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.

TriNect

The aim is to generate an architectural response through a playful loop between the digital and the physical. Digital tools such as Rhino and Grasshopper are used  in order to carry out analysis and generate buildable three-dimensional forms. Interplay between physical fabrication and digital experiments enable to become an inventor of a system. Here is mine.

TriNect is a flexible system of triangular elements with slots at their vertices. Elements interlock with one another creating different space filling polyhedra. The system can be applied in various scales and adapted for different needs.

TriNect

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Auxetic Assemble

As the Maker World develops, we want to have a greater impact on our environment, the spaces we live in. Auxetic Assemble gives you a chance to build your own furniture and have a input in your product. Auxetic Assemble gives you the chance to buy either the cut parts for the product or the instructions and CNC cutting files to then source your own material, cut your own product and assemble your work. The future of this adaptable design system allows the product to be fitted and designed to your require space.

 

The Pavilion

I have set up a Kickstarter Campaign in order to Fund a Pavilion in Hackney. The Pavilion is the next step in the journey to developing this system to its future potential. The construction process used for the plywood shelves will be developed at the larger scale to develop a pavilion to display the process of constructing the shelves and to exhibit the product. The Pavilion walls will become the seating, shelving and tables for the space. This is a chance to explore the system at a larger scale in order for further development for future of housing, an adaptable system that can be applied to a unique space and engages everyone as its workforce to build it.

Kickstarter Page

 

The Products

 

The design system has been developed into shelving product to sell as rewards, both in cardboard and plywood.

Table Top Plywood Shelves

Table Top Cardboard Shelves

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SONY DSC

 

Follow the links to the Kickstarter Page to help this project be realized, Click on any image for the Kickstarter page link. Thank you.

 

‘Entwine’ – Submission for Burning Man 2016

Final Day Render

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.

Thousand Line Construction

Thousand Line Construction :

Hamish Macpherson

A spatial exploration into the interplay of materials, construction techniques, and delicate and precise design.

Inspired by Hanakago; the craft of Japanese Bamboo basketry, to celebrate the western discovery of tea and its associated culture during the renaissance.

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Bending Lattice System

My initial studies stemmed from researching into Stellation. This, in simple terms, is the process of extending  polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions, to form a new figure. Through researching the application of this process, I came across the sculptures created by George Hart, as he has experimented with stellated geometries to which are subdivided to create mathematical interweaving structures.Stellation 1

My Research into the method and calculations of George Hart’s Mathematical Sculpture’s focused on the sculpture ‘Frabjous’. Through rigorous testing and model making I have understood the rules behind the complex form. This is based on the form of a stellated icosahedron, whose shape is contained within a dodecahedron.grey card model

Lines are drawn from one point, to a point mirrored at one edge of the face of the dodecahedron form – as shown in the diagram. This creates intersecting lines at each face as you can see from the diagrams below. Each dividing line has two intersection points, with symmetry at the center of the line. The sculpture aims to avoid the intersections of these lines by introducing a sine curve with the domain 0 to 2*pi. As you can see, each component is exactly the same – for this model, 30 components are used.

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`To simplify the construction of the sculpture, I extracted a build-able section which uses ten components in total. Two of these sections are then weaved together and joined up by a further ten single components to form the entire sculpture.Diagram Sequence of Researched SculptureOne Component ImageryGeometry 2

Following this research, I extracted the concept of avoiding the intersection and subdivided a cube with lines from each corner of the cube. These lines were then weaved around eachother using a sine curve with a domain of 0 to pi. I then mirrored the curves and rotated them to create an intertwining form.Avoiding Self Intersection 2

Another test was created with the same process, however subdividing a cube using the midpoint of each face. – This creates an octahedral geometry.Avoiding Self Intersection octahedron

Using this interweaving geometry, I have created different three dimensional arrays to create a spatial form. The concept of avoiding intersections naturally cause a structure to fail. To form a structurally efficient version of this geometry, I introduced the idea of a reciprocal structure, and allowed the beams to self support by resting on eachother. This did not create a structure strong enough to stand on, however through adding a cube whose dimensions are equal to the width of the beams, the structure became very strong.

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Testing the component at a small scale required the design of a joint which allowed me to assemble these components together through interlocking elements. Each beam element slots into the joint; When two joints and two beams are connected together the curves naturally stay in place due to the angle cut into the joint. Three of these connected elements together form the component.

Diagraming the Joint

As mentioned previously, avoiding intersections create inefficient structures – For this small scale experimentation, the concept of Tensegrity was implemented. Tensegrity is a structural principle based on using isolated compression components within a net of continuous tension, allowing the compression members to not need to touch each other. This model was constructed using 1.5mm plywood which has been laser cut; the modularity of the system ensures minimal material wastage.

Construction Sequence of ModelModel Photographs

The three dimensional array of this geometry creates many interesting shapes and patterns when viewed from different angles – this is visible in the following video:

 

 

 

 

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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