Studies of Scale, pt2

Experiment 3, Moving towards complexity…

Aim: to add more elements without compromising the overall aesthetic.

Awareness of; starting points when joining structures (as determines curvature & can cause kinks/deformation)

Size, length & density of tubes in relation to layers


3mm, 2 of 4 layers


3mm & 4mm layers, 5 of 8 sides


3mm & 4mm layers, 7 of 8 sides, Left: the free-standing form, Right: underside of form

3mm, 4mm & 6mm layers, 10 of 12 sides


3mm, 4mm & 6mm layers, 11 of 12 sides, Free-standing height of approx 30cm

Notes: No colour shift within the dispersal section allows for the form of these sections to aesthetically merge into one another.


3mm, 4mm & 6mm layers, 11 of 12 sides, Free-standing height of approx 30cm
Left: front-view, Right: side-view


3mm, 4mm & 6mm layers, 11 of 12 sides, Flattened, Top-down view


3mm, 4mm & 6mm layers, 12 of 12 sides, Top-down view


3mm, 4mm & 6mm layers, 12 of 12 sides, Side-views, Approx. 30cm free-standing height






Studio View, University of Newcastle, Mon, April 18th, 2016


Studies of Scale, pt 1

Notes on studio practice, exploring architectural ‘form-finding’ experiments & scaling.

Questions: What is the relationship between hook size and thread density? How does it impact upon the aesthetic of the form and it’s structural integrity?

Experiment 1;




Radius of 12, Hexagonal Division Prism

Construction begins from the centre and moves outwards as larger layers are woven and incorporated into the structure. The design is self similar as it moves from one scale to the next, however the centre piece is inverted to show what the ‘underside’ of the outer form might look like. During the construction of the centre piece, the form was initally self-standing and became morphed (and in some respects de-formed) from the addition of outer layers. Notably the 2nd, outer devision of the 2nd internal layer pulled the previously freestanding upward centre chords towards the back of the structure. Variables such as the length of the chord between the layers, along with the staring and ending points for the logarithmic spiral constructions (I sometimes refer to these as ‘pannels’) are factors which effect this morphing of the ‘final’ structure.

These elements pertaining to the relationships between aspects of self-similar crocheted froms has lead to a further detailed study which attempts to mitigate these factors. The observations are subtle progressions towards a better understanding of the material language of the practice. This knowledge will in turn inform material studies on larger scales as I continue to adapt structural designs for large-scale applications.



Colour & Affect

What effect does the cerebral material with which my mind engages while i work have upon the practice? In the case of Carapace, the colours are inspired by a particularly visceral scene in “Words of Radiance” by Brandon Sanderson, describing a chasm creature’s thick shell scraping against rocks. The word “carapace” was interesting to me and after some googling I found myself looking at crab shells. I started to think about the tension, or maybe irony, in depicting a “shell” or “carapace” – which is a hard thing – in a soft material. I decided to apply the concept within the work, echoing the concept of a fleshy centre and hard outer shell in the colours & (to some extent) textures of the work.

*Note. To ensure as much ‘sameness’ in these ‘self-similar’ forms as possible colour continuity is of primary importance. As a result factors of colour availability are taken into account when determining gradients. If there is not enough of a material to be used x times over throughout the different panels, then i will re-engineer the colour pallet.
Experiment 2:

Prism Abstractions



Sample Study 1:


2.5mm hook, 12 nodes, Tetrahedron/Equilateral Triangle division.


Sample Study 2:


2.5mm hook, Open Cube Construction, 5 of 6 sides



2.5mm hook, Closed Cube Construction, 6 of 6 sides



2.5mm & 3.5mm layers, Closed/Open Cube Construction, 8/12 sides




2.5mm & 3.5mm layers, Closed/Open Cube Construction, 9/12 sides




Sample Study 3:

Tetrahedron/Cube Abstraction


2mm & 3mm layers, Tetrahedron division embedded within Cube division

Texture aims to emulate ‘shininess’ coming out of the ‘fuzzyness’

Thicker tubes leads to immediate increase in structural stability

Interesting to observe how the size of the tube sits in relation to the dispersal point and dispersion radius.

