Attractors in Architecture: Attractor-based optimization and design solutions for dynamical systems in architecture

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# Attractors in Architecture
Attractor-based optimization
and
design solutions for dynamical systems in architecture
2nd edtion
Judyta Cichocka, Anastasia Globa

This book produced and published digitally for public use. No part of this book may be reproduced in any manner
whatsoever without permission from the author, except in the context of reviews.
© Code of Space. All rights reserved.
ISBN: 978-83-943176-2-1
2nd edition, September 2016, Wellington, New Zealand
# Attractors in Architecture
Attractor-based optimization
and
design solutions for dynamical systems in architecture
2nd edtion
Judyta Cichocka, Anastasia Globa
ISBN 978-83-943176-2-1
9 788394 317621

Content
1. Intoduction .....................................................................................................................1
2. Dynamical systems..........................................................................................................2
2.1 Movement................................................................................................................3
2.2 Extrusion...................................................................................................................5
2.3 Scaling......................................................................................................................7
2.4 Rotation....................................................................................................................9
2.5 Rotation 3D.............................................................................................................11
2.6 Condition / Reduction of elements..........................................................................13
2.7 Grid Deformation 2D..............................................................................................15
2.8 Grid Deformation 3D...............................................................................................17
3. Attractor-based design strategies in architecture..........................................................19
3.1 Modelling landscape and urban layout....................................................................20
3.2 Modelling the general shape..................................................................................21
3.3 Strategy 1 - optimization for views: Multiple Point Attractor..................................23
3.4 Strategy 2 - optimization for sun path: Multiple Line Attractor...............................25
3.5 Combining strategies..............................................................................................27
4. Art in Structure Pavilion.................................................................................................28
4.1 Competition Entry...................................................................................................28
4.2 Technical drawings and use of the point attractor..................................................29
5. Conclusion.....................................................................................................................31

#1 Introduction
”A violent order is disorder; and a great disorder is an order. These two things are one.”
Wallace Stevens, Connoisseur of Chaos, 1942
The evolution of something over time is the idea of a dynamical system. A dynamical system is
simply a model describing the temporal evolution of a system. The model of growth of a bacteria popula-
tion (Figure 1) or undamped pendulum that continues oscillating forever might be the examples of the
dynamical systems.
Attractors are portions or subsets of the phase space of a dynamical system. We can easily imagine that
one individual of the bacteria population (subset of the phase space) is more “attractive” and around it
the population growth is higher than around the others. In case of the undamped pendulum, we can think
of a huge ball like Earth underneath the oscillating pendulum, that by its gravity force changes the oscilla-
tion over time.
In terms of this handbook attractors are understood as simple geometric subsets of three-dimensional
space, such as:
- a point
 -anitesetofpoints
- a curve
- a surface (a manifold)
Inordertocreatearchitecturaldynamicalsystemwerstlyneedtodecidewhatisthis“something”that
will evolve over time (e.g. panels, openings, colour) and secondly describe the rules that specify how that
“something”evolvesovertime(e.g.rotation,scaling,deforming).Inthenextsectionsyouwillndafew
examples of dynamical systems in architecture followed by the architectural case study of the attractor-
based static optimization.
# 1
Figure 1. Dynamical system: the model of growth of a bacteria population.
source: http://mathinsight.org/dynamical_system_idea#statespace

