Tag Archives: Geometry

Sound is a hidden code when it unlocks allows us to perceive it as a set of geometrical patterns.Einstein believes the key to unlocking the universe is through the hidden geometry and mathematics, the mechanic of sound is translated visually through frequency and amplitude represents itself with beautiful geometries as code from the universe. My design recreates Sound’s geometries into a physical symbolic Sanctuary for users to retreat their senses in the desert,to unravel meaning behind the symbol of Sound by deconstructing it and re-dressing it with physical form. Making Sound visible.

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The structure measures 13.77 feet in length &12.8 feet in height. The material for the structure would be paneled by birch plywood(4ft. x 2ft. panel).2-D dimensional geometry is translated into 3-Dimensional form by folding and joining edges.The sanctuary is made up of three mirroring layers, stacking vertically. The construction of the structure is to explore double curvature design with single curvature paneling and assembly. The ground storey encourages private space for reflection; individual sitting and resting area are carved inwards towards the air-well  ,in contrast, the upper storey is the communal area within the enclosure where users can access from a ladder. Pocket of windows are generated by the stacking and mirroring of sound vibration patterns.  Users enters into the enclosure and view the desert from within.

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Live feeding of Sound and the changing LED lights


In the night, live feeding of sound is captured when in contact with the surfaces of the sanctuary. With a contact microphone attaches onto the surface, it captures the sound amplitude when a user touches or tap as sound travels through the surface as a medium. The device(computer coding with Arduino) then translates the amplitude variation (loudness) into changing colours of LED lights. The lights are attached on the rim of the panels.



Studies of Sound patterns through water




Eigen vector


Hello WeWantToLearn community. We’re going to Burning Man in less than a month!

Our project this year will be a physical manifestation of our collective dreams and is called Tangential Dreams.  It is a seven meters high temporary timber tower displaying inspiring messages from around the world, written on a multitude of swirling “tangents”.

We need your help to realise our project! There is only three days left to collect the missing £5,000 on our crowdfunding campaign to finance the many expenses associated with the creation of such an ambitious project.

Please click on the image below or use the following shortlink to share/help – everything helps: 🙂




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The project is a climbable sinuous tower made from off-the-shelf timber and digitally designed via algorithmic rules. One thousand “tangent” and light wooden pieces, stenciled with inspiring sentences, are strongly held in position by a helicoid sub-structure rotating along a central spine which also forms a safe staircase to climb on. Each one of the poetic branches faces a different angle, based on the tangent vectors of a sweeping sine curve. In line with this year’s theme, the piece is reminiscent of Leonardo’s Vitruvian man’s movement, helicoid inventions such as the “aerial screw” helicopter and Chambord castle helicoid staircase as well as his deep, systematic, understanding of the rules behind form to create art. From a wave to a flame all the way to a giant desert cactus, the complex simplicity of the art piece will trigger many interpretations, many dreams.

The art piece attempts to maximize an inexpensive material by using the output of an algorithm – (the value of the piece being the mathematics behind it, as well as the experience, not the materials being used). The computer outputs information to locate the column, sub-structure and tangents.  We believe digital tools in design are giving rise to a new Renaissance, in which highly sophisticated designs, mimicking natural processes by integrating structural and environmental feedback, can be achieved at a very low cost. We worked very closely with our structural engineer format, sharing our algorithms, to give structural integrity to the piece and resist the strong climbing and wind loads. There are now three “legs” to our proposal, each rotated from each other at 60 degrees angles around a central solid spine, to ensure the stability of the piece, similarly to a tripod. The tangents are not just a decoration, they act as a spiky balustrade to prevent people from falling.

We have a fantastic team for the project:  Philip Olivier, Eira Mooney, Maialen Calleja, Aaron Porterfield, Sebastian Morales, Antony Dobrzensky, Laura Nica, Karina Pitis, Hamish Macpherson, Jon Goodbun, Yannick Yamanga, Matthew Springer ,Josh NG ,Lola Chaine, Dror BenHay, Peter Wang, Charlotte Chambers, Michael DiCarlo, Sandy Kwan.


We want our structure to have an intangible aspect, a magical side, one that is beyond matter and geometry. We want to connect our art with every each of you and make you part of our own BIG DREAM, building Tangential Dreams.

We want our structure to have an intangible aspect, a magical side, one that is beyond matter and geometry. We want to connect our art with every each of you and make you part of our own BIG DREAM, building Tangential Dreams.


We use physical modelling as a way to understand how the pieces fit together, the best assembly sequence as well as the structural integrity of the project. It takes time, material, money to create a truly original project.

We use physical modelling as a way to understand how the pieces fit together, the best assembly sequence as well as the structural integrity of the project. It takes time, material, money to create a truly original project.


Gif Animation of the assembly process. the project will take two weeks to pre-cut and assemble together with volunteers. We need your help for all the expenses.

Gif Animation of the assembly process. the project will take two weeks to pre-cut and assemble together with volunteers. We need your help for all the expenses.