Dispersion radius determines how internal section sits, for example whether the components are pulled inwards or outwards from the centre.





Sample Study 4:


2mm construction, tetrahedron division



Sample Study 4 embedded in Sample Study 1


Sample Study 5:


3mm, 4mm & 6mm layers, Cube Division





Studio Olafur Eliasson


I like to believe that the main part of my work lies in the experience of it.
And the thing that is exhibited or displayed?

It’s rather just a kind of machine.

An experience machine?


And if nobody sees the machine?

Then there is no experience and therefore no work – and I would be a mechanic instead of an artist. Although I don’t distinguish too much these days. An artist can be many things – an entrepreneur, policy­maker, activist, researcher, a gardener of sorts.


The Experience Machine

The Artist Interviews Himself, 1995/2015

Originally sent as a fax to Christiane Schneider, 5 December 1995, by Olafur Eliasson, and expanded in January 2015


Do art and experience go hand in hand?

Even attempting to answer this question would instantly put me into a totally predefined way of thinking.
Ha! The young artist speaking. A lot has happened to the concept of experience during the last de­ cade. It’s been hijacked by the experience indus­ try, commercialized, packaged, and offered for sale and consumption. We artists need to reclaim it by showing trust in the viewers and in the users of art. Experience doesn’t simply arrive from outside; it’s a meeting up of interior and exterior.






…Giving people access to data most often leaves them feeling overwhelmed and disconnected, not empowered and poised for action. This is where art can make a difference. Art does not show people what to do, yet engaging with a good work of art can connect you to your senses, body, and mind. It can make the world felt. And this felt feeling may spur thinking, engagement, and even action.

…Engaging with art is not simply a solitary event. The arts and culture represent one of the few areas in our society where people can come together to share an experience even if they see the world in radically different ways. The important thing is not that we agree about the experience that we share, but that we consider it worthwhile sharing an experience at all. In art and other forms of cultural expression, disagreement is accepted and embraced as an essential ingredient. In this sense, the community created by arts and culture is potentially a great source of inspiration for politicians and activists who work to transcend the polarizing populism and stigmatization of other people, positions, and world views that is sadly so endemic in public discourse today.

Why Art Has the Power to Change the World 

Blog post from January 23rd, 2016 by Olafur Eliasson as part of a series produced by The Huffington Post and The World Economic Forum to mark the Forum’s Annual Meeting 2016 (in Davos-Klosters, Switzerland, Jan. 20-23)

theory of forms



LM: I think I disagree with the extended notion that the “forms” exist seperate to ourselves and are an innate aspect of reality. To me, this idea of objective truth seems flawed because, when representated via semantics, it seems to be a subjective interpretive experience. The notion of studying the “building blocks” of language and how it functions as an iconographical code of signifiers, however, seems very useful. Indeed it is the foundation of how we communicate and translate meaning.
In terms of the poetry of understanding, although I may not fully accept Plato’s theory, the thought that “forms” are forgotten memories being relearned or remembered is interesting. I find it difficult to accept because there is no scientific foundation upon which to situate this logic, however there is something compelling in proposing a link between ideas and collective memory. To me, it brings to mind thoughts of dreams and how they might relate to the human experience.

Tomas Saraceno


“Tomas Saraceno is the inaugural Visiting Artist at MIT’s new Center for Art, Science & Technology (CAST). An artist trained as an architect, Saraceno deploys theoretical frameworks and insights from engineering, physics, chemistry, aeronautics and materials science.