# 3
2.1 Movement
Architecture. Responsive / Interactive structures
There can be a large number of interpretations (applications) of the idea of movement in architecture.
Movement can be used as a design approach for the form-making process. For example, by positioning
(moving) the elements in 3D space depending on certain criteria, such as the proximity to the surround-
ing buildings, sun path, wind direction etc. In this case, the nal design output can be static, whereas the
‘movement of elements’ approach can be an integral part of the form-making process. The other way to
employ the idea of movent in architecture is to develop responsive / interactive structures. This concept
is illustrated by the ‘HygroScope – Meteorosensitive Morphology‘ (Centre Pompidou, Place Georges
Pompidou, F-75004 Paris) project by Achim Menges Architekt et al. ‘The project explores a novel mode of
responsive architecture based on the combination of material inherent behaviour and computational mor-
phogenesis. The dimensional instability of wood in relation to moisture content is employed to construct
a climate responsive architectural morphology.’
(http://www.achimmenges.net/?p=5083).
# 3
2.1 Movement of the elements in the system
Exercise Objective: To move elements along the ‘Z’ vector depending on their proximity to
the attractor point.
The rst step is to create a grid of hexagons (which serves as a base for the ‘dynamic system’) and by
creating a point running along the curve - (which serves as an ‘attractor’). The second step is to measure
the distance between the center of each polygon and the attractor point. These distance values are used
to inform the values for the movement of polygons in space. In theory the elements of the system can be
moved in any direction. In this particular exercise the polygons are being moved up, (along the ‘Z‘ vector).
To get a better control over the behaviour of the system, the distance values are being ‘remapped‘ into a
new numeric domain. This gives an opportunity to set the minimum and maximum movement values. For
example to set the minimum movement as 0.1 mm (start of the domain) and the maximum movement
value as 100 mm (end of the domain). ‘Remapping’ allows to easily reverse the effect of the attractor on
the movement values. This can achieved by swapping the start of the domain to a larger number and the
end of the domain to a smaller number.
#4
Figure 1. HygroScope – Meteorosensitive Morphology‘ (Centre Pompidou) by Achim Menges Architekt
Figure 2. Moving elements along the ‘Z’ vector

# 4
2.1 Movement
Architecture. Responsive / Interactive structures
There can be a large number of interpretations (applications) of the idea of movement in architecture.
Movement can be used as a design approach for the form-making process. For example, by positioning
(moving) the elements in 3D space depending on certain criteria, such as the proximity to the surround-
ing buildings, sun path, wind direction etc. In this case, the nal design output can be static, whereas the
‘movement of elements’ approach can be an integral part of the form-making process. The other way to
employ the idea of movent in architecture is to develop responsive / interactive structures. This concept
is illustrated by the ‘HygroScope – Meteorosensitive Morphology‘ (Centre Pompidou, Place Georges
Pompidou, F-75004 Paris) project by Achim Menges Architekt et al. ‘The project explores a novel mode of
responsive architecture based on the combination of material inherent behaviour and computational mor-
phogenesis. The dimensional instability of wood in relation to moisture content is employed to construct
a climate responsive architectural morphology.’
(http://www.achimmenges.net/?p=5083).
# 3
2.1 Movement of the elements in the system
Exercise Objective: To move elements along the ‘Z’ vector depending on their proximity to
the attractor point.
The rst step is to create a grid of hexagons (which serves as a base for the ‘dynamic system’) and by
creating a point running along the curve - (which serves as an ‘attractor’). The second step is to measure
the distance between the center of each polygon and the attractor point. These distance values are used
to inform the values for the movement of polygons in space. In theory the elements of the system can be
moved in any direction. In this particular exercise the polygons are being moved up, (along the ‘Z‘ vector).
To get a better control over the behaviour of the system, the distance values are being ‘remapped‘ into a
new numeric domain. This gives an opportunity to set the minimum and maximum movement values. For
example to set the minimum movement as 0.1 mm (start of the domain) and the maximum movement
value as 100 mm (end of the domain). ‘Remapping’ allows to easily reverse the effect of the attractor on
the movement values. This can achieved by swapping the start of the domain to a larger number and the
end of the domain to a smaller number.
#4
Figure 1. HygroScope – Meteorosensitive Morphology‘ (Centre Pompidou) by Achim Menges Architekt
Figure 2. Moving elements along the ‘Z’ vector

