create the spaces that will host the program (info point, exhibition area, press area). Certain criteria are set (distance between the volumes, shape of the public area etc.) which have to be met in order for the algorithm to position the space. The second algorithm is finding the bounding box of the 3 spaces and is then stochastically generating vertical cutting planes that define a structural system that creates a canopy above the 3 volumes. A rather weak linear element - that of a plane cutting a box - is repeated and weaved in such a way that the result becomes rigid and structural.

The light strategy followed is shifting the focus of what is being perceived as the dominant element during the day and during the night, from the structural canopy (day) to the glowing rectangular volumes (night).

(in collaboration with katerina tryfonidou, fotis vassilakis, dora christoforidou)

L-SYS_HRRU

2008-05-18T10:21:00.000+03:00

Some experiments with L-systems and how they can be used as form generating processes. Here is an example for a highrise structure. The l-system in this case is used more as a procedural modeling tool, than a truly generative system, but still recursion plays an important role for the development of the form.

Conferences_log

2008-04-15T09:15:00.000+03:00

While the future is uncertain (…) here are some events that I will certainly be participating this spring/summer:

Critical Digital Conference: What Matter(s)?
This coming weekend I will be in Boston for the Critical Digital Conference at the gsd. I will be presenting together with Katerina Tryfonidou. The title of the presentation is “What comes first: the chicken or the egg? Pattern Formation Models in Biology, Music and Design”. More information here.

EAAE/ARCC 2008 Research Conference.
25 - 28 June 2008 in Copenhagen. I will be presenting with Katerina Tryfonidou and Magdalena Pantazi. The title of the presentation: “Pattern Formation Models”.
More information here.

XXIII UIA World Congress of Architecture. Torino 2008.
June 29 – July 3 in Torino. Presenting with Katerina Tryfonidou and Magdalena Pantazi: “Digital Cartographies: mapping the global and local networks”. More information here.

v.2

2008-04-01T10:33:00.000+03:00

Pattern Formation Models

2008-02-19T04:55:00.000+02:00

Here is a link to the blog of the class that I am teaching this semester at Washington University. The class is looking at several different pattern formation models, deriving mainly from biology or mathematics, and how they can organized through the concepts of pre-formation and self-organization.

What if NYC... competition. Honorable mention.

2008-02-11T02:11:00.001+02:00

This the entry for the "What if new york city..." competition, that got a honorable mention. The idea is a development of the "inflateit" project. Here the focus is on the implementation of the project while inflateit was more about the development of a protocol. Also the inflatable units are following a different pattern in this version. More information for the project here. The competition website with all the entries here.

InflateIt

2008-02-11T02:00:00.000+02:00

InflateIt is an idea for the development of a protocol for the production of modular housing units. The units are developed in a hexagonal pattern, while the walls are inflatable. The elevation pattern is defined through a light study. The production of more units results in the expansion of the database with the lighting solutions. More information here.

Shifting Lines final review and exhibition (12/10/07)

2008-02-08T23:33:00.000+02:00

Photographs from the review and the exhibition for the Shifting lines to surfaces/Virtual to empirical class. The exhibition was up at Givens Hall from 12/09/07 to 01/05/08.
Guest reviewers were Heather Woofter, Dr. Mitchell Joachim and Sung Ho Kim.

interactive wall

2008-01-10T23:15:00.000+02:00

A study for an interactive wall, developed together with Fotis Vasilakis. The idea was that a tiled surface will react to the presence of people close to it, which will cause the tiles to rotate around their vertical axis, locally. Obviously an idea like this has to be based on sensors in order to operate, however is still in a very primitive stage.
This study was implemented using expressions and wire parameters in 3dstudio max.

axi:ome.net

2007-11-30T17:55:00.000+02:00

Axi:Ome's website is up and running! It took us some time to finish, but it is finally done...