His residency at MIT focuses on advancing new work for the ongoing Cloud Cities series, in which Saraceno creates inflatable and airborne biospheres with the morphology of soap bubbles, spider webs, neural networks, or cloud formations, which are speculative models for alternate ways of living. ”

via MIT


Galaxies Forming along Filaments, like Droplets along the Strands of a Spider’s Web, 2009. Installation view, 53. Biennale di Venezia, 2009, with the support of Fondazione Garrone, Genoa, Italy and Fondazione Sambuca, Palermo, Italy, special thanks to pinksummer contemporary art. Courtesy the artist; Tanya Bonakdar Gallery, New York; Andersen’s Contemporary, Copenhagen; Pinksummer contemporary art, Genoa; Esther Schipper, Berlin. Photography © 2009 Alessandro Coco



Tomás Saraceno (b.1973, Argentina)

After attaining his architecture degree at Universidad Nacional de Buenos Aires in Argentina, Tomás received postgraduate degrees in Art and Architecture from Escuela Superior de Bellas Artes de la Nación Ernesto de la Carcova, Buenos Aires (2000) and Städelschule, Frankfurt am Main (2003).
In 2009, he attended the International Space Studies Program at NASA Ames. The same year Saraceno presented a major installation at the 53rd Biennale di Venezia, and was later on awarded the prestigious Calder Prize.
In the last years, Saraceno’s work has been shown in international solo and group exhibitions such as Le Bord des Mondes, at Palais de Tokyo, Paris (2015), In orbit at Kunstsammlung Nordrhein-Westfalen K21 in Düsseldorf (2013-15) and On Space time foam at Hangar Bicocca in Milan (2012-13), amongst others. His work has also been exhibited in public museums like The Metropolitan Museum of Art in New York (2012), the Kemper Museum of Contemporary Art in St. Louis (2011-12), and Hamburger Bahnhof, Berlin (2011-12).
Saraceno’s oeuvre could be seen as an ongoing research, informed by the worlds of art, architecture, natural sciences and engineering; his floating sculptures and interactive installations propose and explore new, sustainable ways of inhabiting and sensing the environment towards an aerosolar becoming.


Via the Artist’s website




Tomás Saraceno, “On Space Time Foam” at Hangar Bicocca, Milan, 2012. Curated by Andrea Lissoni. Hosted by Hangar Bicocca Foundation
© Photography by Alessandro Coco, 2012



Tomás Saraceno: In Orbit at Kunstsammlung Nordrhein-Westfalen, K21 Ständehaus, Düsseldorf 2013 © Photography by Studio Tomás Saraceno, 2013



Frei Otto



The Structure of Vagueness

by Lars Spuybroek


Around the beginning of the 1990s, Frei Otto and his team at the Institute for Lightweight Structures in Stuttgart studied what they called “optimized path systems.” Previously, similar to the chain modeling technique Gaudí used for the Sagrada Familia, they had experimented with material systems for calculating form. Each of these material machines was devised so that, through numerous interactions among its elements over a certain time span, the machine restruc- tures, or as Frei Otto says, “finds (a) form.” Most of them consist of materials that process forces by transformation, which is a special form of analog com- puting. Since the materials function as “agents,” it is essential that they have a certain flexibility, a certain amount of freedom to act. It is also essential howev- er, that this freedom is limited to a certain degree set by the structure of the machine itself.

The material interactions frequently result in a geometry that is based on complex material behaviour of elasticity and variability. Sand, balloons, paper, soap film (including the famous minimal surfaces for the Munich Olympic Stadium), soap bubbles, glue, varnish, and the ones I will be referring to here: the wool-thread machines. This last tech- nique was used to calculate the shape of two-dimensional city patterns, but also of three-dimensional cancellous bone structure or branching column systems. They are all similar vectorized systems that economize on the number of paths, meaning they share a geometry of merging and bifurcating.



Wool Thread Experiments | Frei Otto + The Institute for Lightweight Structures







Video: Frei Otto Experimenting with Soap Bubbles

15 March, 2015 by 

Translated by Katie Watkins




“The computer can only calculate what is already conceptually inside of it; you can only find what you look for in computers. Nevertheless, you can find what you haven’t searched for with free experimentation.” – From A Conversation with Frei Otto, by Juan Maria Songel


For Frei Otto, experimentation with models and maquettes was a fundamental part of his work as an architect. In 1961, he began to conduct a series of experiments with soap bubbles (featured in the video above). His experiments centered on suspending soap film and dropping a looped string into it to form a perfect circle. By then trying to pull the string out a minimal surface was created. It was these created surfaces that Otto experimented with.