# 5
2.2 Extrusion
Architecture. Extrusion and deformation as a form-making strategy.
Attractors can inuence various aspects of elements’ behaviour in the dynamic systems. Alongside with
the movement of elements it can also inform the rotation, scaling, deformation or extrusion values.
The application of the ‘extrusion‘ idea can be illustrated using the ViscoPlasty project, designed by Alex-
andra Singer-Bieder, Soa Bennani and Agathe Michel (the nalist of the international TEX-FAB Plasticity
competition, ACADIA 2014, Los Angeles). Designers used small diameter straws and varied the length of
the tubes.
The Viscoplasty prototype shows exactly what the fabrication process should be for an architectural
scale installation. Using digital fabrication tool (CNC milling machine and lasercut), the mold is the base
of the prototype and enable a perfect control of the assembling process by giving the shape the robot
has to follow to melt the topographic surface.
<http://www.straw-k.com/viscoplasty2/>.
# 5
2.2 Extrusion
Exercise Objective: To extrude elements along the ‘Z’ vector depending on their proximity to
the attractor point.
This ‘Extrusion‘ exercise uses the same hexagonal grid and the attractor point set-up as the previous
‘Movement‘ exercise. To allow a better control of how the dynamic system responds to the attractor
location the distance values are being manipulated by a numeric mapping function (‘Graph Mapper‘). The
use of this function provides an opportunity to establish a nonlinear relationship between the position of
the attractor point and the extrusion value of each polygon.
# 6
Figure 3. ViscoPlasty project, by Alexandra Singer-Bieder, Soa Bennani and Agathe Michel
Figure 4. Extruding the polygons based on the proximity to the attractor point

# 6
2.2 Extrusion
Architecture. Extrusion and deformation as a form-making strategy.
Attractors can inuence various aspects of elements’ behaviour in the dynamic systems. Alongside with
the movement of elements it can also inform the rotation, scaling, deformation or extrusion values.
The application of the ‘extrusion‘ idea can be illustrated using the ViscoPlasty project, designed by Alex-
andra Singer-Bieder, Soa Bennani and Agathe Michel (the nalist of the international TEX-FAB Plasticity
competition, ACADIA 2014, Los Angeles). Designers used small diameter straws and varied the length of
the tubes.
The Viscoplasty prototype shows exactly what the fabrication process should be for an architectural
scale installation. Using digital fabrication tool (CNC milling machine and lasercut), the mold is the base
of the prototype and enable a perfect control of the assembling process by giving the shape the robot
has to follow to melt the topographic surface.
<http://www.straw-k.com/viscoplasty2/>.
# 5
2.2 Extrusion
Exercise Objective: To extrude elements along the ‘Z’ vector depending on their proximity to
the attractor point.
This ‘Extrusion‘ exercise uses the same hexagonal grid and the attractor point set-up as the previous
‘Movement‘ exercise. To allow a better control of how the dynamic system responds to the attractor
location the distance values are being manipulated by a numeric mapping function (‘Graph Mapper‘). The
use of this function provides an opportunity to establish a nonlinear relationship between the position of
the attractor point and the extrusion value of each polygon.
# 6
Figure 3. ViscoPlasty project, by Alexandra Singer-Bieder, Soa Bennani and Agathe Michel
Figure 4. Extruding the polygons based on the proximity to the attractor point

#7
2.3 Scaling
Architecture. Scaling of elements in the system.
An architectural example of the application of the ‘scaling‘ design strategy is a facade of the De Young
Museum in San Francisco, USA (by Herzog & de Meuron, Basel (Planning), Fong & Chan Architects
(Implementation)). To structure the impressive façade, thousands of copper sheets were embossed and
perforated with individual patterns so that the modern architecture would blend into the natural surround-
ings of the park landscape as much as possible <http://www.kme.com/en/deyoungmuseum>.
# 7
2.3 Changing size of the elements in the system
Exercise Objective: To scale elements depending on their proximity to the attractor point.
The ‘Scaling‘ exercise uses the same grid and attractor set-up as the ‘Movement‘ exercise 2.1. The
panels (hexagons) are scaled around their centers (starting point of scaling). The scaling domain is set
between 0 and 1, to avoid the overlapping of scaled polygons.
To further illustrate the possibilities of the dynamic nonlinear response of the attractor based systems the
sine (‘Sin‘) function is applied to compute the sine of the distance values (see the bottom image of Figure
6).
# 8
Figure 6. Scaling elements based on their proximity to the attractor point
Figure 5. Facade of De Young Museum in San Francisco, USA

