The Curves of Life

“An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be an unlikely and an unusual circumstance. Rates vary, proportions change, and the whole configuration alters accordingly.” – D’Arcy Wentworth Thompson

“This is the classic reference on how the golden ratio applies to spirals and helices in nature.” – Martin Gardner

The Curves Of Life

What makes this book particularly enjoyable to flip through is an abundance of beautiful hand drawings and diagrams. Sir Theodore Andrea Cook explores, in great detail, the nature of spirals in the structure of plants, animals, physiology, the periodic table, galaxies etc. – from tusks, to rare seashells, to exquisite architecture.

He writes, “a staircase whose form and construction so vividly recalled a natural growth would, it appeared to me, be more probably the work of a man to whom biology and architecture were equally familiar than that of a builder of less wide attainments. It would, in fact, be likely that the design had come from some great artist and architect who had studied Nature for the sake of his art, and had deeply investigated the secrets of the one in order to employ them as the principles of the other.

Cook especially believes in a hands-on approach, as oppose to mathematic nation or scientific nomenclature – seeing and drawing curves is far more revealing than formulas.

252264because I believe very strongly that if a man can make a thing and see what he has made, he will understand it much better than if he read a score of books about it or studied a hundred diagrams and formulae. And I have pursued this method here, in defiance of all modern mathematical technicalities, because my main object is not mathematics, but the growth of natural objects and the beauty (either in Nature or in art) which is inherent in vitality.

Despite this, it is clear that Theodore Cook has a deep love of mathematics. He describes it at the beautifully precise instrument that allows humans to satisfy their need to catalog, label and define the innumerable facts of life. This ultimately leads him into profoundly fascinating investigations into the geometry of the natural world.

 

Relevant Material

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“An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be an unlikely and an unusual circumstance. Rates vary, proportions change, and the whole configuration alters accordingly.” – D’Arcy Wentworth Thompson

D’Arcy Wentworth Thompson wrote, on an extensive level, why living things and physical phenomena take the form that they do. By analysing mathematical and physical aspects of biological processes, he expresses correlations between biological forms and mechanical phenomena.

He puts emphasis on the roles of physical laws and mechanics as the fundamental determinants of form and structure of living organisms. D’Arcy describes how certain patterns of growth conform to the golden ratio, the Fibonacci sequence, as well as mathematics principles described by Vitruvius, Da Vinci, Dürer, Plato, Pythagoras, Archimedes, and more.

While his work does not reject natural selection, it holds ‘survival of the fittest’ as secondary to the origin of biological form. The shape of any structure is, to a large degree, imposed by what materials are used, and how. A simple analogy would be looking at it in terms of architects and engineers. They cannot create any shape building they want, they are confined by physical limits of the properties of the materials they use. The same is true to any living organism; the limits of what is possible are set by the laws of physics, and there can be no exception.

 

Further Reading:

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Biomimicry in Architecture by Michael Pawlyn

“You could look at nature as being like a catalogue of products, and all of those have benefited from a 3.8 billion year research and development period. And given that level of investment, it makes sense to use it.” – Michael Pawlyn

Michael Pawlyn, one of the leading advocates of biomimicry, describes nature as being a kind of source-book that will help facilitate our transition from the industrial age to the ecological age of mankind. He distinguishes three major aspects of the built environment that benefit from studying biological organisms:

The first being the quantity on resources that use, the second being the type of energy we consume and the third being how effectively we are using the energy that we are consuming.

Exemplary use of materials could often be seen in plants, as they use a minimal amount of material to create relatively large structures with high surface to material ratios. As observed by Julian Vincent, a professor in Biomimetics, “materials are expensive and shape is cheap” as opposed to technology where the inverse is often true.

Plants, and other organisms, are well know to use double curves, ribs, folding, vaulting, inflation, as well as a plethora of other techniques to create forms that demonstrate incredible efficiency.

Fractalized Gates – A journey of Self Discovery

renders01The project is inspired by the interaction between people. It celebrates the female and male union and brings together people that already know each other or are completely strangers. Its interactive, it challenges its visitors, its playful.