Through these types of experimentation he was able to build forms and structures that were previously believed to be impossible. “Now it can be calculated, but for more than 40 years it was impossible to calculate it. I have not waited for it to be calculated in order to build it.”



Skeletons, Soap Bubbles and Spider Webs

 Insight, 27. March 2015

…After the rigid, weighty formalism of the Third Reich, post-war architecture in West Germany strove above all for lightness and openness, transparency and elegance. More than any other German architect, Frei Otto embodies this endeavor to create lightweight structures that, being derived from nature, make efficient use of materials – designs that are both stunningly beautiful and functional. His work was soon given labels such as “organic”, “Gothic” and “democratic.”

His first name, Frei, which also means “free,” matched his thinking. For him, an architect was simultaneously an explorer, an inventor, an engineer, a humanist and, above all, an interdisciplinary team-worker. Otto’s designs are all the product of collaboration. He worked with Rob Krier, Günther Behnisch, Christoph Ingenhoven and Shigeru Ban – some of the most interesting architects of the twentieth century. It says a lot for Otto that he engaged with the work of such very different architects and cooperated with them so successfully. He referred to himself as a “source of ideas” who “has built little and instead devises ‘castles in the air’” – an understatement if ever there was one.

…His designs, which followed the principle of “do more with less,” were simultaneously experimental, original and unprecedented. Otto’s sophisticated and almost sculptural lightweight structures, using cable nets, lattice shells, or other tensile constructions, made him one of the most important architects and engineers of the twentieth century. His thinking harmonized structural engineering with spatial composition in a way equaled only by Richard Buckminster Fuller in the 1960s and Santiago Calatrava today. Frei Otto was mostly inspired by natural phenomena such as skeletons, spider webs and bubbles – his works express both lightness and stability, fusing architecture with landscape, wall with ceiling, and interior with exterior.



German Pavilion at Expo 67 in Montreal (Photo: Burkhardt)



Working model of light scoops for the main station Stuttgart (Photo: saai)









I first ran into Gaudi’s work in Barcelona about 7 years ago, literally on the street. I missed the cathedral but I remember roaming around the city and seeing some unique, unusual buildings. The striking aesthetic created vivid memories, and maybe subconsciously coloured the texture & experience of the city. It was unlike anything I’d seen. It was awesome.

Casa BatllóBarcelonaAttribution: Rapomon

Alternative names Casa dels ossos (House of Bones)





Recently I’ve been researching architecture & it’s cross-overs with art, studying designers who work in a space between creativity, engineering and function. I found this;



 Emergent Explorations: Analog and Digital Scripting

Master of Architecture thesis paper by Alexander Worden


This book documents an exploration of emergent and linear modes of defining space, form, and structure. The thesis highlights a dialog between analog and digital modeling techniques, in concept and project development. It identifies that analog modeling techniques, coupled with judgment, can be used to develop complex forms. The thesis project employs critical judgment and the textile techniques of crochet as a vehicle generate form.Crochet lends itself to this investigation because it is a serial process of fabrication that allows for the introduction of specific non-linear modifications. The resulting emergent forms produced by this mode of working can be precisely described by digital modeling techniques. These analog crochet models are translated into the digital through the employment of advanced digital modeling tools. This translation enables the visualization, development, testing, and execution of an architectural space, form, and structure.

Really useful and relevant as Worden critically reflections upon analog design processes and their relationship to digital representations, using crochet as a case study!

But it gets better, the first artistic reference being put forward (I’m skipping over boatbuilding techniques) is Gaudi and his use of string models.