# 8
2.3 Scaling
Architecture. Scaling of elements in the system.
An architectural example of the application of the ‘scaling‘ design strategy is a facade of the De Young
Museum in San Francisco, USA (by Herzog & de Meuron, Basel (Planning), Fong & Chan Architects
(Implementation)). To structure the impressive façade, thousands of copper sheets were embossed and
perforated with individual patterns so that the modern architecture would blend into the natural surround-
ings of the park landscape as much as possible <http://www.kme.com/en/deyoungmuseum>.
# 7
2.3 Changing size of the elements in the system
Exercise Objective: To scale elements depending on their proximity to the attractor point.
The ‘Scaling‘ exercise uses the same grid and attractor set-up as the ‘Movement‘ exercise 2.1. The
panels (hexagons) are scaled around their centers (starting point of scaling). The scaling domain is set
between 0 and 1, to avoid the overlapping of scaled polygons.
To further illustrate the possibilities of the dynamic nonlinear response of the attractor based systems the
sine (‘Sin‘) function is applied to compute the sine of the distance values (see the bottom image of Figure
6).
# 8
Figure 6. Scaling elements based on their proximity to the attractor point
Figure 5. Facade of De Young Museum in San Francisco, USA

2.4 Rotation of elements in a plane
Exercise Objective: To rotate elements depending on their proximity to the attractor point.
This exercise illustrates the rotation of elements ‘in a plane‘ (Rotate objects in a plane). For example, ro-
tating panels vertically in a ‘XZ‘ plane or rotating panels horizontally in a ‘XY‘ plane. Note that the default
rotation units (angle ‘A‘) in Grasshopper are Radians, but they can be easily switched to Degrees (right
click on the ‘A‘ input of the ‘Rotate‘ component and choose Degrees).
# 10 # 9
Figure 8. Rotation of elements in a plane
2.4 Rotation
Architecture. Rotation of elements in the system.
In architecture one the examples for the ‘Rotation’ form-making approach is the facade of the Eskenazi
Hospital in Indianapolis, IN - Completed 2014, designed by Rob Ley. A eld of 7,000 angled metal panels
in conjunction with an articulated east/west colour strategy creates a dynamic façade system that offers
observers a unique visual experience depending on their vantage point and the pace at which they are
moving through the site. In this way, pedestrians and slow moving vehicles within close proximity to the
hospital will experience a noticeable, dappled shift in colour and transparency as they move across the
hospital grounds <http://rob-ley.com/May-September >.
Figure 7. Eskenazi Hospital in Indianapolis, 2014, by Rob Ley
# 9

#10
2.4 Rotation of elements in a plane
Exercise Objective: To rotate elements depending on their proximity to the attractor point.
This exercise illustrates the rotation of elements ‘in a plane‘ (Rotate objects in a plane). For example, ro-
tating panels vertically in a ‘XZ‘ plane or rotating panels horizontally in a ‘XY‘ plane. Note that the default
rotation units (angle ‘A‘) in Grasshopper are Radians, but they can be easily switched to Degrees (right
click on the ‘A‘ input of the ‘Rotate‘ component and choose Degrees).
# 10
# 9
Figure 8. Rotation of elements in a plane
2.4 Rotation
Architecture. Rotation of elements in the system.
In architecture one the examples for the ‘Rotation’ form-making approach is the facade of the Eskenazi
Hospital in Indianapolis, IN - Completed 2014, designed by Rob Ley. A eld of 7,000 angled metal panels
in conjunction with an articulated east/west colour strategy creates a dynamic façade system that offers
observers a unique visual experience depending on their vantage point and the pace at which they are
moving through the site. In this way, pedestrians and slow moving vehicles within close proximity to the
hospital will experience a noticeable, dappled shift in colour and transparency as they move across the
hospital grounds <http://rob-ley.com/May-September >.
Figure 7. Eskenazi Hospital in Indianapolis, 2014, by Rob Ley