Exciting rewards to thank you for your supports! from top left to bottom right: Pendants, Earrings, T-Shirts, Tangents, Vase, Ceiling Panels, 3D Printed Smoke Stool, Full Physical Model.

Exciting rewards to thank you for your supports! from top left to bottom right: Pendants, Earrings, T-Shirts, Tangents, Vase, Ceiling Panels, 3D Printed Smoke Stool, Full Physical Model.



Final Day Render


Entwine is a timber frame structure which has been developed through rigorous physical and digital testing to ensure a safe climbing frame for all to enjoy. When exploring Entwine, the vast expanse of the playa is framed through beautiful intertwining curved plywood beams. Burners can view the event from glorious vantage points nestled amidst multiple communal spaces that encourage interaction and play.

The structure predominantly consists of strips of curved plywood which have been connected together using pioneering construction techniques, specifically the utilisation of conflicting forces, similar to those apparent in ‘Tensegrital’ design. Drawing inspiration from Leonardo Da Vinci and his various experimentations with physical form, ‘Entwine’ is a marvel of geometry. The piece is formed from an arrangement of 19 octahedral components, each consisting of six beams, which are paired and positioned upon one of three axis. These three elements represent the unity of man, nature and the universe that surrounds us.

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Each modular component is tessellated to form an octahedral space frame structure. The rigidity resulting from this tessellation is in direct contrast to the curving structural beams which exude an organic aesthetic. As Burners view Entwine from different aspects, a remarkable array of different patterns and forms are revealed, many bearing resemblance to sacred geometry, specifically the Flower of Life, which was a significant study within Leonardo Da Vinci’s work.


Entwine is unorthodox in its composition, and this is a contributing factor to what makes it so unique: Each module is constructed through tensioning layers of ¼ inch thick plywood, which are then mechanically fixed together when a desired radius has been reached. By laminating the plywood in this manner, each component retains its curvature but remains in compression. These conflicting forces are integral to the design of Entwine: Each octahedral module is constructed from these compressed plywood elements, and are held together with tensioning ropes creating a structure of isolated components in compression within a net of continuous tension.MODEL PHOTOGRAPHSMODEL PHOTOGRAPHS 2The form of the structure is based on the octahedron, which is a Platonic solid composed of eight equilateral triangles; four of which meet at each vertex. One of the eight triangles acts as a base for the structure. This results in one edge creating a small cantilever, whilst the counter edge can be anchored to the ground. As previously studied by Buckminster Fuller, the geometry of an octahedron is particularly good at forming space frames with a strong cantilevers.


Entwine Construction Proposal

The participatory aspect of the installation voids the role of the ‘spectator’ and creates more active engagement. In many of Leonardo Da Vinci’s paintings, his subjects are framed by surreal, dreamlike landscapes. This is reflected within Entwine: As Burners become part of the installation, they are framed by the awe inspiring backdrop of Black Rock Desert: In many ways Entwine becomes the artist, the playa the canvas, and Burners the subjects.

“the artist is not a special sort of person, but every person is a special sort of artist.”

This is not only true in the sense of physical involvement but during the construction the ‘spectator’ becomes involved in making strategic decisions in the realisation of the work of art. The development, design and construction of the project embodies the principles of self-reliance and self-expression, whilst a proposal that is safe, interactive and beautiful will be gifted to the community at Burning Man.

Entwine’s curving form will be illuminated using LED spot lights to enhance the organic patterning existent within the structure. This allows the full form of the structure to be fully visible.

Geometry can be found on the smallest of scales, as is proven by the beautiful work of the butterfly in creating her eggs. The butterflies’ metamorphosis is a recognised story, but few know about the start of the journey. The egg from which the caterpillar emerges is in itself a magnificently beautiful object. The tiny eggs, barely visible to the naked eye, serve as home for the developing larva as well as their first meal.

White Royal [Pratapa deva relata] HuDie's Microphotography

White Royal [Pratapa deva relata] HuDie’s Microphotography

shapes copy

Clockwise: Hesperidae, Nymphalidae, Satyridae, Pieridae

Each kind of butterfly has its unique egg design, creating a myriad of beautiful variations.

These are some of the typical shapes that each family produce.

But it is the Lycaenidae family that have the most geometrical and intricate eggs.



Other eggs

Lycaenidae eggs from left to right: Acacia Blue [Surendra vivarna amisena], Aberrant Oakblue [Arhopala abseus], Miletus [Miletus biggsii], Malayan [Megisba malaya sikkima]. HuDie’s Microphotography


Biomimetics, or biomimicry is an exciting concept that suggests that every field and industry has something to learn from the natural world. The story of evolution is full of problems that have been innovatively solved.


There are thousands of species of butterfly, each with their unique egg design. 3A truncated icosahedron for a frame, the opposite of a football. Instead of panels pushed out, they are pulled in.


Fractals are commonly occurring in nature, and can be described as a never-ending pattern on different scales. People are subconsciously familiar with fractals, so are inherently more relaxed when surrounded by them.


