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A hyperbolic paraboloid is an infinite surface in three dimensions with both hyperbolic and parabolic cross-sections. A playful and intuitive way of visualising and parameterising this concept can be achieved via the implementation of origami folding techniques.

The images below show how to create and tile a basic hyperbolic parabola with origami. Once fully formed, the result is flexible and malleable along its two axes.

This playfulness only increases as additional sides are added to the initial parametric shape. This, in turn directly correlates with the increase of the number of axes along which the paraboloid is able to form. For example, a hexagonal initial sheet with six sides, will also have six axes.

Octagonal and decagonal paraboloids are particularly enjoyable to create and play with.

When deconstructed, a decagonal paraboloid is comprised entirely of a series of ever diminishing, 72 degree trapezoids, that when tiled next to one another, come together to comprise individual components of one, larger trapezoid, or wedge. When tiled and secured along its long edge, a decagon is formed, and once folded, a hyperbolic paraboloid is possible.

It is through research and testing with digital fabrication how best to form and therefore scale this wedge component that a successful, parametric and human scale origami form might be accomplished.

The images below are further tests in a failed attempt at forming a larger, scalable hexagonal paraboloid. Previously, flexible material such as paper and polypropylene had been used to successfully form basic, octagonal and decagonal paraboloids. However, in this test, 4mm ply was used, and has proved to be most inflexible. Thusly, it is unable to bend universally along each of the six axes. Further testing is required.

 

Some images of our final cross-crit of the year! Our students presented their Brief03:FutureCities. Have a look at how the next generation of architects envision the future of our cities.

Thank you to Andrei Jipa, Kester Rattenbury and Lindsay Bremner. Final sprint to the portfolio submission and end of year!

Eva Ciocyte - Aral City - As the earth gets too polluted to allow the growth of any edible crop, Aral City attempts to purify the soil progressively by building giant evaporative and inhabitable greenhouses.

Eva Ciocyte – Aral City – As the earth gets too polluted to allow the growth of any edible crop, Aral City attempts to purify the soil progressively by building giant evaporative and inhabitable greenhouses.

Alex Berciu, The Algorithmic City, In the presented scenario, the natural environment in which human beings live today will no longer exist, having been replaced by fully computer generated habitation. As the Earth’s surface will have been largely damaged by pollution and natural disasters, the only  solution for living pushed human society upwards in suspended structures developed through the  technique of extruding concrete and drone assembly. Based on a growth algorithm that evolves with  relation to continuous feedback gathered from climate data, structural qualities and population needs,  the system can perform in any given location. in the generated structure, the algorithm places accordingly a selection of 8 typologies considered  suitable for the needs of the future human society. These are: aliment production/farming, aliment  storage, housing, education hubs, culture hubs, spiritual hubs, places of sin and production  laboratories. Each typology is designed to fit within the modular grid and is placed according to  density and distance rules. The ratio between the 8 typologies is also adaptable, responding to  possible changes in societal needs.

Alex Berciu, The Algorithmic City, In the presented scenario, the natural environment in which human beings live today will no longer exist, having been replaced by fully computer generated habitation. As the Earth’s surface will have been largely damaged by pollution and natural disasters, the only solution for living pushed human society upwards in suspended structures developed through the technique of extruding concrete and drone assembly. Based on a growth algorithm that evolves with relation to continuous feedback gathered from climate data, structural qualities and population needs, the system can perform in any given location. in the generated structure, the algorithm places accordingly a selection of 8 typologies considered suitable for the needs of the future human society. These are: aliment production/farming, aliment storage, housing, education hubs, culture hubs, spiritual hubs, places of sin and production laboratories. Each typology is designed to fit within the modular grid and is placed according to density and distance rules. The ratio between the 8 typologies is also adaptable, responding to possible changes in societal needs.

