An exploration of the simplest Hyperbolic Paraboloidic ‘saddle’ form has lead to the development of a modular system that combines the principles of the hypar (Hyperbolic Paraboloid) and elastic potential energy.

A hyperbolic paraboloid is an infinite doubly ruled surface in three dimensions with hyperbolic and parabolic cross-sections. It can be parametrized using the following equations:

Mathematical:   z = x2 – yor  x = y z

Parametric:   x(u,v)=u   y(u,v)=v   z(u,v)=uv

The physical manifestation of the above equations can be achieved by constructing a square and forcing the surface area to minimalise by introducing cross bracing that has shorter lengths than the  square edges.

A particular square hypar defined by b = n * √2 (b=boundary, n=initial geometry or ‘cross bracing’) thus constricting the four points to the corners of a cube leads to interesting tessellations in three dimensions.

Using a simple elastic lashing system to construct a hypar module binds all intersections together whilst allowing rotational movement. The rotational movement at any given intersection is proportionally distributed to all others. This combined with the elasticity of the joints means that the module has elastic potential energy (spring-like properties) therefore an array of many modules can adopt the same elastic properties.

The system can be scaled, shaped, locked and adapted to suit programmatic requirements.

## The Cloud

So easily can fun and playfulness be neglected within Architecture. My proposal stands as an embodiment of these aspects, creating an area of inclusive participation, a space that can be explored and is only complete when occupied.

Fallen from the sky and tied down in the middle of Black Rock City ‘The Cloud’ stands as a mirage for weary-eyed travellers from far and wide, a beacon of sanctuary that creates spaces that provide respite from the harsh conditions of the desert using permeable fabric to create a cool atmosphere diffusing light within daylight and emitting a soft glow from within in the evening.

Walking through the dessert after a long journey along the silk road ‘The Cloud’ emerges as a whimsical mirage. Mimicking the form of a cloud the easily recognisable form is transformed into Architecture; a sinuous billowing form allowing us to fulfil a childhood dream, walking on clouds.

The principle structure of the cloud is composed of hollow rolled steel tubes ,sandwiched between thick perforated fabric, strategically placed to withstand the extreme wind conditions as well as human interaction. Elevated from the floor these tubes are secured to the ground using the kandy kane re-bar method.
Keeping the form soft and playful so that not only is the installation safe but also malleable, responding to people climbing and walking it, bungee rope is securely looped over the steel tubes and threaded through the ‘ground’ fabric to hold it up, as illustrated in the accompanying drawing.

Interactivity is an integral part of the installation. Bringing to life the stranded cloud people are encouraged to explore the piece climbing in, over and around it, finding intricate crevasses that provide discreet hidden entrances to the inner cloud where an intimate social environment softly illuminated by the diffused daylight, providing an area of solace.

DIMENSIONS // 5000mm(l) x 3100mm(w) x 4100mm(h)

## 28th November 2013 Cross-Crit 2

Very enjoyable crit day for DS10 at Westminster University. It was our second cross-crit of the year and students showed their proposal for Brief2A, building an interactive structure for Burning Man or the festival of their choice.

Thank you very much to our helpful crits Harri Lewis (Ramboll RCD our engineers for last year’s Shipwreck and Fractal Cult), Marie-Isabel de Monseignat (Tutor at DRS1 Chelsea College of Art), Dusan Decermic, Anthony Boulanger and Katherine Herron. Here are couple pictures:

## NEAR UNISON | Burning Man Festival | Black Rock Desert

NEAR UNISON is an installation that allows participants to visualize the harmonic relationships between them. Pairs of sit-on pendulum swings create several large scale harmonographs that scratch drawings onto the surface of the Black Rock Playa. The structure that holds these harmonographs is itself a physical representation of a harmonographic form that can be seen from a distance across the Black Rock Playa.

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The harmonograph was a 19th century machine that was invented to explore the geometry of sine waves. It was soon developed into a popular parlour room toy that was capable of producing beautiful and delicate drawings simply by mapping the relationship between two swinging pendulums. By changing the lengths of the pendulums, their wavelength and oscillating frequency are changed. When the ratio of these two frequencies is something complex like 35:73, there is no discernible pattern, but as soon as it hits a simple ratio such as 3:5 or 2:3 a clear pattern emerges. The relationship between visual harmony and mathematical ratio is exactly the same those found in musical harmonies: the ratios that produce beautiful drawings are the same as produce harmonious musical chords.

