Wood is one of architecture’s more magnanimous materials, and is celebrated for it’s sustainability, quality and speed of construction. Brief 02 will see our students present a credible scenario for a sustainable community, of which the project’s architectural language should form a continuity with their brief 01 system. What starts a community could be a product or a service and we want our students to understand how as an architect you can intervene to materialise the network that binds these people together around this life cycle.

Below are the briefing documents issued to DS10 students:

‘Minimal Matters’ utilises the several geometric benefits of an asymptotic curve network to optimise cost and fabrication. From differential geometry, it is determined asymptotic curves are not curved in the surface normal direction. As opposed to traditional gridshells, this means they can be **formed from straight, planar strips** perpendicular to the surface. In combination with **90° intersections** that appear on all minimal surfaces (soap films) this method offers a simple and affordable construction method. Asymptotic curves have a vanishing normal curvature, and thus only exist on anticlastic surface-regions.

Asymptotic curves can be plotted on any anticlastic surface using differential geometry.

On minimal surfaces, the deviation angle α is always 45 (due to the bisecting property of asymptotic curves and principle curvature lines). Both principle curvature networks and asymptotic curve networks consist of two families of curves that follow a direction field. The designer can only pick a starting point, but cannot alter their path.

*(a) Planes of principle curvature are where the curvature takes its maximum and minimum values. They are always perpendicular, and intersect the tangent plane.*

*(b) Surface geometry at a generic point on a minimal surface. At any point there are two orthogonal principal directions (Blue), along which the curves on the surface are most convex and concave.Their curvature is quantified by the inverse of the radii (R1 and R2) of circles fitted to the sectional curves along these directions. Exactly between these principal directions are the asymptotic directions (orange), along which the surface curves least.*

*(c) The direction and magnitude for these directions vary between points on a surface.*

*(d) Starting from point, lines can be drawn to connect points along the paths of principal and asymptotic directions on the respective surface.*

The next step is to create the asymptotic curve network for the Gyroid minimal surface; chosen from my research into Triply Periodic Minimal Surfaces.

As the designer, I can merely pick a starting point on an anticlastic surface from which two asymptotic paths will originate. It is crucial to understand the behaviour of asymptotic curves and its dependency on the Gaussian curvature of the surface.

Through rotational symmetry, it is resolved to only require six unique strips for the complete grid structure (Seven including the repeated perimeter piece).

The node to node distance, measured along the asymptotic curves, is the only variable information needed to draw the flat and straight strips. They are then cut flat and bent and twisted into an asymptotic support structure.

Eight fundamental units complete the cubit unit cell of a Gyroid surface. Due to the scale of the proposal, I have introduced two layers of lamellas. This is to ensure each layer is sufficiently slender to be easily bent and twisted into its target geometry, whilst providing enough stiffness to resist buckling under compression loads.

‘Minimal Matters’ aims to create an explorative, meditative and interactive experience for visitors. It is a strained grid shell utilising the geometrical benefits of an asymptotic curve network; digitally designed via algorithmic rules to minimise material, cost, and construction time.

]]>The proposal takes the form of a crystalline structure found in nature, interpreted through parametric design into a timber grid art piece. In the sense of repeating themselves in three dimensions, a gyroid is an infinitely connected triply periodic minimal surface. A minimal surface is a single surface articulation which minimises that amount of surface needed to occupy space. The proposal represents restoring a balance in energy, taking only that of the earth’s resources required to fulfil the form. Our inability to distinguish our needs from our greeds leads to excessive desires for life’s commodities. The efficiency of the design complements the beauty of rotational symmetry of a single node.

The lattice structure will create foot and hand holds to help climbers onto the series of sloping platforms; allowing users to survey the desert camp from different perspectives.

More than just a climbable structure, Minimal Matters is to be a resting place for festival-goers and a shelter from the strong sun of the site. The layers of grids cast shadows of varied patterns throughout the day. At night, LED lighting along the lamellas will celebrate it’s form and illuminate the playa.

Inspired by nature, the proposal brings a parametrically designed structure into the realm of physical interaction. The piece is a culmination of thorough research and physical exploration of timber’s potential. The combination of conceptual bravery matched with architectural reality seeks an architecture of playfulness and beauty which will respond to the inclusive environment of Burning Man. It will celebrate a new design method for timber grid construction, and symbolise the harmony between nature and computational design.