It invites people to take part and be interactive with each other. It is called like that as it challenges people to reach the final gate and come together. It acts indeed like a mistletoe. Mysterious and magical. The moment you stand beneath the final gate you stand where all the magic happens. You feel the power and need to kiss the other person. Its design celebrates this union and offers a magical mutation.

It offers a labyrinth of complex, intriguing that seek to nourish individual experiences.

Black rock city seems to be the promised land, the promise of freedom, of self-expression, of immediacy and creativity and community. In a community like Burning Man you can assume the right to approach any random person and have an interesting interaction. You can overly express interest and curiosity. The Desert Mistletoe aims to give people a chance to be more expressed, more playful. Its for those people who want deeper connections, more meaningful interactions, less seriousness and more play.

Hugs and affection are a particularly significant aspect in which to expect more from strangers. We all need love, hugs and kisses are one of the best ways to deliver it. Take the risk to go in for a kiss. Of course some people will be hesitant. The project challenges people to express affection and admiration and relax. Hugs and kisses bring us together. At Burning Man, the endless parade of people flaunting their unusualness brings joy and excitement.

The unusual is both delightful and challenging. People love the unusual, the extraordinary and anything out of our everyday lives and routines. At Burning Man you do not need to sacrifice your wonderful weirdness. On the contrary you are challenged to explore your playful impulses and discover or express your freaky freedom.

The project is inspired specifically by the people of Burning Man.

‘Burners respect the gift of being touched’

 

Inspiration – The Symbol of Sri Yantra

axonometric explanationSymbolism

The Sri Yantra is conceived as a place of spiritual pilgrimage. It is a representation of the cosmos at the macrocosmic level and of the human body at the microcosmic level. It is a Journey. A spiritual journey from the stage of material existence to the union of the individual soul with the divine. The spiritual journey is taken as a pilgrimage in which every step is an ascent to the center. It represents a movement beyond one’s limited existence and every level is nearer to the goal. All the stages are within a gated frame, which is called the ‘earth citadel’ and forms an enclosed space.

The geometry

The symbol consists of nine interlocking triangles, centered around a bindu ( the central point). The five downward pointing triangles represent Shakti; the female principle. The four upright triangles represent Shiva; the male principle. The nine interlocking triangles form 43 small triangles each representing a particular aspect of existence.

 

The Concept – Fractals & Koch Snowflake

The proposed project is inspired by the concept of fractals – a never ending pattern, applied to a specific geometry. They are infinitely complex patterns created by repeating a simple process over and over, creating patterns that are self-similar across different scales. Fractals are images of dynamic systems that are driven by recursion.

The idea is based on the Koch Snowflake, a mathematical curve which has a finite area bounded by an infinitely long line.

For the project a script was created in Grasshopper and different patterns were created based on the triangles extracted from the Sri Yantra symbol.

fractals-experimentsBelow: Acrylic model based on the fractal pattern that was created above

fractals-experiments-model-01The model below is based on the fractal pattern created by

  1. the triangles representing the Female principle
  2. the triangles representing the Male principle

Together they represent, like the Sri Yantra symbol, the union of female and male. A celebration of our Creation.

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Developing the design and the creation of a journey through a structure

The initial idea was to extract some patterns and create something that will look like gates. Gates that could provide a journey to their visitors.

first-attemptFurther development of the gates was undertaken. The final concept consists of 4 gates which intersect with each other in order to provide a journey. There are 4 different designs for each gate. Each gate has a dense pattern in order to create something elegant and ornamental. The pattern is based on the Koch snowflake concept and has been applied to multiple directions. The gates have different heights and dimensions with the last one reaching up to 10m height. This was designed in such a way to provide a climax of the visitor journey at the final gate/stage.

final-gatesThe design is all about a journey. A personal journey with different experiences. A welcoming structure, inviting the visitors to interact with each other. It says a story, it represents a story and it invites you to create one.

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Experiment model in order to understand at what points the gates could intersect. At this point, the gates are connecting only on the top.

This has as a result to have an ’empty’ structure on the sides.

initial-ideasFinal Design Concept

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All the gates are connected with each other not only at the top but also on the sides. To achieve best results and better connections, the 3 gates are duplicated and connected with each other. The second gate will be connected with the third one only at the bottom. The 4rth gate has three sides creating a triangular central space. The gates have been rotated along the 2 other sides allowing for its visitors to enter from different directions. This also creates an enclosed space, like the Sri Yantra symbol.