Shifting Lines mid review

2007-11-19T04:40:00.000+02:00

Some photographs from the mid review for Shifting Lines to Surfaces, the class I am teaching at Washington University. The reviewers were Heather Woofter, Katerina Tryfonidou and Jen Maigret.

Algorithmic body... reactions.

2007-11-12T17:36:00.000+02:00

It is amazing how fast information can travel today, and it is even more important that this can promote dialogue and exchange of opinions, in a way that would have been impossible using just the traditional “printed” means. This was the first thought that occurred to me when I was browsing archiblog today and I came across the article entitled “Of Buildings, Computers and Telescopes” published originally on the HAD blog, by Rafael, a computer science student in the University of Sussex (unfortunately no further information is available). Subject of this article is to justify how one of my projects, Algorithmic Body, is using “invalid”, “grossly-erroneous reasoning methods” and totally fails to meet its aims by “contradicting its architectural intentions”. The above comments of the author are used in order to justify the thesis of the article which more or less is that:

“it is possible for a computer scientist to acquire the knowledge necessary to produce software that automatically designs buildings” while

“it is not possible for an architect to acquire such knowledge without formally studying computer science, or becoming a computer scientist”.

I will not stay to the fact that academic dignity requires at least a full identity when attacking somebody else’s academic work, and especially when using terms as the ones I just mentioned. That is not really the point, and as I already mentioned, the nature of the internet is totally different from the nature of printed media. But I think that it does make sense to try to answer to the claims of the article, since that would bring forward some important issues that architecture is facing today. And I will start from the first part, my “grossly-erroneous” project:

The main argument that justifies the grossness, according to the HADblog posting, is that I state in the description of my project that “one of the most interesting characteristics of algorithms is that they can be totally self-referential. An internal quality that can produce a process independent and autonomous, that relies only on its own rules.” According to the HAD posting by that I:

“ascribe to algorithms a property that is fundamentally incompatible with the concept of "algorithm" (i.e. "total self-reference").” And I

“Judge this non-existing property in algorithms ("total self-reference") as "an interesting feature of algorithms".”.

Quite interesting I must admit…Now let me elaborate the way I see it: the algorithm that I was referring to, and which I used in my project, is a cellular automaton algorithm. Now, it might be because I am Greek, but to me it seems rather self-evident (which in Greek would be auto – noito) that the word “automaton” (which in English would be self-powered) is inside the expression “cellular automaton” for a reason. But since not everybody is able to understand the reason behind the use of words I will try to explain: The word automaton is made out of the word ‘auto-’ which means self and the word ‘-maton’ which means power. Therefore: self-powered. To clarify things here is what dictionary.com has to say:

Au-tom-a-ton

1. a mechanical figure or contrivance constructed to act as if by its own motive power; robot.

2. a person or animal that acts in a monotonous, routine manner, without active intelligence.

3. something capable of acting automatically or without an external motive force.

[Origin: 1605–15; L: automatic device Gk, n. use of neut. of autómatos spontaneous, acting without human agency, equiv. to auto- auto-1 + -matos, adj. deriv. from base of memonénai to intend, ménos might, force]

Therefore a cellular automaton is an a priory self- powered system. While a cellular automaton algorithm is running, it is using only the rules found inside the algorithm itself in order to define its next generation. Therefore it is always and totally self-referential. Of course it needs an initial state (input) and it provides a final result (output), but obviously enough, the first comes before the algorithm (and can be defined in many ways, algorithmically or not) and the second comes after the algorithm (and of course can be manipulated in any way in order to be transformed into a building or anything else). The algorithm itself remains an automaton. In other words, a cellular automaton algorithm is by nature self-referential; other algorithms may not be. However, all recursive algorithms tend to be self referential. (1)

In any case, what is important in an architectural context is not the question whether the algorithm is self-referential or not, but the fact that the architectural process is self-referential. Therefore the process in my project is a process using rules that are internal to it and are not referring to any of the traditional external architectural factors, like program requirements or site conditions.