Minimal surfaces have a constant mean curvature of zero, i.e. the sum of the principal curvatures at each point is zero. Particularly fascinating are minimal surfaces that have a crystalline structure, in the sense of repeating themselves in three dimensions, in other words being triply periodic.

Many triply periodic minimal surfaces are known. The first examples of TPMS were the surfaces described by Schwarz in 1865, followed by a surface described by his student Neovius in 1883. In 1970 Alan Schoen, a then NASA scientist, described 12 more TPMS, and in 1989 H. Karcher proved their existence.

My research into grid structures with the goal of simplifying fabrication through repetitive elements prompted an exploration of TPMS. The highly symmetrical and optimised physical properties of a TPMS, in particular the Gyroid surface, inspired my studio proposal, Minimal Matters.

The gyroid is an infinitely connected periodic minimal surface discovered by Schoen in 1970. It has three-fold rotational symmetry but no embedded straight lines or mirror symmetries.

The boundary of the surface patch is based on the six faces of a cube. Eight of the surface patch forms the cubic unit cell of a Gyroid.

For every patch formed by the six edges, only three of them is connected with the surrounding patches.

Note that the cube faces are not symmetry planes. There is a C3 symmetry axis along the cube diagonal from the upper right corner when repeating the cubic unit cell.

Curiously, like some other triply periodic minimal surfaces, the gyroid surface can be trigonometrically approximated by a short equation:

**cos(x)sin(y)+cos(y)sin(z)+cos(z)sin(x)=0**

Using Grasshopper and the ‘Iso Surface’ component of Millipede, many TPMS can be generated by finding the result of it’s implicit equation.

Standard F(x,y,z) functions of minimal surfaces are defined to determine the shapes within a bounding box. The resulting points form a mesh that describes the geometry.

- A cube of points are constructed via a domain and fed into a function. Inputs of standard minimal surfaces are used as the equation.
- The resulting function values are plugged into Millipede’s Isosurface component.
- The bounding box sets up the restrictions for the geometry.
- Xres, Yres, Zres [Integer]: The resolution of the three dimensional grid.
- Isovalue: The ‘IsoValue’ input generates the surface in shells, with zero being the outermost shell, and moving inward.
- Merge: If true the resulting mesh will have its coinciding vertices fused and will look smoother (continuous, not faceted)

The above diagrams show Triply Periodic Minimal surfaces generated from their implicit mathematical equations. The functions are plotted with a domain of negative and positive Pi. By adjusting the domain to 0.5, the surface patch can be generated.

Many TPMS can best be understood and constructed in terms of fundamental regions (or surface patches) bounded by mirror symmetry planes. For example, the fundamental region formed in the kaleidoscopic cell of a Schwarz P surface is a quadrilateral in a tetrahedron, which 1 /48 of a cube (shown below left). Four of which create the surface patch. The right image shows a cubic unit cell, comprising eight of the surface patch.

Schoen’s batwing surface has the quadrilateral tetrahedron (1/48 of a cube) as it’s kaleidoscopic cell, with a C2 symmetry axis. As shown in the evolution diagram below, the appearance of two fundamental regions is the source of the name ‘batwing’. Twelve of the fundamental regions form the cubic unit cell; however this is still only 1/8 of the complete minimal surface lattice cell.

‘Growth From The Ger’ seeks to analyse the vernacular structure of the traditional nomad home and use parametric thinking to create a deployable structure that can grow by modular.

‘Ger’ meaning ‘home’ is a Mongolian word which describes the portable dwelling. Commonly known as a ‘yurt’, a Turkish word, the yurt offered a sustainable lifestyle for the nomadic tribes of the steppes of Central Asia. It allowed nomads to migrate seasonally, catering to their livestock, water access and in relation to the status of wars/conflicts. An ancient structure, it has developed in material and joinery, however the concept prominently remaining the same.

Growing up in London, I fell in love with the transportable home when I first visited Mongolia at the age of 17. The symmetrical framework and circulating walls create a calm and peaceful environment. In the winter it keeps the cold out and in the summer keeps the heat out. The traditional understanding of placement and ways of living within it, which seems similar to a place of worship, builds upon the concept of respect towards life and its offerings.