& so began the googling…


Antoni Gaudí

From Wikipedia, the free encyclopedia

Antoni Gaudí i Cornet (Catalan pronunciation: [ənˈtɔni ɣəwˈði]; 25 June 1852 – 10 June 1926) was a Spanish Catalan architect from Reus/Riudoms and the best known practitioner of Catalan Modernism. Gaudí’s works reflect an individualized and distinctive style. Most are located in Barcelona, including his magnum opus, the Sagrada Família.
Under the influence of neo-Gothic art and Oriental techniques, Gaudí became part of the Modernista movement which was reaching its peak in the late 19th and early 20th centuries. His work transcended mainstream Modernisme, culminating in an organic style inspired by natural forms. Gaudí rarely drew detailed plans of his works, instead preferring to create them as three-dimensional scale models and molding the details as he conceived them.


Quest for a new architectural language

Gaudí is usually considered the great master of Catalan Modernism, but his works go beyond any one style or classification. They are imaginative works that find their main inspiration in nature. Gaudí studied organic and anarchic geometric forms of nature thoroughly, searching for a way to give expression to these forms in architecture. Some of his greatest inspirations came from visits to the mountain of Montserrat, the caves of Mallorca, the saltpetre caves in Collbató, the crag of Fra Guerau in the Prades Mountains behind Reus, the Pareis mountain in the north of Mallorca and Sant Miquel del Fai in Bigues i Riells.[59]


Geometrical forms

The nave in the Sagrada Familia with a hyperboloid vault. Inspiration from nature is taken from a tree, as the pillar and branches symbolise trees rising up to the roof.

This study of nature translated into his use of ruled geometrical forms such as the hyperbolic paraboloid, the hyperboloid, the helicoid and the cone, which reflect the forms Gaudí found in nature.[60] Ruled surfaces are forms generated by a straight line known as the generatrix, as it moves over one or several lines known as directrices. Gaudí found abundant examples of them in nature, for instance in rushesreeds and bones; he used to say that there is no better structure than the trunk of a tree or a human skeleton. These forms are at the same time functional and aesthetic, and Gaudí discovered how to adapt the language of nature to the structural forms of architecture. He used to equate the helicoid form to movement and the hyperboloid to light. Concerning ruled surfaces, he said:

Paraboloids, hyperboloids and helicoids, constantly varying the incidence of the light, are rich in matrices themselves, which make ornamentation and even modelling unnecessary.[61]


Gaudí evolved from plane to spatial geometry, to ruled geometry. These constructional forms are highly suited to the use of cheap materials such as brick. Gaudí frequently used brick laid with mortar in successive layers, as in the traditional Catalan vault, using the brick laid flat instead of on its side.[63] This quest for new structural solutions culminated between 1910 and 1920, when he exploited his research and experience in his masterpiece, the Sagrada Família. Gaudí conceived the interior of the church as if it were a forest, with a set of tree-like columns divided into various branches to support a structure of intertwined hyperboloid vaults. He inclined the columns so they could better resist the perpendicular pressure on their section. He also gave them a double-turn helicoidal shape (right turn and left turn), as in the branches and trunks of trees. This created a structure that is now known as fractal.[64] Together with a modulation of the space that divides it into small, independent and self-supporting modules, it creates a structure that perfectly supports the mechanical traction forces without need for buttresses, as required by the neo-Gothic style.[65] Gaudí thus achieved a rational, structured and perfectly logical solution, creating at the same time a new architectural style that was original, simple, practical and aesthetic.


