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


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.


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.


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.


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.



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.


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.


In physics, elasticity (from Greek ἐλαστός “ductible”) is the ability of a body to resist a distorting influence or stress and to return to its original size and shape when the stress is removed.


This can be explained looking closer at the components which form the cytoskeleton – the cellular structure – formed of elastic and semi-elastic arrangements of proteins, which are adaptable to the cell’s requirements. Not only do they hold the structural integrity of the cell, but they also also perform functions of communication, transport combined with other “plug-in” proteins, whilst elastically responding to external forces or stimuli.


Elastic bending is used in both natural as well as man-made environments, expanding surfaces and volumes of various deployable structures.


The force responsible for elastic bending can be described in terms of the amount of deformation (strain) resulting from a given stress, a ratio known as Young’s Modulus. Hooke’s Law adds that the force responsible with restoring the initial shape of a bent material is proportional to the amount of stretch.


Using the formulas given by Young’s Modulus and Hooke’s Law, we can determine how much a certain material will bend when a force is applied to it.


Deploying structures using bending is a space and construction time saving method of producing structural elements which mimic the behaviour of natural systems.


After the structure is deployed, equilibrium  of forces is required in order to keep the structure open and usable.

This can either be achieved by combining bending elements with meshes,


or by using the acting forces of bending elements against the reacting forces of other bending elements in both 2D and 3D.


Using these principles of acting forces vs. reacting forces, an elastic module in equilibrium is created, which can be stacked using its geometry to achieve various configurations.



Furthermore, using the same principles, a larger module is created containing groups of elements producing forces acting and reacting against each other, in order to achieve equilibrium.


However, due to the elastic properties of the newly formed module, the structure can bend and morph shape without losing integrity or equilibrium, in order to form various shapes, or respond to or external factors or users requirements, similarly to the cytoskeleton initially studied.



  • Mihai Chiriac

A deployable structure includes an enclosed mechanical linkage capable of transformation between expanded and collapsed configurations while maintaining its shape.

These types of structures have the advantage of creating versatile, modulated spaces, with easy and fast assembly which generate benefits such as adaptability, flexibility and space transformation.

Charles Hoberman pioneered a type of deployable structure based on curved scissor pairs as seen in his Hoberman sphere. The unfolding structure resembles an expanding geodesic sphere which can reach a size up to five times larger than the initial one. It consists of six loop assemblies (or great circles), each made of 60 elements which fold and unfold in a scissor-like motion. Portfolio 2.jpg

Hoberman Sphere by Charles Hoberman

A loop assembly is formed of at least three scissors-pairs, at least two of the pairs comprising two identical rigid angulated strut elements, each having a central and two terminal pivot points with centres which do not lie in a straight line, each strut being pivotally joined to the other of its pair by their central pivot points. The terminal pivot points of each of the scissors-pairs are pivotally joined to the terminal pivot points of the adjacent pair such that both scissors-pairs lie essentially in the same plane.Portfolio 22

Regular curved scissor-pairs in motion

When this loop is folded and unfolded certain critical angles are constant and unchanging. These unchanging angles allow for the overall geometry of structure to remain constant as it expands or collapses.Portfolio 23

Regular and irregular curved scissor-pairs in motion

The above diagrams show a closed loop-assembly of irregular scissors pairs where each scissors-pair is pivotally joined by its two pairs of terminal pivot points to the terminal pivot points of its two adjacent scissors-pairs. This loop-assembly is an approximation of a polygon in the sense that the distances between adjacent central pivot points are equal to the corresponding lengths of the sides of the polygon. Further, the angles between the lines joining adjacent central pivot points with other similarly formed lines in the assembly are equal to the corresponding angles in the polygon.