Understanding the beauty of the lifestyle, I also understand the struggles that come with it and with these in mind, I wanted to explore ways of solving it whilst keeping the positives of the lifestyle it offers.

**Pros:** Deployable, transportable, timber, vernacular, can be assembled and dissembled by one family, can vary in size/easily scaleable depending on user, low maintenance, sustainable, autonomous.

**Cons:** Difficult to sustain singularly, not water proof, no privacy, no separation of space, low ceiling height, can’t attach gers together, low levels of security.

To understand the possibilities of the lattice wall, I created a 1:20 plywood model using 1mm fishing wire as the joinery. This created various circular spirals and curves. The loose fit of the wire within the holes of timber pieces allowed such curves to happen and created an expanding body. The expansion and flexible joinery allows it to cover a wider space in relation to the amount of material used.

I created the same latticework at 1:2 scale to see if the same curvature was created.

Locking the curve to create a habitable space. I did this by changing the types of joints in different parts of the structure.

To create a smoother and more beautiful curve I change the baton to a dowel and densify the structure.

To lock the lattice curve in expansion I extrude legs that meet the ground and tie together.

The model made from sheet plywood cost approximately £30 and took one working day to make for one person. However, a more sustainable material and process needed to be considered as the process of making plywood contradicted this.

This model can be made by one person with the use of a wood workshop. The timber pieces were bought at 18mm x 95mm x 4200mm, 13 pieces of these were enough to make three modules, roughly costing £170 in total. Each module takes approximately 5 hours to construct, this involves the tying of the measured length twine joints. The structure is lightweight and each module is easily transportable by one person.

The layout of the panels ensures that material waste is reduced to a minimum.

The project has evolved as a result of series of experiments and explorations of different ways of creating curvature from plywood. It initially started as an ambition of bending plywood on a formwork, using vacuum bags and lamination which proved to be non-cost effective, time consuming and not environmentally friendly due to the lamination process. The idea then shifted into curved structure composed out of 2D panels interlocking with each other, which led to its final form.

]]>The project began with a study in generating mathematical symmetry using imaginary functions in grasshopper. The use of imaginary numbers created patterns which would be challenging to create manually, all of which were symmetrical either in reflection or rotation. The equation µ(t)= 3√(x+it) created a pattern of straight lines which would combine to create curves in the style of a hyperbolic parabaloid. This outcome would initiate my interest in tensegrity as a way to create beautiful curving geometry through the use of solely straight elements.

Force testing using kangaroo engineering plugin for grasshopper, allowed visualisation of the forces acting on each member of the tensegrity system prior to construction. The first step is to identify the cross sectional area and youngs modulus of the tension and compression elements in the system. This information is applied to a kangaroo physics model, which is already in a state of compression and tension, to reveal the exact force running through each member. The data output is used to analyse if the model can hold its shape and that the materials used can withstand the forces applied to them. In this instance, the hemp rope would have the strength to tension the model, but would not be able to resist the additional force of human touch, resulting in catastrophic failure. A more substantial tensioning material would be required, steel tension cable. In addition, bamboo has a relatively weak shear force, meaning that the twist created from tensioning each end of bamboo would snap the member. To resolve this issue, end caps were developed to spin independently on each bamboo pole, transferring the shear force into the connection.

There would be two stages to the construction process, the tensegrity module and the connections between modules which form the inhabitable space. The tensgrity module was designed for ease of manufacture, all bamboo components are identical in length at 1220mm (material ships in 2440mm lengths). Pre-manufactured aluminium caps are fitted to the ends of each bamboo piece, then assembled into ‘ladders’ with the use of a jig, steel tension cable and cable crimps. Each tensegrity module consists of three identical ‘ladders’, which are twisted to connect to each other in a spiral arrangment. The module has six connection nodes, five of which can be pre-assembled prior to arrival on site. With the connection of the sixth node the module becomes a three-dimensional, stable shape. This technology results in the assembly of modules in-situe in under five minutes. The second stage of connecting the modules to form the inhabitable space, requires the insertion of pre-cut bamboo poles into the longer aluminium end caps, a process which can be completed in a further five minute period.