Surpassing the Gothic

Another of Gaudí’s innovations in the technical realm was the use of a scale model to calculate structures: for the church of the Colònia Güell, he built a 1:10 scale model with a height of 4 metres (13 ft) in a shed next to the building. There, he set up a model that had strings with small bags full of birdshot hanging from them. On a drawing board that was attached to the ceiling he drew the floor of the church, and he hung the strings (for the catenaries) with the birdshot (for the weight) from the supporting points of the building—columns, intersection of walls. These weights produced a catenary curve in both the arches and vaults. At that point, he took a picture that, when inverted, showed the structure for columns and arches that Gaudí was looking for. Gaudí then painted over these photographs with gouache or pastel. The outline of the church defined, he recorded every single detail of the building: architectural, stylistic and decorative.[68]



Gaudí’s position in the history of architecture is that of a creative genius who, inspired by nature, developed a style of his own that attained technical perfection as well as aesthetic value, and bore the mark of his character. Gaudí’s structural innovations were to an extent the result of his journey through various styles, from Doric to Baroque via Gothic, his main inspiration. It could be said that these styles culminated in his work, which reinterpreted and perfected them.


LM: I remember the gothic Architecture as a feature of Barcelona, so it makes sense to me that this landscape might have inspired Gaudi. Part of his genius seems to be the ability to contribute something to the city which pays homage to this history while furthering ideas of what is creatively possible.



After his death, Gaudí’s works suffered a period of neglect and were largely unpopular among international critics, who regarded them as baroque and excessively imaginative. In his homeland he was equally disdained by Noucentisme, the new movement which took the place of Modernisme. In 1936, during the Spanish Civil War, Gaudí’s workshop in the Sagrada Família was ransacked and a great number of his documents, plans and scale models were destroyed.

Gaudí’s reputation was beginning to recover by the 1950s, when his work was championed not only by Salvador Dalí but also by architect Josep Lluís Sert. In 1952, the centenary year of the architect’s birth, the Asociación de Amigos de Gaudí (Friends of Gaudí Association) was founded with the aim of disseminating and conserving his legacy. Four years later, a retrospective was organised at the Saló del Tinell in Barcelona, and the Gaudí Chair at the Polytechnic University of Catalonia was created with the purpose of deepening the study of the Gaudí’s works and participating in their conservation. These events were followed in 1957 by Gaudí’s first international exhibition, held at the Museum of Modern Art in New York City. In 1976, on the 50th anniversary of his death, the Spanish Ministry of Foreign Affairs organised an exhibition about Gaudí and his works that toured the globe.[148]

Between 1950 and 1960, research and writings by international critics like George R. Collins, Nikolaus Pevsner and Roberto Pane spread a renewed awareness of Gaudí’s work, while in his homeland it was admired and promoted by Alexandre Cirici, Juan Eduardo Cirlot and Oriol Bohigas. Gaudí’s work has since gained widespread international appreciation, such as in Japan where notable studies have been published by Kenji Imai and Tokutoshi Torii. International recognition of Gaudí’s contributions to the field of architecture and design culminated in the 1984 listing of Gaudí’s key works as UNESCO World Heritage Sites.[149] Gaudí’s style have subsequently influenced contemporary architects such as Santiago Calatrava[150] and Norman Foster.[151]

Due to Gaudí’s profoundly religious and ascetic lifestyle, the archbishop of Barcelona, Ricard Maria Carles proposed Gaudí’s beatification in 1998. His beatification was approved by the Vatican in 2000.[152] In 1999, American composer Christopher Rouse wrote the guitar concerto Concert de Gaudí, which was inspired by Gaudí’s work; it went on to win the 2002 Grammy Award for Best Classical Contemporary Composition.[153]





The Geometry of Antoni Gaudi

Antoni Gaudi i Cornet (1852-1926) was a well-known architect from Spain. He was born in 1852 as the son of a copper-smith. He studied architecture in Barcelona and combined an interest in history, mathematics and nature to create a rather unique style.



Detail of pillar at the Parc Guell.

Wall at the Parc Guell.

Gaudi used mosaics in many of his works and he created several tiled floors and ceilings in the houses and parks he designed. The mosaics used in Gaudi’s work are an example of Catalan modernism and are sometimes referred to as trencadís.

There are several true periodic tessellations. Many of them are based on the square, but there are also a couple of tessellations based on the hexagon and a wood inlay with a pattern consisting of triangles.