The beams forming scissor-pairs can be of almost any shape, providing that the three connection points form a triangle. The angle of the apex would dictate the number of scissor-pairs that can be linked together to form a closed loop.Portfolio 28.jpg

Scissor-pairs of varying morphologies

My physical experiments started with materials that would allow a degree of bending and torsion in order to test the limits of the system. Using polypropylene for the angular beams and metal screws for the joints, I created these playful models that bend as they expand and contract.Portfolio 214.jpg

Later I started using MDF for the beams as well as joints and noticed that a degree of bending was present in the expanded state of the larger circle.Portfolio 215.jpg

After using curved scissor pairs of the same angle to form closed linkages, I decided to combine two types of scissors and vary the proportion between the elements to achieve a loop which would offer the highest ratio between the expanded and contracted state.Portfolio 216.jpg

900 curved scissors loops

Portfolio 217.jpg

900 curved scissors with linear scissors loops

The above diagrams show a combination of 900 curved scissors with linear (1800) scissors to form rectangles that expand and contract. The length of the 900 beam was gradually increased  and by measuring the diagonals  of the most expanded and most contracted forms, I obtained the following ratios for the three rectangles:

R1 = 0.87

R2 = 0.67

R3 = 0.64

By keeping the curved scissor with the best ratio, I created three more rectangles, this time by varying the length of the linear beam. The following ratios were obtained:

R1 = 0.64

R2 = 0.59

R3 = 0.67Portfolio 218.jpg

900 curved scissors with linear scissors loops

I then took the linkage with the best ratio of 0.59 and rotated it 900 to form a cube which expands and contracts.Portfolio 219.jpgPortfolio 220.jpg

Combined linkage cubes

The change of state from open to closed is visually attractive and could have the potential of creating spaces that are transitional.Portfolio 223If more linear scissors are placed between the 900 scissors, a better contraction ratio is obtained.Portfolio 222

Combined linkage cubes with two linear scissors


A hyperbolic paraboloid is an infinite surface in three dimensions with both hyperbolic and parabolic cross-sections. A playful and intuitive way of visualising and parameterising this concept can be achieved via the implementation of origami folding techniques.

The images below show how to create and tile a basic hyperbolic parabola with origami. Once fully formed, the result is flexible and malleable along its two axes.

This playfulness only increases as additional sides are added to the initial parametric shape. This, in turn directly correlates with the increase of the number of axes along which the paraboloid is able to form. For example, a hexagonal initial sheet with six sides, will also have six axes.

Octagonal and decagonal paraboloids are particularly enjoyable to create and play with.

When deconstructed, a decagonal paraboloid is comprised entirely of a series of ever diminishing, 72 degree trapezoids, that when tiled next to one another, come together to comprise individual components of one, larger trapezoid, or wedge. When tiled and secured along its long edge, a decagon is formed, and once folded, a hyperbolic paraboloid is possible.

It is through research and testing with digital fabrication how best to form and therefore scale this wedge component that a successful, parametric and human scale origami form might be accomplished.

The images below are further tests in a failed attempt at forming a larger, scalable hexagonal paraboloid. Previously, flexible material such as paper and polypropylene had been used to successfully form basic, octagonal and decagonal paraboloids. However, in this test, 4mm ply was used, and has proved to be most inflexible. Thusly, it is unable to bend universally along each of the six axes. Further testing is required.


Auxetics are materials that have a negative Poisson’s Ratio. When stretched they become thicker perpendicular to the applied force, from our own experiences when a material is stretched we expect the material to not only become longer but also thinner. Auxetics behave in a different way because of there internal structure.

Poisson’s ratio (v) of a material is the ratio of the lateral contractile strain to the longitudinal tensile strain for materials undergoing tension in the longitudinal direction. It shows how much a material becomes thinner when stretched, therefore most materials have a positive Poisson’s ratio.


The images below show modules of four structures that have Auxetic behavior. The images show the change in state of the structure as they undergo tension in the longitudinal direction.























This video shows an interesting application of an auxetic structure with inflatables by Fergal Coulter.





Get every new post delivered to your Inbox.

Join 4,910 other followers