# 11
2.5 Rotation 3D
Exercise Objective: To rotate elements depending on their proximity to the attractor point
(rotate around an axis).
In this exercise the panels are being rotated around the center point and an axis vector. The axis vector
is determined by a line between a center of each polygon and the attractor point. The rotation value is
determined by the proximity between the center of the polygons and the attractor point.
# 11 # 12
2.5 Rotation 3D
Architecture. Rotation of elements in the system
The idea of interactive architectural structures is illustrated in the ‘hexi’ responsive wall project by thibaut
sld. <http://www.thibautsld.com>. The hexagonal panels are situated on the surface of the interior
space . The system uses the real-time data collected from motion-tracking technology to decode and
interpret the gestures and actions of a person within close range (digital simulation).
Figure 9. Responsive ‘Hexi’ wall uctuates based on nearby movements
Figure 10. Rotation of elements around the center and an axis vector

#12
2.5 Rotation 3D
Exercise Objective: To rotate elements depending on their proximity to the attractor point
(rotate around an axis).
In this exercise the panels are being rotated around the center point and an axis vector. The axis vector
is determined by a line between a center of each polygon and the attractor point. The rotation value is
determined by the proximity between the center of the polygons and the attractor point.
# 11 # 12
2.5 Rotation 3D
Architecture. Rotation of elements in the system
The idea of interactive architectural structures is illustrated in the ‘hexi’ responsive wall project by thibaut
sld. <http://www.thibautsld.com>. The hexagonal panels are situated on the surface of the interior
space . The system uses the real-time data collected from motion-tracking technology to decode and
interpret the gestures and actions of a person within close range (digital simulation).
Figure 9. Responsive ‘Hexi’ wall uctuates based on nearby movements
Figure 10. Rotation of elements around the center and an axis vector

#13
2.6 Condition / Reduction of elements
Exercise Objective: To randomly reduce the number of panels around the attractor point.
The ‘Dispatch’ component is used to split the list of elements in the system into two target lists (list ‘A‘
and list ‘B‘). The condition for the dispatch is the proximity to the attractor point. The dispatched panels
in the list ‘A‘ are then being randomly reduced.
# 13 # 14
Figure 11. Condition based on the proximity. Random reduce of panels, which are close to the attractor.
Exercise Objective: To colour the panels depending on how far they are from the attractor
point.
The distance between the remaining elements and the attractor point is used to inform the colouring of
the panels. A multiple colour gradient component (‘Gradient‘) interprets the distance values as corre-
sponding colours withing the chosen spectrum. To change the gradient type - right click on the Gradient
component and choose the Presets option.
Figure 12. Colouring of the elements, based on the proximity to the attractor.

#14
2.6 Condition / Reduction of elements
Exercise Objective: To randomly reduce the number of panels around the attractor point.
The ‘Dispatch’ component is used to split the list of elements in the system into two target lists (list ‘A‘
and list ‘B‘). The condition for the dispatch is the proximity to the attractor point. The dispatched panels
in the list ‘A‘ are then being randomly reduced.
# 13 # 14
Figure 11. Condition based on the proximity. Random reduce of panels, which are close to the attractor.
Exercise Objective: To colour the panels depending on how far they are from the attractor
point.
The distance between the remaining elements and the attractor point is used to inform the colouring of
the panels. A multiple colour gradient component (‘Gradient‘) interprets the distance values as corre-
sponding colours withing the chosen spectrum. To change the gradient type - right click on the Gradient
component and choose the Presets option.
Figure 12. Colouring of the elements, based on the proximity to the attractor.

# 15
# 15
Exercise Objective: To map a 2D pattern onto a surface.
The ‘Map to Surface’ component is used to transfer a ‘Grid Deformation‘ pattern (from the previous part
of the 2.7 exercise) onto a curvilinear surface (Target surface) via control points. Note that the curves in
the deformed grid pattern are grouped before being connected to the ‘Bounding Box’ component, which
is used as a reference for the initial coordinate space.
# 16
2.7 Grid Deformation 2D + Pattern Mapping
Exercise Objective: To deform a grid of points based on the proximity to a set of attractors.
This exercise uses a series of attractors located on a curve. The deformation of the original regular ‘Hex-
agonal grid’ is done by the elimination of the points in the grid (‘input stream 0’ in the ‘Pick and Choose‘
component), based on their proximity to the attractors (Pattern of input indices) and by using the attrac-
tor points instead (‘input stream 1’). The deformed grid of points is then used to build curves running in
both ‘U’ and ‘V’ directions (See Figure 13).
Figure 13. Grid Deformation. Reduction of points in the grid
Figure 14. Map a 2D pattern (curves) onto a surface