Gaudi tessellations in Barcelona
Gaudi-tess1.JPG Gaudi-tess2.jpg Gaudi-tess-hex1.png
A tessellation based on squares. Another tessellation based on squares, A hexagonal tessellation, but only 3-fold symmetry.
Tess-hex-2.jpg Triangular-tess-Gaudi.jpg Tiling-Gaudi.jpg
Tessellation and optical illusion Triangular tessellation Another tiling


Catenary Arches and Catenoids

catenary arch is the shape one gets when we suspend a rope or chain from its endpoints. Gaudi used catenary arches in many of his projects. The advantage of the catenary arch is that it can be constructed from relatively light materials while still being able to support great weights.

In La Pedrera (also known as Casa Milà) a model of suspended chains is on view. A mirror below the model shows the reflected image of the structures.


Casa-Mila-Catenary.jpg Casa-Mila-reflect-catenoid.jpg
Suspended chains form catenoids The reflection shows at outline of arched buildings



The design of the Church at Santa Coloma de Cervello.


Ruled Surfaces

Ruled surfaces are created by sweeping a line through space.[2] A simple example of a ruled surface is the cylinder one gets if we connect all the points in one circle with their corresponding point on another circle (see image below in the hyperboloid of one sheet section). Gaudi used several of these ruled surfaces in his designs.

Hyperboloids of One Sheet

hyperboloid can be created if a column of strings is twisted about its central axis. Gaudi used this type of curved surface in the construction of some of the windows in the Sagrada Família in Barcelona.

The cloister walls have window created from 10 hyperboloid sheets which are arranged in a hexagonal honeycomb pattern.

Hyperboloid.JPG Hyperboloid-model.jpg Cloister-Windows.JPG
Twisting a cylinder gives a hyperboloid. Model of Hyperboloid Cloister wall, Sagrada Familia.

Hyperbolic Paraboloids

The hyperbolic paraboloid looks somewhat like a saddle. A simple formula for such a surface is z = x y. [3]

Gaudi-hyperbolic-paraboloid.JPG HyperbolicParaboloid.png HyperbolicParaboloid-Gaudi.jpg
Model of hyperbolic paraboloid from the Museum at the Sagrada Familia Computer generated model Arch by Gaudi

Some of the cross sections of the hyperbolic paraboloids are parabolas. This can be used to create parabolic arches.




Image by memetician


Gaudí’s hanging chain models: parametric design avant la lettre?

By  2012/08/16

Funicular chain model of Colonia Güell church project by Antoni Gaudí, as exhibited at Colonia Güell Interpretive Centre.
Only the crypt was realized.

Interior view of Colonia Güell Crypt

It is known that Gaudí hated drawing and preferred to use models as design tools; especially ones made of chains hung from a ceiling, or strings with small weights attached. Through experimentation with such models, he discovered a way to use traditional Catalan masonry techniques in new, more complex ways. A chain suspended simply from both its ends results in a catenary curve that naturally distributes the static load — in this case tension — evenly between the links of the chain. When this shape is flipped vertically and the materials become brick or stone, then the static load — now compressive — is similarly evenly distributed, resulting in an optimally efficient arch. This was already known for centuries. What Gaudí did was to apply this tension-compression analogy to chains hanging from chains (or arches superimposed on arches) asymmetrically, permitting him to design a much more fluid architecture.
Gaudí made the models of his buildings upside-down, then, using mirrors on the floor, visualized his designs downside-up. He also took photographs of these “wire-frame” models of sorts and “filled” them in with color to generate “solid model renderings”, so to speak. All this has been well-documented in publications and exhibitions.
What is interesting is how, in the process, Gaudí effectively invented a kind of “parametric” design process long before the invention of the computer (let alone the development of software such as Maya or the Grasshopper plug-in for Rhino). One feature of so-called parametric design software is that it updates a complete three-dimensional digital model of a building every time any parameters are altered, allowing alternatives to be studied and compared in the search for a design that performs optimally (although to many architects who use this software it seems that the most important parameter is aesthetic form). Gaudí’s hanging chains do exactly that: if a chain end-point is moved so as to enlarge or reduce, say, the floor plan in one corner, then the shape of the entire hanging chain model shifts and settles into a newly optimized catenary geometry. Of course, parametric design software does a great deal more, but at their conceptual root both of these modeling tools — one physical and the other digital — are analogous.