Marine Pollution has become a growing plaque as plastics are accumulated into patches within the gyres around the world, damaging the marine ecosystem and entering the marine food web. As these plastics are not biodegradable, they continue to pose a threat to the marine wildlife as well as humanity. Centuries into the future, people have begun to seek for ocean colonization in an attempt to tackle marine pollution and the rising sea level. The Fluas is a self-sufficient city that realises the potential of ocean plastics as a source of reusable material. Situated within the North Pacific Gyre and consisting of clusters of floating platforms, the city is centred on the collection and recycling of these materials into elements of the city - in the form of pneumatic structures. As plastics are salvaged from the gyre, the inflated city continues to grow while its inhabitants live a seaborne lifestyle.

Garis Iu – The Inflated City – Marine Pollution has become a growing plaque as plastics are accumulated into patches within the gyres around the world, damaging the marine ecosystem and entering the marine food web. As these plastics are not biodegradable, they continue to pose a threat to the marine wildlife as well as humanity. Centuries into the future, people have begun to seek for ocean colonization in an attempt to tackle marine pollution and the rising sea level. The Fluas is a self-sufficient city that realises the potential of ocean plastics as a source of reusable material. Situated within the North Pacific Gyre and consisting of clusters of floating platforms, the city is centred on the collection and recycling of these materials into elements of the city – in the form of pneumatic structures. As plastics are salvaged from the gyre, the inflated city continues to grow while its inhabitants live a seaborne lifestyle.

Garis Iu The Inflated City

Cidade de Árvores The Atlantic Forest in southern Brazil has long been viewed as a vast quilt of rain forest interspersed by small river outposts. The surging population growth has seen these remote settlements transform this ancient rural vision to an expansive city scale. Cidade de Árvores (City of Trees) envisions an environment where both the city’s infrastructure and its inhabitants maintain a symbiotic relationship with the surrounding natural environment.  Built entirely from locally grown timber, the Cidade de Árvores exists as a network of steam bent beams, joined to form a structural space frame.  Like the forest, the frame is allowed to grow and develop organically over time with inhabitants adding to structure to meet their requirements. The city is powered through the use of micro wind turbine electricity generation which manifests as a series of towers scattered throughout the forest. For the city and the environment to function in harmony, the city access routes manifest as elevated walkways around large courtyards, allowing light to penetrate to the forest floor.

Joe Leach – Cidade de Árvores
The Atlantic Forest in southern Brazil has long been viewed as a vast quilt of rain forest interspersed by small river outposts. The surging population growth has seen these remote settlements transform this ancient rural vision to an expansive city scale. Cidade de Árvores (City of Trees) envisions an environment where both the city’s infrastructure and its inhabitants maintain a symbiotic relationship with the surrounding natural environment. Built entirely from locally grown timber, the Cidade de Árvores exists as a network of steam bent beams, joined to form a structural space frame. Like the forest, the frame is allowed to grow and develop organically over time with inhabitants adding to structure to meet their requirements. The city is powered through the use of micro wind turbine electricity generation which manifests as a series of towers scattered throughout the forest. For the city and the environment to function in harmony, the city access routes manifest as elevated walkways around large courtyards, allowing light to penetrate to the forest floor.

Tobias Power's Infinity Tree for Burning Man development

Tobias Power’s Infinity Tree for Burning Man development

The Infinity Tree - Updated structure with the help of Format Engineers and Ramboll

The Infinity Tree – Updated structure with the help of Format Engineers and Ramboll

This project seeks to develop a response to the combined challenges of natural disasters, the aging population and  over-fishing. All three are closely connected in Japan. In Japan, where life expectancy is one of the highest in the  world, 1 in 3 people will be over 60 by 2050. Unfortunately, Japan is also a country that has been hit by major natural  disasters such as tsunamis, during which the vulnerable elderly suffered the most. Finally, in Japan fish is the main  food source and over fishing may become a major issue in the future. Moreover, Japan has one of the highest  percentages of labour force of people aged 60 and over within the fishing industry. I am proposing a self-sufficient,  resilient city for the super-aging Japanese fishing community along the coast, as a response to these future scenarios.  The structure of the proposal would not only act as a vertical evacuation point, and accommodation for the elderly and  their families, but would also be used as sustainable fish-farming.