This project has many benefits, namely due to its simplicity, it can be built in a garage without the use of specialist tools, requiring only a saw, drill and pliers. Identical length components means manufacturing is intuitive, efficient and cheap, whilst the speed of deployment, and ease of flat pack storage, could have real benefits in the temporary shelter market.

]]>Inspired by the Islamic pattern, I discovered that some of the Islamic tiling pattern in shrine are similar to the Penrose tiling discovered by Sir Roger Penrose. Looking into the Penrose tiling, it has 3 types and they all follows the rule of golden ratio. These Penrose tiling arrangements each form a reflection and five-fold rotational symmetry.

After doing more in-depth research, I discovered that the rhombic triacontahedron which made up of rhombuses has a similarity to the Penrose tiling type P3, also with rhombuses. These two geometric patterns can be arranged such that by using a single module (golden rhombus), we can form a 3D rhombic triacontahedron with the guide of Penrose tiling as a 2D plane pattern.

The rhombus modules are folded in different sets of angles, it can form a volumetric space while still follows the grid of Penrose tiling from the top view. These are done in 4 angles: 36 degree, 72 degree, 108 degree, and 144 degree.

By doing the physical model with CNC-ing 6mm thick plywood with the desired angle, it allow the folding modules fitting into the shape I wanted. The custom metal bracket in between planes of plywood rhombus also helps in forming the shape. It will also allow insulation and waterproofing which will be further developed next as it comprised of double layer of plywood.

]]>Inspired by Japanese basketry weaving, Twisted Pellucidity takes this technique into an architectural scale. Through creating a set of twisted modules varied with a standard weave in between, the design flows between closed and open creating potential for naturally ventilated housing in hot regions of the world. It has been designed for disassembly to ease transportation and enable adaptations of the size and shape of the design. Thanks to the module’s structural strength, very thin ply strips were used making the structure light and delicate whilst allowing elegant passage of light.

The project started with the exploration of weaving patterns and their strength and bending qualities. Through a series of experiments I have tested a number of single and double curvatures that could be potentially applied on an architectural scale.

Since bending quality of plywood, whether as a woven sheet or as a singular strip, has always been of interest, I have started looking into combining both of those methods. Thanks to bending, large volumes can be created – which seemed ideal for potential enclosure areas. I have therefore decided to research further into the bend-active qualities of plywood. Starting with a single bend, I have developed the geometry into a triple – twist which created a very structurally strong, symmetrical module. Through Grasshopper scripting of the observed geometry of the physical model I have gained a thorough understanding of the behaviour of twisted strip of plywood which I then further enhanced and through a number of Kangaroo physical simulations I have gained a deep understanding of forces acting on a bent and twisted three times strip of plywood. Those experiments helped explain and understand why and how does a strip of plywood gain an extraordinary structural strength.

Twisting and bending the strip showed a great impact on the properties of the entire module. Thanks to bend-active and torsional forces acting against each other, the module gains incredible strength in both tension and compression with its strength rising about 10 times in comparison to original elements. This allows for almost never-ending possibilities of use when arrayed in different ways.

As I was particularly interested in how the action I have chosen affected the original material, the natural course of action was to test it in a larger scale as an array and combine it with the original research into weaving patterns and their properties. This has naturally created a Field Condition.

*Field Condition is any formal or spatial matrix capable of unifying diverse elements while respecting the identity of each. That leads to the overall shape and extent being highly fluid and less important than the internal relationships of parts which determine the behaviour of the field.*

Thanks to the overall qualities of the system, the final design became an unexpected result of adding modules and then connecting each the ends to create an enclosed circular space. This can vary in diameter until it reaches the structural strength capabilities of the chosen thickness of plywood. For 0.8mm strips the largest structurally stable diameter is approximately 1m. This could be larger for thicker and wider strips however this required further research.

Assembly of the final model turned out to be time-consuming but rewarding. Due to great intricacy of the module and a number of connections, it took approximately 80 hours to complete the final model.

Final Model ended up taking shape of a tower – large enough to fit myself in it. This process proved the Field Condition properties of the system allowing to create a variety of designs – displayed tower being one of them.

Overall, it was a challenging but extremely rewarding journey which I am excited to draw further conclusions from in the second semester.

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