The proposed installation aims to be part of this beautiful journey of self-discovery. It takes part of expecting more from strangers, while noticing the weirdness of others and encourages everybody to express themselves. With expecting more of strangers it increases the likelihood that the people you meet will become a part of that sometimes elusive network of connections we call community.

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‘Entwine’ – Submission for Burning Man 2016

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INSTALLATION SUBMISSION TO BURNING MAN 2016 – ‘Entwine’

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.

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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.

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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.

Hexagonal Patterned Spacial Definitions

The inspiration for this research came from the Asian artist Ren Ri, who uses bees in order to generate his sculptural  work. He predefines the space for the bees to work with, and allows for a time period for the honeycombs to take shape.Portfolio__Page_06Portfolio__Page_07Portfolio__Page_08Portfolio__Page_09

There are three types of surface division that manage to fill up all the area with prime geometric space – triangular (S3), square (S4) and hexagonal (S6). Other types of surface division, either leave gaps between the prime elements, which need to be filled by secondary shapes, or are confined to irregular shapes.
Research shows that the most efficient way of dividing a surface is through a minimum number of achievable line intersections, or a maximum number of membranes. In either case, the hexagonal division fits the case. This type of organization is a second degree iteration from the triangular division. It is formed by identifying and connecting the triangular cell centroids.
Such as in the case of soap-bubble theory, these cells expand, tending to fill up all the surface area around them, and finally joining through communicating membranes.
From a structural point of view, the best integration is the triangular one, because of the way each element (beam) reacts to the variation of the adjacent elements.
By converting the elemental intersection in the hexagonal division from a single triple intersection to a triple double intersection, the structure would gain sufficient structural resistance. This can be done through two methods – translation or rotation. Translation implies moving the elements away from the initial state in order to open up a triangular gap at the existing intersection. This method results in uneven shapes. In the case of rotation, the elements are adjusted around each middle point until a sufficient structural component is created. It is through rotation that the shape is maintained to a relative hexagonal aspect, due to the unique transformation method.

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Pursuing the opportunity to test the system through a 1:1 scale project, I was offered the chance to design a bar installation for a private event at the Saatchi Gallery. The project has been a success and represents a stage test for the system.Portfolio__Page_36Portfolio__Page_37Portfolio__Page_38Portfolio__Page_39Portfolio__Page_40Portfolio__Page_41Portfolio__Page_42Portfolio__Page_43Portfolio__Page_44Portfolio__Page_45Portfolio__Page_47Portfolio__Page_49Portfolio__Page_46Portfolio__Page_48Portfolio__Page_50Portfolio__Page_51

Moving further, the attempt was to implement dynamic force analysis to the design, through variation of the elemental thickness. The first test was a bridge design. The structure was anchored on 2 sides, and had a span of 5m.  Portfolio__Page_54Portfolio__Page_55

The next testing phase includes domed structures, replicating modular structures and double curved instances.
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Students create installations for global engineering practice’s London office refurbishment

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At the end of a marathon day during which 23 students presented project work to BuroHappold Engineering’s top executives, four students from Diploma Studio 10 (DS10) at the University of Westminster were selected to build temporary installations for the global engineering practice’s soon to be refurbished London offices. The presentations were overseen by their tutors Arthur Mamou-Mani and Toby Burgess, and Neil Billett, Andrew Best, Emma Greenough and James Solly from BuroHappold.

The winners of the competition were:

  • Garis Iu (71 Newman Street window) with The Meander, an 12 meters long flowing  cluster of laser-cut curved origami filtering views on street level towards the reception area.
  • Diana Raican (17 Newman Street window) with The Colliding Cubes,  a dramatic 5 meters wide wall suspended above the street and assembled with friction-based component dissolving through one another, parametrically designed to filter light and views.
  • Joe Leach (17 Newman Street Staircase) with The Falling Leaves, an innovative laser-cut curved truss system assembled around a series of nodes holding a beautiful array of wooden leaves.
  • Charlotte Yates (17 Newman Street separating screen) with The Jitterbuga kinetic installation inspired by Buckminster Fuller and made from punch-pressed aluminium icosahedron opening and closing depending on space requirements.