The Origami City – Naomi Danos – This project seeks to develop a response to the combined challenges of natural disasters, the aging population and over-fishing. All three are closely connected in Japan. In Japan, where life expectancy is one of the highest in the world, 1 in 3 people will be over 60 by 2050. Unfortunately, Japan is also a country that has been hit by major natural disasters such as tsunamis, during which the vulnerable elderly suffered the most. Finally, in Japan fish is the main food source and over fishing may become a major issue in the future. Moreover, Japan has one of the highest percentages of labour force of people aged 60 and over within the fishing industry. I am proposing a self-sufficient, resilient city for the super-aging Japanese fishing community along the coast, as a response to these future scenarios. The structure of the proposal would not only act as a vertical evacuation point, and accommodation for the elderly and their families, but would also be used as sustainable fish-farming.

Naomi Danos, The Origami City

Naomi Danos, The Origami City

Lorna Jackson presenting her Burning Man proposal and future city for women only.

Lorna Jackson presenting her Burning Man proposal and future city for women only.

Fractal BreakCity will act as defence and breakwater structures against tsunamis and floods.  Benefiting of internalised creation of food, resources and objects, a trade based economy will  emerge, while the cult of product marketing will shrink to its essential.  The city is based on recursive aggregation: one geometry is repeated in a self-similar way to create a  complex looking aggregation, following a fractal pattern. The system consists of one module, with structures of different scales according to their function, so that the bathroom will be the smallest box unit, the bedroom slightly larger and so on. The largest box unit at the center of an aggregated module, will consist of the communal and production based spaces. Cellulose mixed with water, can be 3D printed to create structures stronger than steel and will become structural elements for the city, while aerogel wall components (made of silica, which is found in sand, across the world) will clad each unit’s sides.

Diana Raican – Fractal BreakCity will act as defence and breakwater structures against tsunamis and floods. Benefiting of internalised creation of food, resources and objects, a trade based economy will emerge, while the cult of product marketing will shrink to its essential. The city is based on recursive aggregation: one geometry is repeated in a self-similar way to create a complex looking aggregation, following a fractal pattern. The system consists of one module, with structures of different scales according to their function, so that the bathroom will be the smallest box unit, the bedroom slightly larger and so on. The largest box unit at the center of an aggregated module, will consist of the communal and production based spaces. Cellulose mixed with water, can be 3D printed to create structures stronger than steel and will become structural elements for the city, while aerogel wall components (made of silica, which is found in sand, across the world) will clad each unit’s sides.

Jon Leung's developments on the Bismuth Bivouac for Burning Man

Jon Leung’s developments on the Bismuth Bivouac for Burning Man

Jon Leung's Bismuth Bivouac updated render with latest development with the help of format engineers.

Jon Leung’s Bismuth Bivouac updated render with latest development with the help of format engineers.

John Koning's power generating Ron Resch origami city

John Koning’s power generating Ron Resch origami city

Irina Ghuizan's flying city

Irina Ghuizan’s flying city

Toby Plunket's Silent City in China

Toby Plunket’s Silent City in China

Some joyous proposals for both Burning Man and Buro Happold’s London office at yesterdays crit, the first of the year.

Our guest critics were Andrew Best, James Solly, Andrei Jipa, Harry Charringdon and Ben Stringer. Thank you all for your inspiring comments and tireless enthusiasm throughout the day.

Here are some images of the exciting work coming out of the studio this year, more to come 🙂

Frozen music pavilion by Toby Plunkett inspired by the soundwaves inside a cube

Frozen music pavilion by Toby Plunkett inspired by the soundwaves inside a cube

Diana

Diana Raican’s transforming cubes model

 

Diana Raican

Burning Man proposal by Diana Raican exploring fractal cubes

 

Garis Iu

Bent timber pavilion by Garis Iu

Naomi Danos Andrei Jipa

Guest critic and DS10 alumni Andrei Jipa with Naomi Danos’s hypar surfaces model

 

