Cortex Structures
Christoph Klemmt, Orproject
Rajat Sodhi, Orproject
Maria Villafane, Atelier 1
1: INTRODUCTION
1.1: Cortex Morphologies
Cortex morphologies are key biological structural systems that are found in almost every living organism at
different scales. They form barks and roots of topiaries, the veins of leaves, cardiovascular and respiratory
systems, neural networks or the cerebral cortex. These systems perform both as circulation and structure
and therefore their morphologies can be deployed as architectural strategies at different scales.
This paper analyses two forms of cortex morphologies tests their architectural potential using digital
simulation techniques: Venation and vascularisation systems, which form the structure of trees, veins and
vascular morphologies, and the root structures of Ficus spp., that form linear directional systems.
2: VENATION & VASCULARISATION SYSTEMS
2.1: The Network Diagram and its Cortex Surface
Cortex morphologies can be abstracted as a venation network surrounded by an epidermis which can be
studied at three scales.
On a large scale, the venation system can be thought of as a network of centre-lines. This network diagram
of centre lines can be linear, or it can form open or closed branching patterns. At a medium scale, the
epidermis becomes visible, forming a cortex morphology around the network of centre-lines. These
surfaces can have varying distances from the centre lines, and around the nodes they often form minimal
surface geometries. On a small scale, the thickness of the cortex surface becomes visible, thereby turning
the surface into a volume with varying thickness.
Cortex morphologies achieve two tasks - they form a circulation system that simultaneously provides
structural support. The network diagram of the centre-lines, cortex surface and the volume defined by the
thickness of this surface thus need to perform to both circulatory and structural requirements.
2.2: Linear venation & its single surface
Or1
The research into architectural applications of cortex morphologies started with the development of a cortex
in tension around a single straight line as the venation diagram. The installation Or1 was designed and built,
by Orproject in collaboration with Scenario Architecture, for the Milan International Furniture Fair 2008 as a
vortex shaped surface that reacts to sunlight.
Or1 uses polygonal segments made up of photochromic polymer panels that react to the ultra-violet
component of sunlight, mapping the position and intensity of solar rays. In sunlight the panels turn blue,
flooding the space below with different hues of light that are indicators of weather and daylight. When in
shade, the segments become translucent white, at night transforming into an atmospheric space for events
and gatherings.
The shape of Or1 was designed to cover a courtyard and to turn into a column as it touches the floor in the
centre. The cortex circles around a beam which points towards the sun and varies in thickness around this
straight centre line. The tensile surface is panelised and the individual segments are suspended off the
edge of the courtyard.
2.2: Auto-merging Surfaces
Or2
The cortex surface of a topiary structure is defined by a branching network of centre-lines, where the cortex
starts as a bark and gradually diverges into smaller branches till it becomes thinner around the surface of
the leaves. On the contrary, the cortex of Or1 becomes larger the further it ascends along its centre line and
turns into an almost horizontal surface.
In order to achieve a more self-supporting installation, Or2 was developed as a branching network, inspired
by the internal geometries of sea squirts. The trunk gains compressive strength by the bending of the
individual segments around the centre-lines, while the cortex branches out and folds back onto itself at the
top to form an auto-merging minimal surface.
Or2 was designed for the Italian Cultural Institute in Belgrave Square, London and was exhibited as part of
the London Festival of Architecture 2010.
2.3: L-Systems versus Venation and Vascularisation Systems
The Lindenmayer Systems or L-Systems are probably the most famously used for modelling tree-similar
branching networks. In its simplest form a branch splits up at its end into two branches at defined angles
and lengths, and this process is carried out recursively. The variation in the angles and lengths allows it to
produce a range of branching conditions.
While the branching networks produced using L-systems may look similar to trees, they are unable to
emulate the natural venation and vascularisation networks as they lack the logic for the direction of their
growth. In nature, topiaries grow towards sunlight to achieve a maximum exposure for each leaf, employing
the venation in leaves to create a connection system to auxin sources across its surface. Similarly
vascularisation aims to create a network that is able to reach each cell within the body.
Simulation algorithms have been developed to emulate directional growth of branching networks that
produce two distinct types of centre-line diagrams: open venation systems and closed venation systems.
The principle of these algorithms is to generate a three dimensional centre-line branching diagram that
grows towards a set of evenly or unevenly distributed aims, such as auxin sources, placed within a target
surface or volume. The distribution of these points can be controlled to stay fixed or change conditionally
during the evaluation of the algorithm based on how close the branching diagram has reached the target
points, thereby achieving a mechanism to control the directional growth dynamically.