3D Printing is a relatively new technology that is set to change our world. Innovations in the uses of 3D printers, combined with falling costs, means that they could be a ubiquitous tool in every home and industry. 3D printers and scanners are already used a great deal in everything from the biomedical field to art studios, and experiments are currently being done to construct entire homes. This technology is in its infancy, and it is exactly for this reason that every effort should be taken to research its potential. It is common to use 3D printers in architecture to show small working models, I would like to now use it to make a large and complex structure at full scale.


This research will underpin the design of a sculptural installation in which people can interact with live butterflies. With the ever-declining numbers of butterflies worldwide and in the UK, conservation and education are paramount.

The link between butterflies and humans in our ecosystem is one that is vital and should be conserved and celebrated.

I can imagine an ethereal space filled with dappled light where people can come for contemplation and perhaps their own personal metamorphosis.



In mathematics, a Scherk surface (named after Heinrich Scherk in 1834) is an example of a minimal surface. A minimal surface is a surface that locally minimizes its area (or having a mean curvature of zero). The classical minimal surfaces of H.F. Scherk were initially an attempt to solve Gergonne’s problem, a boundary value problem in the cube.

The term ‘minimal surface’ is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, minimal surface of revolution, Saddle Towers etc.).

Scherk's Surface Soap experiments

Scherk’s minimal surface arises from the solution to a differential equation that describes a minimal monge patch (a patch that maps [u, v] to [u, v, f(u, v)]). The full surface is obtained by putting a large number the small units next to each other in a chessboard pattern. The plots were made by plotting the implicit definition of the surface.

An implicit formula for the Scherk tower is:

sin(x) · sin(z) = sin(y),

where x, y and z denote the usual coordinates of R3.

Scherk’s second surface can be written parametrically as:

x = ln((1+r²+2rcosθ)/(1+r²-2rcosθ))

y = ((1+r²-2rsinθ)/(1+r²+2rsinθ)) 

z = 2tan-1[(2r²sin(2θ))/(r-1)]      

for θ in [0,2), and r in (0,1).

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Scherk described two complete embedded minimal surfaces in 1834; his first surface is a doubly periodic surface, his second surface is singly periodic. They were the third non-trivial examples of minimal surfaces (the first two were the catenoid and helicoid). The two surfaces are conjugates of each other.

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Scherk’s first surface

Scherk’s first surface is asymptotic to two infinite families of parallel planes, orthogonal to each other, that meet near z = 0 in a checkerboard pattern of bridging arches. It contains an infinite number of straight vertical lines.

Scherk’s second surface

Scherk’s second surface looks globally like two orthogonal planes whose intersection consists of a sequence of tunnels in alternating directions. Its intersections with horizontal planes consists of alternating hyperbolas.

Other types are:

  1. The doubly periodic Scherk surface
  2. The Karcher-Scherk surface
  3. The sheared (Karcher-)Scherk surface
  4. The doubly periodic Scherk surface with handles
  5. The Meeks-Rosenberg surfaces

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Scherk’s surface can have many iterations, according to the number of saddle branches, number of holes, turn around the axis and bends towards the axis. Some of the design iterations and adaptations of the system are presented below:

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Scherk’s Surface can be adapted to several design possibilities, with multiple ways of fabrication. Interlocked slices using laser cut plywood sheets, folded planes of metal or CNC stacked wooden slices. With its versatile and flexible form it is adaptable to any interior space as an installation or temporary furniture.

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Throughout this studio group we have explored natural, mathematical and physical anomalies and tried to find the hidden data within it. Everything that exists gives out some sort of sound or vibration and the process of visualising this is called Cymatics. In it’s elementary form it is is often the process of vibrating a medium such as sand or water in order the generate shapes.Cymatics

The history of Cymatics originates from research into resonance by Da Vinici, Galileo and Robert Hook and then Ernest Chladini – Cladidi experimented with using a metal plate and sand to show the standing wave – or Chladini Patterns – a plate creates.

Chladni Pattern

There are a multitude of other mediums that can be used to visualise sound or even generate sound from visual.

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Cymatics is in it’s early days of exploration, it is a looking glass into a hidden world previously unseen and the list of scientific applications growing each day. Consider that sound has a form which you can see and that it can affect matter and cause a form within matter – now imagine the architectural applications possible.

Having had a look at 2000-2015 sci-fi glimpses into the future, climate change remained a constant, unchanged factor of influence. This study investigates the basics of desertification, how dunes are formed and how they are shaped and moved by external forces.

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A couple of experiments investigate the wind effects on sand formation and also an interesting method of solidifying the resulted dune with adhesive and heat.10.11.2014 Portfolio_Page_10 10.11.2014 Portfolio_Page_11 10.11.2014 Portfolio_Page_12 10.11.2014 Portfolio_Page_13 10.11.2014 Portfolio_Page_14 10.11.2014 Portfolio_Page_15