Inspired by Cairo tesselation, playful pavillion by Sarah Stell

Sarah Stell’s model capturing the translation of cubes into dodecahedrons

Lianne Clark’s animated keyframe light and shadow explorations

Jon Leung’s bismuth inspired pavilion

Aslan Adnan’s perturbated pavilion inspired by crystal growth patterns

The Tower of Power by Tobias Power

Rheotomic surface installation by Tobias Power

Charlotte Yates animated jitterbug model proposed for Buro Happold

lorna

Lorna Jackson’s spidron installations at different scales

joe

Joe Leach’s pavilion of timber tension

ttt

Tom Jelley’s anamorphosis experiments remapping geometry

Tom

Tom jelley’s magical anamorphic proposal

We are approaching the first “crit” of the term and our students are already proposing joyful projects for the Burning Man festival and Buro Happold’s newly refurbished HQ on Newman Street. The talented photographer NK Guy (http://nkguy.com/ and http://burningcam.com/) gave an excellent evening lecture at our campus to inspire our students and for the release of the book “The Art of Burning Man” (Taschen) which will feature some of our studio’s work. Here are couple images of the student’s project and of our buzzing DS10 space (pictures by Toby Burgess):

Aslan Adnan's early proposals for Buro Happold and Burning Man

Aslan Adnan’s early proposals for Buro Happold and Burning Man

Aslan Adnan's Explosive Recursion

Aslan Adnan’s Explosive Recursion

Joe Leach's early proposal for Burning Man

Joe Leach’s early proposal for Burning Man

Tom Jelley's Mirror deformation of 3d geometry using the inversion principle.

Tom Jelley’s Mirror deformation of 3d geometry using the inversion principle.

Lorna Jackson's kerfed Spirohedron. (spidron ™ )

Lorna Jackson’s kerfed Spirohedron. (spidron ™ )

Garis Iu's Curved Folding Components

Garis Iu’s Curved Folding Components

Toby Plunket's 3D Cymatic

Toby Plunket’s 3D Cymatic

Lorna Jackson's kerfed Spirohedron. (spidron ™ )

Lorna Jackson’s kerfed Spirohedron. (spidron ™ )

DS10 WeWanttoLearn's  buzzing Studio Space

DS10 WeWanttoLearn’s buzzing Studio Space

Ieva Ciocyte's Tree Bundling Truss

Ieva Ciocyte’s Tree Bundling Truss

Naomi Danos Folded Hypar volumes

Naomi Danos Folded Hypar volumes

NK Guy, author of The Art of Burning Man giving a lecture to our students

NK Guy, author of The Art of Burning Man giving a lecture to our students

NK Guy, author of The Art of Burning Man giving a lecture to our students

NK Guy, author of The Art of Burning Man giving a lecture to our students

I have been researching Miura pattern origami as a structural solution for rapidly deployable structures. Miura ori are interesting as structures due to their ability to develop from a flat surface to a 3D form, and become fully rigid, with no degrees of freedom, once constrained at certain points. 141110_Year 2 working folio2 Physical and digital experiments with Miura Ori have taught me that certain topographies can be generated by developing a modified Miura pattern. With the help of Tomohiro Tachi’s excellent research on the subject of curved Miura ori, including his Freeform Origami simulator (http://www.tsg.ne.jp/TT/index.html) I have learned that Miura ori surfaces that curve in the X and Y axes can be generated by modifying the tessellating components, however these modifications require some flexibility in the material, or looseness of the hinges. 141110_Year 2 working folio6 As a system for a rapidly deployable structure, I am most interested in the potential for the modified Miura ori to work as a structure built with cheap, readily available sheet materials which are generally planar, so I will continue to develop this system as a rigid panel system with loose hinges that can be tightened after the structure is deployed. 141110_Year 2 working folio4 In order to test the crease pattern’s ability to form a curved surface, I have defined a component within the Miura pattern that can tessellate with itself. The radius of this component’s developed surface is measured as it is gradually altered.