Nevertheless, there is a even more important problem in the thinking behind the discussed article, that doesn’t have to do with the correct or erroneous use of words: The problem is that the concept of algorithm as employed in architecture is evaluated in relation to the concept of algorithm as used in computer science. Concepts and ideas transferred from one field to another, not only can be altered and redefined, but they have to undergo such a process, if we want them to produce new ways of thinking. Of course that is a position, that underlies my work, and is largely based on the writings of Gilles Deleuze and Felix Guattari (look for example the way that they use concepts like rhizome, diagram, machine etc). Supporters of ‘universal truths’ and “pure reason” will of course disagree. And in that context it makes sense that the posting refers to Alan Sokal, author of the notorious book Fashionable Nonsense, where he tries to render the work of post-modern thinkers like Deleuze, Lacan, Kristeva and Baudrillard as nonsense, based on the idea of a ‘misuse’ of scientific terms and concepts. What does not make any sense at all is that on a previous article on the same blog, Manual DeLanda’s article “Gilles Deuleuze and the use of genetic algorithms in architecture” is also used in a similar fashion. But that is a whole different discussion.

The above observation is actually answering why computer scientists, unfortunately, will never be able to produce architecture. Because science, as Deleuze and Guattari point out in their last book “What is Philosophy?”, must always isolate a small fraction of reality in order to operate. On the contrary, philosophy, and I will argue, architecture, have to deal with an extremely broader field, which tries to include almost everything. If one succeeds to understand that difference (obviously Sokal and the author of the article is far from success in that aspect) one may very well become an architect without a formal education (in a similar way that Le Corbusier or Tadao Ando did). Similarly an architect can use computer science in architecture, as long as he understands the qualitative and quantitative differences between the two fields.

I will use a quote from an interview of Marcos Novak to explain myself better: “To be fair, though, there are at least two architectures, the architecture of accommodation, and the architecture of excess. Accommodation produces buildings, excess produces 'Architecture.'”(1) So, it might be possible for someone to write a software that will produce buildings; it is a whole other story to produce Architecture. Architecture goes far beyond problem solving, to suggest new ways of thinking and inhabiting space.

I will conclude with a phrase from the beginning of the HAD posting that triggered this text. And let me replace the words computer science with the word architecture:

“It is understandable that people who are not exposed to architecture miss the breadth of the discipline and relate it to something more familiar.”

References:

(1) “A recursive definition or a recursive algorithm is characterized by self reference. Typically with recursion, a function is defined in terms of an earlier version of itself” Cragal,J.M. Descrete Mathematics for Neophytes: Number Theory, Probability, Algorithms and Other Stuff.

Algorithmic Body on Surface magazine

2007-11-09T19:18:00.000+02:00

Algorithmic body has been published on the November issue of San Francisco's design magazine Surface (is*68). The publication is part of the annual avant guardian project: "In our annual Guide to outstanding undergraduate and graduate design, we salute this year's crop of students-laureates, who focus on smart and economical flat-pack solutions for everything from products to architecture, and explore the user-as-catalyst approach that's turning design into a participatory process..."

MAP: 5th SUS aluminum competition. Honorable mention.

2007-11-05T05:46:00.000+02:00

A project for a modular aluminum kiosk developed in collaboration with Claudia Barahona for the 5th SUS aluminum competition, where we won an honorable mention. Visit the competition site for all the entries. More information for the project here.

flash tests...

2007-10-18T01:59:00.000+03:00

Algorithmic body: physical models

2007-10-11T08:59:00.000+03:00

Widmann exhibition; May 2007

2007-09-30T22:11:00.000+03:00

This post is a little bit outdated, but actually all the previous ones were :-) The layout and some photographs from the widmann exhibition that took place on May 2007 in Washington University in St. Louis. My participation had the title design/research and included most of my work from September 2005 to April 2007. In other words... old staff... A good way, I suppose, to summarize and move forward...