# 16
# 15
Exercise Objective: To map a 2D pattern onto a surface.
The ‘Map to Surface’ component is used to transfer a ‘Grid Deformation‘ pattern (from the previous part
of the 2.7 exercise) onto a curvilinear surface (Target surface) via control points. Note that the curves in
the deformed grid pattern are grouped before being connected to the ‘Bounding Box’ component, which
is used as a reference for the initial coordinate space.
# 16
2.7 Grid Deformation 2D + Pattern Mapping
Exercise Objective: To deform a grid of points based on the proximity to a set of attractors.
This exercise uses a series of attractors located on a curve. The deformation of the original regular ‘Hex-
agonal grid’ is done by the elimination of the points in the grid (‘input stream 0’ in the ‘Pick and Choose‘
component), based on their proximity to the attractors (Pattern of input indices) and by using the attrac-
tor points instead (‘input stream 1’). The deformed grid of points is then used to build curves running in
both ‘U’ and ‘V’ directions (See Figure 13).
Figure 13. Grid Deformation. Reduction of points in the grid
Figure 14. Map a 2D pattern (curves) onto a surface

# 17
# 17
2.8 Grid Deformation 3D
Exercise Objective: To deform a grid of points in 3D.
The ‘Grid Deformation 3D‘ exercise uses attractor points to inform the move value and direction of the
original points in the grid. The points in the grid are being pushed away from the attractors. The resulting
deformed 3D grid of points is used to create a wafe structure.
# 18
Figure 15. 3D grid deformation (Grasshopper Denition)
Figure 16. 3D grid deformation (output model)

# 18
# 17
2.8 Grid Deformation 3D
Exercise Objective: To deform a grid of points in 3D.
The ‘Grid Deformation 3D‘ exercise uses attractor points to inform the move value and direction of the
original points in the grid. The points in the grid are being pushed away from the attractors. The resulting
deformed 3D grid of points is used to create a wafe structure.
# 18
Figure 15. 3D grid deformation (Grasshopper Denition)
Figure 16. 3D grid deformation (output model)

#3 Attractor-based design strategies in architecture
Several examples of the dynamic systems were presented in the previous section. In this part two
attractor-based design approaches will be applied to the architectural design. The discussed case study
is located in New Zealand in Wellington, on the top of the hill in the Roseneath district (Figure 3.1). The
northern facade of the building is optimized to maximized the insolation in the interior and to have panels
overlooking to the two view points in the landscape.
# 19
Figure 18. The outcome from two mixed approaches.
Figure 17. Location of the case study in context.

3.1 Modelling landscape and urban layout
In order to create the context for the architectural application of the attractor- based strategies, the
basic landscape and street layout were created. Landscape was modelled with usage of Image Sampler
component and the black and white hypsometric map of the project site.
# 20
Elk is a set of tools to generate map using open
source data from the OpenStreepMap.org. The Mi-
norRoads components generates the street layout,
while GenericOSM with the plugged key “Building”
retrieve feature points of the existing buildings. Elk
can be also used to create the topographical sur-
faces utilizing the Shuttle Radar Topography Mission
(SRTM). The resolution of the SRTM data over Unit-
ed States is 30m and only 90m over the rest of the
world. Therefore, in this case study landscape was
created with usage of accurate hypsometric map.
Figure 19. Projected layout of the streets and the buildings
outlines.
DivideSurfacecreatestheatsurfacebasedonthepoint-grid.Thegridpointsaremovedupwiththe
verticalvectors,whichlengthdependonthecolor-codeofthehypsometricmap.Thespeciccoloris
remapped to the value between 0 and 190. 0 is the lower bound of Target domain (T) in Remap Num-
bers as it is the sea level and the 190 is the height of the highest pick - 190m above the sea level. The
largertheUandVparametersare,thehigher“theresolution”ofthenallandscapeis.