2.4: Open Venation Systems
Pera
Pera is a permanent installation for the entertainment room of a private client in Mumbai, India. The
installation was designed to cover two concrete columns in the space and integrate with the lighting layout.
The branching centre-line network for the two trees was set up using the centre of the two columns as start
points and fixed target points were distributed in the ceiling to avoid the lights. By merging the cortex with
itself, the open venation algorithm resulted in a single surface connecting the branching networks from the
two start points within a defined range along the ceiling.
The tensile structure is manufactured as a network of triangulated stainless steel pieces connected by loose
rings. Consequently, a small irregularity or distortion of the surface at any point would result in a distortion
along the entire length of the surface which required special considerations from the structural engineers.
Pera : Structural Engineering Considerations, Atelier 1
In the dynamic relaxation process, a structure is modelled as a set of nodes, which, in this case, are at the
vertices of each triangular component of the mesh. A fictional mass is assigned to each node, and each
node is connected to the others immediately adjacent to it by fictional, weightless elastic springs. Each
spring obeys some variant of Hooke’s law, in that it has a rest length and, if it is stretched beyond that rest
length, it applies a force along its axis which acts in the direction which would return it to its rest length. The
springs do not provide any resistance to compression.
Gravity is applied to the system, so that a force is exerted on each node in proportion to its mass and, as a
result, each node begins to move. The forces on each node are then made up of: the forces in the springs,
the gravitational forces and the inertial forces resulting from the movement of each mass. Since, by
Newton’s second law, the inertial force is proportional to acceleration, balancing these forces requires the
solution of a differential equation. To do this, the solver uses standard numerical methods for solving
ordinary differential equations.
If the rest length of the springs is set to be equal to their original length, then the dynamic relaxation method
is similar to a finite element simulation of the structure. The difference is that the iteration in the dynamic
relaxation process allows for geometric nonlinearity, as the change in shape of the structure changes the
distribution of forces, and material nonlinearity, as the structure is able to resist tensile forces, but not
compressive. Finite element analysis, in contrast, is a purely linear process.
The original form of the structure was subjected to the dynamic relaxation process with the rest length of the
springs set to be equal to their original length. It was found that the structure sagged and the nodes near
the base folded in on one another, the springs in that region providing no resistance to the compressive
loads applied to them. A similar response could therefore be expected were the real structure constructed
with this geometry.
By taking the original form, and adjusting the rest length of all the springs to be a proportion, less than 1, of
the distance between the respective nodes, the structure could be caused to dynamically contract and find
a relaxed form in which all of the springs are in tension. It was found that if the proportional rest length used
was the same over the entire surface, the resulting surface clashed with the columns. To avoid it doing so
required the diameter of the bottom rings to be enlarged, resulting in an undesired distortion of the original
form.
By dividing the structure into sections, and applying a different proportional rest length to the springs in
each section, a relaxed surface could be found which was close to the original form, in which all of the
springs between nodes were in tension and which did not clash with the columns. This relaxed surface
could then be used to form a new initial shape for the structure, which could be tested for the realistic
conditions, in which the rest length of each spring is equal to the initial distance between the nodes it
connects. This test showed that the revised form would hang satisfactorily, with tensile forces everywhere in
the surface.
Mayfair Arcade
The proposal for Mayfair Arcade in London uses a similar growth model to that of Pera to design a glass
canopy. Here the start points for the venation simulation were the centres of five larger public open areas
along the shopping passage.
Using glass in tension, Mayfair Arcade has been designed as a hanging structure without the support of a
traditional steel frame structure. The specialist glazing engineer proposed to use a shear bolt connection at
each node point between the glass panels to create a semi water proof canopy.
2.5: Closed Venation and Vascularisation Systems
Open venation and vascularisation systems were developed by adjusting the algorithm to form closed loops
within the branching centre-line network diagram. In nature, these systems are found in leaves where more
than one branch can grow towards the same auxin source, thereby merging the ends of two separate
branches to form a loop.
Architecturally, the resulting morphologies allow applications for closed network diagrams that can be
developed directionally. They have the structural potential to form compression based systems as the
cross-connections between neighbouring branches allows for the possibility to create vertically connected
network diagrams.
Lianhua
Similar to the structures of Nympaea sp., a closed venation system was developed for the design of the roof
structure of Lianhua. The centre-line network develops from multiple load bearing nodes and grows from
them to form the structural network of the roof.
In the digital simulation, the branches grow towards a distribution of loads on a flat roof surface instead of
auxin sources. The thickness of each branch and trunk is influenced by the loads that it needs to support,
similar to the venation of a leaf where the diameter of the branches depend on the auxin supply capacity.