The projects celebrate 40 years of innovative structural solutions from BuroHappold and the practice’s commitment to supporting education in the fields of architecture, engineering and digital fabrication and will have a lifespan of a year before the next DS10 intake follow the same process and vie for an exhibition space.

We would like to thank David Scott and Edward Lancaster from the University of Westminster’s Fabrication Laboratory for all their support.

Here are images of the winning designs. More news to come on the expected launch date.

The Meander by Garis Iu - DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)
The Meander by Garis Iu – DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)
The Colliding Cubes by Diana Raican - DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)
The Colliding Cubes by Diana Raican – DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)
Jitterbug by Charlotte Yates - DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)
Jitterbug by Charlotte Yates – DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)
Falling Leaves by Joe Leach - DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)
Falling Leaves by Joe Leach – DS10 Univeristy of Westminster for BuroHappold Engineering (led by Arthur Mamou-Mani and Toby Burgess)

The student work will join the permanent installation “Wooden Waves” designed by DS10 tutor Arthur Mamou-Mani. More information on this project may be found on http://mamou-mani.com/BuroHappold.

TheWoodenWaves by Mamou-Mani at 17 and 71 Newman Street.
TheWoodenWaves by Mamou-Mani at 17 and 71 Newman Street.

Burning Man Festival | Bismuth Bivouac

Help us reach our Kickstarter target! http://kck.st/1ESCVFb

Inspired by the geometry from the crystalline growth pattern of the element Bismuth (Bi), the Bismuth Bivouac is a playful pavilion that celebrates the orthogonal geometries that can exist in natural Bismuth crystals to form an intriguing cubic structure, with spiralling disruptions on each face that are governed by the golden ratio. From a distance, the structure appears as a seemingly solid cube, but upon closer inspection, the internal spaces can be explored and utilised.The beautiful iridescent colours of crystal are to be translated into the proposal through coloured LED strip lighting, built into the simple dimensional lumber structure of the pavilion, so at night the Bismuth Bivouac gives has the same visually mesmerizing, colourful effect of the bismuth crystals in nature. The project aims to play with the participants perception of depth and scale in this mirroring structure – from afar, the structure will appear as a dense cube that sits on the playa, but as the participants move towards the structure, they will begin to be able to see through parts of the structure due to the stepped nature of the geometry and holes formed from spiral disruptions. The structure provides sheltered from harsh desert sun, but also provides a plaything for the sun to casts its shadows during the day, and for people to cast their own shadows with their own illuminations at night.

Development

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Construction

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Visualizations

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23rd January 2015 – Interim Portfolio Day

Here we are – we have reached the middle of the academic year at the University of Westminster. Time to assess and appreciate our students portfolios and hard work during a lively “interim cross-marking” with our colleagues. Here are couple examples of the most remarkable portfolios in our Diploma Studio 10. Very excited to start our new brief03 on future cities. We will soon announce the three winners in our studio which will get the opportunity to build installations at the new headquarters of Buro Happold and students will soon post their Burning Man proposals on this blog. Oh and we are also going to our unit trip to Copenhagen next week!! Pictures by Toby Burgess.

Our Studio Space at the University of Westminster
Our Studio Space at the University of Westminster
Sarah Stell's Inhabitable Geometric Transitions
Sarah Stell’s Inhabitable Geometric Transitions
Joe Leach's Flower of Life Curved Playful Truss
Joe Leach’s Flower of Life Curved Playful Truss
Jonathan Leung's Bismuth Bivouac
Jonathan Leung’s Bismuth Bivouac
Aslan Adnan's recusrsive explosion
Aslan Adnan’s recusrsive explosion
Lorna Jackson's Spirohedron Confessional
Lorna Jackson’s Spirohedron Confessional
Maria Vergopoulou's copper sulfate crystals and mirrors
Maria Vergopoulou’s copper sulfate crystals and mirrors

Diana Raican's Interlocking Wooden Fractals Toby Plunket's spatial study of sound

John Konings's Giant Wooden Miura-Ori  Origami
John Konings’s Giant Wooden Miura-Ori Origami