3.2 Modelling the general shape
The main geometry is modelled via simple Loft operation. Two curves are moved up and the third bot-
tom one is projected to the landscape. Afterwards there are divided with DivideCurve. Points at divisions
are the input for Interpolate Curve. The rotation of initial Circles (Rotate components connected to the
Circles) enable us to choose the desirable part of the skin for the penalization.
# 21
Figure 20.Construction of the main geometry. Initial three circle-like curves and the interpolated curves to be lofted.

The interpolated curves are chosen for the loft operation, as the result is the geometry of type Un-
trimmed Surface that wraps the building. You could also choose directly circle-like curves or some other
curves from your design, however every time you have to assure that the resulting geometry is Surface
type. Open brep that is not suitable for penalization.
# 22
Figure 22. The selected part of the surface for the panelization.
Figure 21. The main geometry resulting from Loft.

3.3 Strategy 1 - optimization for views: multiple point attractor
In this section the attractor points will be used to modify panels of the façade to overlook to the interest-
ing views. Attractors in the 3D space were created as Points in Rhinoceros and in the case study it is the
fountain in the Oriental Bay, the top of the Mt Victoria and the point when sun rises.
# 23
Figure 23. Attractor points as points to be well visible from the project site.
Inthe rststep inthe Grasshopperdenition (Denition3.3.1) theHexagonal gridfrom its2D formis
mapped to the surface of the facade. The coordinates of the grid points are extracted with usage of De-
construct. The x and y values are translated to the u and v coordinates of the 3-dimensional surface. Firstly
the x,y coordinates are remapped (Remap Numbers) to the target domain from 0 to 1. Secondly, they are
translated with a simple function {u,v} in Expression, to the u,v coordinates of the surface.

The points mapped to the surface have the same data structure as before the mapping and there are 6
points in every tree branch. Polyline connects all six vertexes of the hexagons and recreates the grid on
thesurface.TheAveragecomponentconnectedtotheoutputPinEvaluateSurfacendsthecentresof
the hexagonal panels and Average connected to the N output gives the normal vectors at these centres.
Attractor points in the landscape are manually selected in the Rhino viewport (right click on the Point
component and Set One Point/Set Multiple Points option).
# 24
Figure 24. The created panels and overlooks’ directions.
Hexagonal panels are scaled and moved with direction of their normal vectors. Then they are rotated using
theRotatecomponent.Initialdirectionisthedirectionofindividualnormalvectorofthepanel,thenal
direction is the smallest angle between the vectors pointing at the attractor points in the landscape and the
normal direction for each panel. For every single panel measurement for every attractor point is given and
aftersynchronizedsortingthelistofnumericanglevaluesandthevectors,ListItemselectstherstvector
fromthesortedlist.Theselectedvectorsaretheindividualnaldirectionsforeachpanel.Inthisexercise
every panel overlooks to one of the attractor points in the landscape by the rotation of its one edge.

3.4 Strategy 2 - optimization for sun path: multiple line attractor
In the second strategy the sun paths are the attractor lines, which affects the size of the openings in
the panels. Two sun paths are found and baked with usage of Ladybug_SunPath. One is on the Winter
Solstice (the longest night and the shortest day) on 21st of June and the other on the longest summer
day (22th of December).
# 25
Figure 25. Attractor points as ponts to be well visible from the project site.

The original sun path is projected onto the building skin. The distances from the panels’ centres to the
curves on the skin are the indicators of the opening factor of the panels. All distances are remapped to
match the scale factors. The panels closer to the attractor lines have bigger openings. The scaled outlines
of the panels are moved in the Normal direction. By lofting the initial panels’ outlines and the scaled and
moved ones the Panels B are created.
# 26
Figure 26. The outcome from the second strategy.