3: ROOT GROWTH SYSTEMS
3.1: Ficus Root Growth
Cortex morphologies of aerial roots of Ficus spp. have the distinct anatomical characteristic of fusion where, upon contact, two aerial roots merge to form a single root. This merging of the cortices of two roots
leads to a re-adjustment of both cortices and the formation of a new cortex for a single root. Unlike the
diverging, tree-like logic of the venation model, the root growth model examines the growth and interaction
between individual roots.
Additionally, like the Banyan trees which engulf the temple of Ta Prohm in Cambodia, a challenge for the
growth model was to test how a directional growth model can negotiate a complex three dimensional
volume. The algorithm employs gravity as a parameter to directionally guide the centre-line of each branch
and uses a pre-defined volume that the new branches must avoid. Iteratively, it searches for proximity
between the different branches and when two branches intersect, the centre-line network merges and a
gravity induced relaxation is applied to the whole network.
There are three morphological differences between the root growth algorithm and venation simulation - the
directional growth of the roots, relaxation of the network diagram and negotiations within a specified
volume. The root growth systems thus lend themselves as circulation diagrams, vertical structures and
systems that can negotiate existing site conditions.
Selfridges Glamroots
The permanent light installation Glamroots was designed for Selfridges department stores. It is a group of
root-like branches that grow from the ceiling to the floor of the central atrium and on their way downwards
maintain clear circulation space on the escalators.
The cortex of Glamroots is built up of segmented rhombi, made from glass with a dichroic film. Solar cells
on the roof of the building collect energy, which gets distributed into the atrium through the roots and
emitted by concealed LED lights on the inside. Where the roots of a Banyan tree transport water and
nutrients, Glamroots transport energy and light.
3.2: Root Networks as Structural Systems
The second function of the aerial roots of Ficus spp. is to structurally support the branches of the tree.
Consequently the roots have a tendency to grow downwards vertically, which makes their morphologies
suitable as a structural system for high rise construction.
A Skyscraper That Grows Like A Tree
This has been tested with A Skyscraper That Grows Like A Tree. The proposal utilises the growth simulation
to form the exoskeletal structure of the tower that defines the extent of the building skin and floor plates. The
conglomeration of the roots result in a multi-layered façade structure which, based on its location and
orientation, is used to form single and double skin systems, separate rooms within the façade structure, and
multi height atriums to control the climatic performance of the building.
3.3: Epidermis Edodermis
A special condition which frequently occurs within the root systems on Banyan trees, but rarely in venation
patterns, is the formation of very dense networks, around which the cortex morphology results in complex
minimal surfaces.
The cortex around the centre lines grows to a thickness that is larger than the remaining diameter of the
openings in-between, as a result the centre lines of the holes may appear as the driving factors behind the
formation of the surface, similar to the morphologies formed from the auto-merging surfaces. When the
complex inner parts of the cortex are inspected in isolation, the inside-outside relationships of the surface
become unclear. The surface becomes an in-between, the separator between two equal sides.
Shantiniketan
This effect of the dense pattern has been utilised in the permanent installation Shantiniketan, inside the
courtyard of a multi storey private residence in New Delhi, India. The courtyard acts as a source of light for
the adjacent rooms, but due to their privacy requirements, the client required a structure to block view but
not light.
The cortex surface of a dense root growth simulation was applied here to form a modulating separation
between the different spaces, keeping an open connection across the courtyard from the top of the skylight
to the ground. The surface has been designed to be built using translucent glass panels that diffuse the
light yet block direct views into the rooms.
The continuous surface forms a separation between its two sides, but it is impossible to define which side of
the surface forms the inside or the outside of the enclosing volume.
CONCLUSIONS
Cortex morphologies as found in nature fulfil both transportation and structural requirements, two of the
main requirements of buildings and architecture. Their application in architectural design has been tested in
projects at varying scales, by digitally simulating their development and behaviour.
The environmental and inherent constraints that drive their development can be translated into different
architectural strategies: Cortex structures can be applied architecturally as distribution systems to efficiently
control and diffuse light, create load paths and provide for vertical circulation and structure, resulting in
complex yet functional shapes.
Structurally the morphologies were applicable as tensile surfaces, as compression based shapes, and as
column networks. Either the centre line diagrams or the cortex surfaces around them could be used
structurally and the natural transportation routes could be translated into load paths.
Due to their versatile behaviour and their inherent connection of form, function and structure, cortex
surfaces can comprise complex, highly performative applications in biomimetic architectural design. Many
of their capacities are yet to be investigated further, such as their application in master planning, in human
transport organisation, and their possibility to evolve over time.
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