The title ‘NEAR UNISON’ is derived from the set of patterns that occur when the ratio of the two pendulums is very close to 1:1, as will occur when people of a similar weight are using the interactive harmonograph. It is expected that the patterns produced by these interactive harmonographs will describe, in an abstracted manner, the similarity of all human beings, while emphasizing the subtle differences between individuals.

The overall form of the structure is also derived from a 3D harmonographic surface with a ratio that is in this ‘near unison’ region. A plywood structure supports pipes that trace the harmonographic lines through space to create a delicately curved sculptural form that sits directly on the Playa. Suspended from this structure are a series of connected pendulums that participants are able to ride like swings. When they are are used, these pendulums trace harmonographic patterns onto the surface of Playa. The drawings that are created will map the interaction between pairs of participants.

## Wax Structures

These images show the results of some recent experiments using wax and water.
To achieve the structures I filled a container with hot melted wax, weighted it so it would sink, then dropped it into a larger container full of cold tap water (approx 10 degrees)
Due to the lower density of the wax it rises to the surface of the water, and in doing so exposes an increasing surface area to the water allowing it to cool and solidify on its way up.
This technique has resulted in some exciting organic flowing structures which I hope to analyse further and develop more architecturally.

## Stick and Fabric Evolution through Physical testing

Below is a pictorial timeline of how my Burning Man project has progressed and developed through physical modelling. It began with a regular grid which has developed to be able to control the parameters (such as column length and fabric tension) to create an arched structure. The form proposed for the Burning Man Festival is a double Arched system, which works with the axis of the Playa. (see portfolio for further explanation)

## Colourscape Festival by Cwmni Colourscape and Eye Music Trust

Below is an amazing reference for anyone looking either at inflatable structures, light, colours, acoustics, performing arts etc. The Project  is entitled “Colourscape” and is organised several times a year by Eye Music Trust while actual spaces are designed and built by the renowned artistic partnership of Peter Jones and Lynne Dickens (see video below).

By linking music, colour, light, space and movement the festival aims to give new dimensions to public perception and new understanding of contemporary music and performing arts. Even though exterior of the building (especially from aerial view) is not particularly aesthetically pleasing, the effect of sunlight and colours is unbelievable while you are inside. Also, pay attention to how cleverly they solved the issue of entering an inflatable building.

Another quite recent similar example (on a larger scale though) is Anish Kapoor’s “Leviathan” in Grand Palais, Paris (see pictures below).

Above: “COLOURSCAPE” by Cwmni Colourscape

Above: “LEVIATHAN” by Anish Kapoor

## Quasicrystals

When researching the close packing of tetrahedrons I came across a reasonably new discovery, The Quasicrystal.  Its current impact or potential impact can be gauged by the fact that Dan Shechtman, who made the finding, was this year awarded the Nobel Prize in Chemistry.

“Quasicrystals are a fascinating aspect of chemical and material science – crystals that break all the rules of being a crystal at all.”

So what is a Quasicrystal?

Basically they are formed when tetrahedra are compressed into a given volume. In Dan Shechtman’s discovery, the packing achieves an efficiency which fills 82% of space, higher than any previous effort.  The close packing of the tetrahedron forms these intricately complicated and amazingly complex structures. A normal crystal is a material structure which repeats periodically however one of the really interesting things about Quasicrystals is that they don’t actually repeat exactly, despite its regularity.  Quasicrystals represent a class of solids which lack translational symmetry, but nevertheless exhibit perfect long-range order and reveal well defined fivefold rotational symmetries. Translational symmetry is when an image or object can be divided into a sequence of identical repetitions which are translated about a given vector. So without this form of symmetry the Quasicrystal is non-periodic.

Aperiodic and Penrose tiling’s can also be found within Quasicrystals which themselves can be found in medievil Islamic mosaics.

The model shown in the second image is made up of 4000 x 1cm long struts, built thanks to 3D printing!

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/press.pdf

## Alternative fabrication methods using sand

Following on from the tutorial yesterday where Jack talked about possibly casting his experiments with sand using a saline solution sprayed onto the forms created here are two further ways of utilising sand to create rigid structures.

http://www.designboom.com/weblog/cat/16/view/15402/markus-kayser-solar-sinter-3d-printer.html

The first is a 3D printer which concentrates the solar energy to form glass structures from the sand the machine sits on. I know many of you have seen this before but I thought I’d post it in relation to this specific topic. The link is to designboom, a great website with daily updates from the latest innovations in architecture, art and design. Check out the link to find further information on Markus Kayser’s printer.