3.5 Combining strategies.
In the previous sub-sections two design approaches were presented in the design context. In this section
these strategies are combined to achieve project which meets multiple design criteria. On the one hand
the building skin should provide the best possible interior insolation, but on the other it should still give the
possibilities to have openings overlooking the interesting points in the landscape.
# 27
Figure 27. The outcome from two mixed approaches using Dispatch with True and False pattern.
IntherstpropositiontheDispatchcomponentisusedtodiversifypanelsonthebuildingskin.Bothsets
ofpanelsarerstlydividedwith{True/False}pattern.FromthePanelsA(optimizedforviews)onlyevery
second is taken, while from Panels B (optimized for insolation) the initial row and the complementary
panels from the rows with Panels A are combined. The resultant facade is presented below.

# 28
#4 Art in Structure Pavilion
Figure 28. . Hiriwa Pavilion, Runner-up in Art in Structure Competition 2015/2016, designed by J.Cichocka.
4.1 Competition entry
Hiriwa Pavilion is a competition entry for the Art in Structure Competition 2015/2016 organized by Fletcher
Steel Limited trading as Easysteel, Private Bag 92803, Penrose, Auckland 1642, New Zealand. Hiriwa
Pavilion design received runner-up award in the Emerging Designer category and was exhibited as a part
of “VirtualSculpture Park” during public voting on 3rd of April 2016 at the Wynyard Quarter in Auckland.
IDEA HIRIWA PAVILION is an experimental structure which endeavor to reinterpret the function of steel.
In this project steel is used as textile or fabric. The perforated steel plates form a lattice membrane for a
small outdoor pavilion.

4.2 Technical drawings and use of the point attractor
# 29
Figure 29. Form explorations.
FORM
Thesizeofthepavilionisroughly4,5x4,5mx3m.Theform-ndingprocessincludedmethodsstudiedbyof
Heinz Isler or Antoni Gaudi (e.g.fabric forming, membrane under pressure) and mesh relaxation techniques.
Geometry was translated into a grid of non-repeatable steel panels.
STRUCTURE & CONSTRUCTION
The pavilion’s CNC-bent aluminium frame is constructed from 24 sections. The surface of the pavilion
includes 128 unique panels from 2,5mm Atmospheric Corrosion Resistant Steel Plates (corten). In the
presentedprojecteverypanelisconsideredasasingleelement,sothat6-8panelscouldttothesteel
sheet of size 2500x 1250mm. However panels could be laser cut either as separate elements or as larger
clusters. At the connecting two parts edges there are overlaps, that enable to connect parts with each
other.
CREATIVITY & FLEXIBILITY
Parametricdesigntoolsgiveusexibilityandcreativityduringdesignandconstructionprocess.Design
features like size and shape of the pavilion, the amount of panels or the type of perforation could be
adjustedfor feasibility proposesatevery stagebeforethe nalfabrication.Automated layoutingwill
produceimmediatelyupdatedlesforfabrication.

# 30
Figure 30. Front elevation and top view of the pavilion. The attractor point drives the sizing of the perforations.
ROLE OF ATTRACTOR
Point attractor was utilized in rationalizing the openings of the panels. The perforation changes gradually
over the surface. The sizing of the perforation is driven be the distance to the attractor point located in the
middle point of the mesh projected to the ground plane. (Fig.x). The largest openings are in the middle of
the pavilion in order to reduce weight of the skin in the unsupported places.

# 31
Figure 31. The visualization of the Hiriwa Pavilion, Runner-up in Art in Structure Competition 2015/2016, by J.Cichocka.
#5 Conclusion
Attractors are the core of the dynamical systems in architecture. Attractors are used to create gradient,
design interactiveness or introduce non-primitive order into architectural compositions. If they are trans-
lated as the elements of the environment like people, wind, sun (light), humidity or others, they can also
perform dynamic or static optimization.
A simple approach of mixing two types of the building skin panels resulted in the statically optimized
building skin. Both presented design outcomes from Section 3 and 4 are the example of attractor-based
optimization.
“Attractors in Architecture: Attractor based optimization and design solutions for dynamical systems in ar-
chitecture“isbasedontheresearchactivitieswhichwerenanciallysupportedbyEuropeanUnionwithin
the “THELXINOE: Erasmus Euro-Oceanian Smart City Network” grant.