With the objective being to develop a system for the construction of a rapidly deployable structure, I have also been interested in understanding the Miura ori’s characteristics as it is developed from flat. Physical and digital tests were performed to determine the system’s willingness to take on a curve as its crease angles decrease from flat sheet to fully developed. I found the tightest radius was achieved rapidly as the sheet was folded, with the radius angle reaching a plateau. This is interesting from the perspective of one with the desire to create a structure that has a predictable surface topography, as well as from a material optimisation standpoint; the target topography can be achieved without the wasteful deep creases of an almost fully developed Miura ori. 141110_Year 2 working folio5 With the learnings of the modified Miura ori tests in mind, a simple loose hinged cylinder is simulated. As the pattern returns on itself and is fastened, the degrees of freedom are removed and the structure is fully rigid. 141110_Year 2 working folio A physical model of the system was constructed with rigidly planar MDF panels and fabric hinges. The hinges were flexible enough to allow the hinge movement necessary in developing this particular modified Miura ori, however some of the panels’ corners peeled away from the fabric backing as the system was developed from flat. A subsequent test will seek to refine this hinge detail, with a view to creating a scalable construction detail that will allow sufficient flexibility during folding, as well as strength once in final position. 141110_Year 2 working folio3

John Konings

j.e.konings@gmail.com

The history of curved crease folding goes back to as early as the Bauhaus, where a student had scored circular creases onto a paper in order to study its materiality. When a circular surface is folded along concentric rings, the resultant form bends on itself and forms a paraboloid in order to make up for the loss in circumference. Initial investigation involved the replication of such system and multiplying the modules which are then interlocked into each other to create various origami sculptures.

Circular Modules

Circular Modules

The system is then digitally simulated in order to extract the parameters which may affect the resultant geometry of the surface. With a combination of Kangaroo Physics, Hinge Forces and Springs, the digital simulation is created which allows anchor points to be placed, thus dragging for surface into various forms. Tests are carried out on different surfaces, including a closed circle of equal concentric rings, a closed circle of increasing concentric rings as well as an open circular strip with concentric rings. With an increasing fold angle, the bend angle increases.

System Exploration

System Exploration2

System Exploration

System Exploration

Upon cutting the closed circle, the surface becomes an open ended circular strip. The constraints that follow a closed surface no longer presents itself, thus allowing the strip to bend freely – although the principles of the system still applies. With increasing fold angles, the strip bends at greater angle. Having this revelation, different open ended strips are then tested against different parameters to extract the system further.

Parameters

Parameters

Parameters

Parameters

Parameters

In parallel to the research of curved crease folding is the investigation into the probability of transferring the system onto a more rigid, larger material, such as plywood. Here lattice hinge / kerf folds are employed, allowing the plywood to bend in a similar manner to card and paper. The final patterns for the hinges are a result of rigorous testing through trial and error. By repeating the modules we begin to see that, due to the folds, plywood can be as flexible as card.

Lattice

Lattice

First developed in 1979 by Dániel Erdély the Spidron is created by recursively dividing a 2-dimensional hexagon into triangles, forming a pattern that consists of one equilateral followed by one isosceles triangle. The resulting form is of six Spidron legs that, when folded along their edges, deform to create a 3-dimensional Spidron.

Spidron Nest

Spidron System_Parametrics_Lorna Jackson

Initial investigations into the Spidron system using paper resulted in irregular shapes that could not be predicted, and therefore replicated precisely. Progressing onto using rigid materials allowed the system to be broken down into six components, removing unnecessary triangulated fold lines, and developing latch folded Spidron that is precisely the same as that formed parametrically.

Spidron System_Three SPidrons_Lorna Jackson

This relationship between parametric and physical tests of component based Spidrons in both regular and irregular hexagons, as well as various other equal-sided shapes, has enabled the development of large scale models concluding thus far in a 1:2 scale version being built which will continue to be developed as a pavilion for submission to the Burning Man festival.

In parallel there has been an investigation into the system at a smaller scale allowing for the Spidron nest to be made as one component. In order to achieve the 3-dimensional Spidron form lattice hinges, also known as kerf folds, have been employed. Rigorous testing into the best cutting pattern have resulted in a straight line cutting pattern that allows for bending on multiple axis at once.

Developing this smaller scale system for submission to Buro Happold the intention is to create an arrayed system that is a conglomeration of both regular and irregular spidrons with varying depths and apertures that are able to integrate various display models etc. within.