Fractals

2007-09-02T09:43:00.000+03:00

Some experiments with fractals, using chaoscope and gaston. Both applications can generate fractal formations in 3d. However, the models are made out of (millions of) points, so I suppose that it would be impossible to export in any standard 3d format...

Walk through

2007-09-02T02:58:00.000+03:00

A small walk through of the project published at the previous post.

Voronoi Study, part_03: algorithmic body

2007-08-28T01:54:00.000+03:00

In my previous post concerning voronoi diagrams I presented an example where I used program requirements in order to define the initial set of points that will be used in order to create the final voronoi diagram (the problem of deciding on the initial set of points is, I think, one of the most interesting in relation to voronoi diagrams). However, as I wrote before, I find far more intriguing the idea of using an algorithm that can simulate a process of growth for that scope (lets call it a 'growing algorithm'). Therefore I continued my research in that direction by employing a cellular automaton script (same one I used on the space_sound project). So I developed a process, or 'recipe' that can be described by the following steps:
a. a 2d cellular automaton script is executed, with a random or pre-defined initial configuration of cells.
b. every generation of the ca is stacked on top of the previous ones creating this way a 'progression' of active cells.
c. the centers of the active ca cells are used in order to generate the voronoi diagram. The limit of that diagram is defined by the limits of the outer active cells of each generation of the ca.
d. the edges of the voronoi cells are used as the structural system.
e. a smoothed version of the voronoi cells is used in order to define enclosed space.

The above described process is employed in the design of a specific project displayed here (a transportation node + shopping mall downtown St. Louis). For the needs of this project an extra element is added to those of the structure and the enclosed space: a transparent skin wrapped around the composition. Fibercarbon for the structure and ETFE pillows for the skin are proposed as materials.

I think that, independently from the final result, the most interesting part of the project lies in the initial process described in the beginning. A 'growing algorithm' that will help us understand architecture as a growing organism that almost have a life of its own. An idea by no means new (look for example the metabolists or the 'urbican fever' - or fever in urbicand, whichever is the translation in english) but which becomes far more easy to work with through the computer.
More things are to follow on that subject... hopefully...
more information here

Space_Sound

2007-08-24T06:12:00.000+03:00

Space_Sound is a study on the work of composer and architect Iannis Xenakis. The study took the form of an interactive web site (which can be seen here. However there are still some problems with the page so it might not display correctly).

Iannis Xenakis used extensively computation and mathematics in order to create music. The initiative for this project was that while Iannis Xenakis is widely acclaimed and studied as an innovator in avant guard music, his work is not extensively examined in relation to architecture, and when that is done the focus is always on his architectural designs and mostly on the Philips Pavilion. However, Xenakis in his writings was always underlining that his methods in composition are not only applicable to music, but also to the visual arts and most notably to architecture.

Xenakis’ musical scores are composed in such a way that they have an underlying spatial dimension. His scores and diagrams for his compositions share very little resemblance to conventional musical sheets, while they could be undoubtedly “read” as spatial diagrams and architectural blueprints.

Xenakis was one of the first researchers to use computers in his musical/mathematical explorations. With a delay of some decades, the use of the computer in composition reached also the field of architecture and eventually led to a more constant, or more obvious, impact of mathematics to architecture. The architectural avant guard today has to deal with, up to a certain extent, with mathematical or computational processes like cellular automata, L-systems, stochastic process and boolean algebra, all methods employed earlier by Xenakis in his work.