From Wikipedia, the free encyclopedia

In physics and geometry, a catenary[p] is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola: it is a (scaled, rotated) graph of the hyperbolic cosine. The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings.

The catenary is also called the alysoidchainette,[1] or, particularly in the material sciences, funicular.[2]


Antoni Gaudí‘s catenary model at Casa Milà

The word catenary is derived from the Latin word catena, which means “chain“. The English word catenary is usually attributed to Thomas Jefferson,[3][4] who wrote in a letter to Thomas Paine on the construction of an arch for a bridge:


I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientifical work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium.

— [5]



Further Reading:

PDF] Validating Thrust Network Analysis using 3D-printed, structural models

P Block, L Lachauer, M Rippmann – Proceedings of the …, 2010 –
 An example of a similar challenge is the translation of the hanging string model
for the crypt of the Colonia Güell Church into an actual stone structure. It is Antoni
Gaudí who was able to see form through these strings

[PDF]Topological method of construction of point surfaces as physical models

D Kozlov –
Gaudi approximated the catenary with parabolic arches in his early structures, but lately he made several spatial suspended stringmodels for his churches. When the models were inverted, the polygons formed by the strings yielded the directions of the supports. 

Confidence, tolerance, and allowance in biological engineering: The nuts and bolts of living things

M PorcarA DanchinV de Lorenzo – BioEssays, 2015 – Wiley Online Library
 calculations is provided by the techniques developed by the Spanish architect Antoni Gaudí (1852–1926  By creating an upside-down image of such a string-weight model, the arches and … components in a difficult assembly, so that nature itself (ie gravity in Gaudi’s case) provides 

[PDF]The Square Cube Law: From Vitruvius to Gaudi

JL González – Razones Gaudi, 2002 –
 170-80,  The specific shapes of the elements, structural or not, were based on another of Gaudí’s great innovations: ruled  Sagrada Familia was the direct consequence of the experience at the Güell Colony, although the stringmodel was replaced 

Antoni Gaudí and Frei Otto: Essential Precursors to the Parametricism Manifesto

M Burry – Architectural Design, 2016 – Wiley Online Library
 paraboloid was the obvious solution for four conjoined nonplanar straight edges emerging from the string network that formed the flexible hanging model. bottom: Gaudí used naturally occurring hexagonal basalt prisms from Northern Catalunya for the principal columns. 


Physical modelling and form finding

B Addis – Shell Structures for Architecture: Form Finding and …, 2014 –
 engineer Heinrich Hübsch (1795–1863) also used Hooke’s technique, making hanging-string models to determine  who used both two-and three-dimensional hanging models made with strings and bags of  Gaudí used the results of his model tests to complement his use of both 

VIA Page 8 of Emergent Explorations: Analog and Digital Scripting by Alexander Worden;

“Frei Otto and his team from the Institute for Lightweight Structures dedicated an entire IL publication (IL 34: The model) to the reconstruction of Gaudi’s model. Using what little documentation still existed of Gaudi’s original, the IL team was successful in reconstructing the model. Though rebuilding Gaudi’s model occurred in 1982, Otto and his team were exploring natural systems and modeling techniques decades prior to the model. Frei Otto and his team, at the Institute for Lightweight Structures, continued to explore a vast array of different analog machines and natural systems beyond that of the hanging model. Through experiment in techniques and the use of other materials, they continued their search to find form.”

“Emergence is the spontaneous occurrence of an organization or a behavior that is greater than the sum of its parts. – emergence is a change in kind, it is unknown and resembles nothing that we can already see.” (Rahim, 03-80, Catalytic Formations)