Having the above in mind, Xenakis’ work could prove itself extremely helpful in relation to the questions that computation is posing to architecture today. More specifically, Xenakis’ work could provide insights for architectural practice in relation to the computers in two ways:

a. First in a theoretical level. Xenakis provides a very extensive philosophical and theoretical background for his work through his writings, which seems possible to be used also in relation to architecture today.

b. Secondly in a design oriented level. Iannis Xenakis started to use mathematics and computers as his tools for composition in the beginning of the 1960’s and continued this research until the end of his life. Therefore his work has to offer a great variety of methods, techniques and processes for the musical composition. Given the fact that Iannis Xenakis’ way of working with music was based on ‘spatial’ techniques and visualization of his ideas through drawing, a study of his projects could offer precious insight for architectural design. In addition to that, the introduction of those spatial qualities in Xenakis’ research that focuses on sound, arises questions on the relation between space and sound and how the one discipline can offer resources to the other.

So, space_sound consists mainly of visual representations of several methods that Xenakis employed in his work. Through scripting concepts and mathematical ideas like boolean algebra, alleatory distribution of points on a plane, brownian motion, cellular automata etc. are used in order to create small animations that are trying to explore the spatial or architectural qualities that those concepts can activate.

Some direct links to the animations:

brownian motion

aleatory distribution of points on a plane

cellular automata

boolean algebra

Voronoi Study, part_02

2007-08-24T05:38:00.000+03:00

This is a first attempt to use the voronoi diagrams for a specific design. The initial set of points is defined by the program requirements. The edges of the voronoi cells become the structure, while a first idea for enclosed space was to use again the voronoi cells (in a 'smoothed' version) as clusters of space in a configuration that resembles the relation of bones to organs. This project though was not developed further...
more info here

Voronoi Study, part_01

2007-03-02T02:26:00.000+02:00

A voronoi diagram is a way of decomposition or subdivision of space based on an initial set of objects or points (for more information http://en.wikipedia.org/wiki/Voronoi). Voronoi diagrams have countless applications from statistics to biology and urban planning. Lately they are becoming ‘popular’ also in architectural design. There is indeed a number of reasons making voronoi diagrams useful in architectural design:
a. Their structural properties, both in 2d and 3d.
b. As a way to subdivide/organize space, based on proximity/closest neighbor.
c. The fact that they can describe many natural formations, like soap bubbles, sponges or bone cells.

There are two problems arising though. The first is a method to construct them. It looks that the most reliable solution until know is Qhull (http://www.qhull.org/) , in relation to rhino or generative components. Rhino script could be another option.

What is more interesting though is the problem of defining the initial set of points. Of course there can be several different solutions, for example program requirements. Although, it would be far more interesting to use voronoi diagrams in relation to a growing process, for example cellular automata or l-systems. That could produce dynamic voronoi diagrams, and at the same time would be closer to their mathematical/algorithmic nature, by defining a specific simple set of rules for the generation of the initial set of points, in a similar way that the points are defining the voronoi diagram.

Readings:

-Aranda, B., Lasch, C. Tooling New York: Princeton Architectural Press, 2006.
-Bollobas, B., Riordan, O. Percolation Cambridge: Cambridge University Press, 2006.
-Kim, M.S., Shimada, K., (eds.) Geometric Modeling and Processing – GMP 2006 Berlin: Springer, 2006.
-Klein, R. Concrete and Abstract Voronoi Diagrams Berlin: Springer-Verlag, 1987.

-Okabe, A., Boots, B., Sugihara, K., Chiu, S.N. Spatial Tessellations, Concepts and Applications of Voronoi Diagrams West Sussex: John Wiley & Sons Ltd, 2000 (f.e. 1992).

more info here

Design for a new school of architecture, ku campus

2007-02-09T12:34:00.000+02:00

A studio project, for a new school of architecture for the KU.
The idea begun from Frei Otto's studies of lattice structures with rigid joins, and became a study of how a structural system can 'overcome' its main property (that of being structurally efficient) and became a system that is at the same time an 'ornamental' element and the element that defines spaces (and of course the structural system as well). Also an attempt to see how this complexity can be fitted inside (and used in order to define) a volume as simple as that of a box.

At any case Frei Otto’s work is still an endless field of inspiration.

Project for a Garden.

2007-02-09T00:59:00.000+02:00

Technological developments have multiple results in relation to architecture. The ability to observe at the micro level surely falls into those developments. Cells and microbiological structures are offering a whole new world that can help as develop new spatial relationships, understand space in a different way. And that goes well beyond mere formal explorations. Cells of course are displaying unique forms that could be transferred to architecture, but are also displaying ways of organization, ecological strategies and extremely efficient structural systems, all of which can inform architecture in different levels.

This project begun from a cell: xylem vessels. Through detailed 3d modeling, animation and study of its properties it finally led to a design for a garden. More specifically to a system of rain collectors that could be installed in a garden. Xylem vessels are plant cells used in order to transfer water from the ground to the higher parts of the plant. That cell structure is eventually developed/transformed into the rain collector, which is also transferring water, this time following the opposite direction: top>bottom instaid of bottom>top.

more info here

Para*site. St Louis Follies Competition. 2nd price.

2007-02-04T23:05:00.000+02:00

A rather 'fast' project, for the st louis follies competition (http://www.stlfollies.com/index.html) developed with Katerina Tryfonidou.

The competition was a call for installations (for downtown St. Louis) that were supposed to host art exhibitions. Our proposal had to do with the idea of a growing organism that takes over city spaces. Close to the idea of the follies, since there is no specific need for the creation of the organism, the idea of a parasite that uses existing city structures in order to be developed is by no means new to architecture (urbican fever is a very interesting illustration of that ‘architect’s dream’). What makes that idea rather important today though, is that trough scripting we are becoming able to create self-referential organisms that are actually following growth patterns (the L-systems are a good example). In urbican fever the architect is finding that cubic device, he brings it to the city, and then the device starts growing according to its own logic, without the architect being able to intervene. It is a totally ‘interior to the device’ logic that is responsible for the growing pattern. Similarly in the various experiments taking place today with L-systems, cellular automata etc, the architect is in a similar position: He defines the initial rules, the first generation, and then he can only stay back and watch the growing process, which he is rather unable to predict in the first place. And that’s where the whole thing becomes so interesting.

Our project is a rather primitive attempt. A simple honeycomb structure is growing and changes colors, according to the game of life set of rules. Only that the automaton is not totally an ‘automaton’, that is people by entering the structure, can change the state of a cell and therefore affect the whole process. Well, a theme that has to be developed more in the future….

more here

Spiral City

2007-02-04T09:33:00.000+02:00

Exploring the possibilities of a vertical megastructure, and how a single rule (in that case the 'spiral') can be used in order to define every aspect of the composition, from the distribution of the spaces to the structure and the skin.

This project was not so much an attempt to design a 'specific' building but rather a study of the properties of the spiral, therefore the diagrams are much more important than the renderings, which are illustrating just an example...

Suburban house / Land manipulations

2007-02-04T09:20:00.000+02:00

An exploration on the ways that land can be manipulated in order to create space. The topography of different lots within the site is superimposed on one lot and through several transformations and manipulations the form of the house is derived.

Rethinking the box

2007-02-02T10:14:00.000+02:00

A two week studio exersise. The aim was to rethink what a suburban retail store could be. The idea is rather simple: The store is 'pushed' partly underground, the parking is coming above the store, and in the back side are housing units, divided from the retail with a 'garden' lower than the level of the street. At the same time several smaller 'gardens' are dispersed inside the parking area (always at a lower lever) along with vertical translucent surfaces dividing the parking spaces.

The aim was to 'create' different ways in which you can perceive the same object as you move on the street, in the parking lot and inside the store (the object being the trees, the cars, the store itself). Infuenced in a way by Deleuze's description of the point of view as what is taking the place of the missing center...
In this project the 'point of view' is becoming literal. As a general idea though is much more interesting, since it implies that the importance is displaced from the object to relations between objects. Like in the example of the conic sections where what is of importance is not the cone or the plane but the relations established between the cone and the plane.