A402a_Fall 2012

A402aPATTERN OPERABILITYDaniel Nguyen | Neil Leach, Biayna Bogosian

Table of Contents

Introduction.....................................................................................................................................................................1

Islamic Tiling and Muqarnas Dome Studies..................................................................................................................2-7

Biological Systems and Scale Efficiency.....................................................................................................................8-11

Modeling, Material Studies.......................................................................................................................................12-26

Final Design.............................................................................................................................................................27-58

Conclusion...............................................................................................................................................................59-60

Bibliography..................................................................................................................................................................61

The basis of this research is to study a set of patterns found in Islamic tiling architecture, then begin to either contradict that investigation with biological systems, and ultimately demonstrate how these logics can be analyzed and interpreted to be used for architectural purposes. This process will develop a strong argument for implementation in an installation that is computa-tional based on parametricism and pattern logic.

Muqarnas vault studies are examples of static structures that create vaults for buildings with sophisticated patterns, but are unable to change according to new circumstances. Biological and computational studies will demonstrate how systems can scale through growth or move-ment in order to adapt to conditions through their inherent material logic, but still obtain the same initial pattern.

Examine systems/logics that allow them to perform these actions, and introduce those into an installation that would serve as a prototype for a larger object.

Brief

Thesis

Investigation

1

1ISLAMIC TILING AND MUQARNAS DOME STUDIES

1

2

Girih tiles are a set of five tiles that were used in the creation of tiling patterns for decoration of build-ings in Islamic architecture

Pentagon BowtieRegularDecagon

Rhombus Elongated (Irregular Convex) Hexagon

Girih Tiles

Source(s):

“Ancient Islamic Penrose Tiles | Numbers | Science News.” Ancient Islamic Penrose Tiles | Numbers | Science News. 3

The diagrams above consist of a series of common pattern logics that are implemented in Islamic tiling as well as vaulting mechanisms in order to provide a packing logic. In addition, it demonstrates how a series of vectors can be extrapolated to create larger geometries while simply extending the initial linework.

Core Octagon Perpendicular Octangular Star Core Circle Cruciform Octangular Star Basic Octagon Peripheral Circle

Greek Cross

Diamond Greek Cross

Diamond St. Andrew’s Cross

Cruciform Octangular Star

Oblique Octangular Star

Oblique Octangular Star

Source(s):

Pereira, José. The Sacred Architecture of Islam. New Delhi: Aryan International, 2004. Print.

Patterns Used in Islamic Vaults

4

Source(s):

Grabar, Oleg. Muqarnas: An Annual on Islamic Art and Architecture. New Haven: Yale UP, 1983. Print.

The Arabic word for stalactite vault, it is an architectural ornament developed around the middle of the 10th century in north eastern Iran and simultaneously in central North Africa involves 3D architectural decorations of niche-like elements arranged in tiers. Muqarnas take the form of small pointed niches, stacked in tiers projecting beyond those below and can be constructed in brick, stone, stucco or wood. The two-dimensional projection of Muqarnas vaults consists of a small variety of simple geometrical elements.

Islamic Muqarnas

5

The diagrams above illustrate the varying types of Muqarnas, which is a decorative corbel commonly used in Islamic architecture. Their pattern logic al-low them to create vaulted ceilings and conceal a considerable amount of structure within the domes and vaults. The illustration to the left shows the uti-lization of squinches in a dome’s ceiling as a con-struction filling, which would ultimately allow for a base to receive a spherical or octagonal dome.

Squinch

Dome

Drum

Source(s):


Muqarnas Assembly Types

Muqarnas Forming Stalactites

Passage from Square to Circle

Passage from Square to Octagon

Rectilinear Muqarnas

Curvilinear Muqarnas

Muwarnas Niche

6

Gaining an understanding of the underlying pattern logic utilized in these ancient muqarnas domes demonstrates how tiles or cells can come together and can be assembled as a whole aggregated. Further investigation into how these tiles and patterns can be implemented into three dimensional space by variegation their connection points and interrelationships will suggest a more adaptable pattern logic than is available in these static muqarnas domes.

Source(s):Brend, Barbara. Islamic Art. Cambridge, MA: Harvard UP, 1991. Print.Pereira, José. The Sacred Architecture of Islam. New Delhi: Aryan International, 2004. Print.

Geometric Pattern Logic Architectural Tiling Implementations

7

BIOLOGICALSYSTEMS+SCALEEFFICIENCY

2

8

Fibonacci numbers are generated from a function such that adding preceding terms will allow for an increasing set of integers.

Functions: 0, 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, ...Resulting Integers: 0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

Introducing this logic into a series of squares that scale up in size according to the fibonaacci numbers will create what is considered the golden spiral, and it is implemented in several natural systems in order to act as an efficience packing strategy for cells.

Fibonacci Numbers / Sequences

2

3

5

8

1 1

Source(s):

Dunlap, R. A. The Golden Ratio and Fibonacci Numbers. Singapore: World Scientific, 1997. Print.“Flowers and Fibonacci.” Flowers and Fibonacci. N.p., n.d. Web. 25 Nov. 2012. <http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html>. 9

Source(s):

Dunlap, R. A. The Golden Ratio and Fibonacci Numbers. Singapore: World Scientific, 1997. Print.“Flowers and Fibonacci.” Flowers and Fibonacci. N.p., n.d. Web. 25 Nov. 2012. <http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html>.

Pine Cone Scales Sunflower Florets

Geometric Pattern Geometric Pattern

8

13 21

13

Scale Packing Strategies Using Fibonacci Series in Nature

The Fibonacci series is utilized in natural occurrences like the geometry of a pine cone’s scales or florets that grow on a sunflower because it is considered the most efficient packing methodology. In these two instances, there is noticeably 8 scales rotating counterclockwise toward the edge and 13 rotating clockwise, while the sunflower features 13 counterclock-wise cells rotating to the exterior edge and 21 rotating clockwise.

10

Source(s):

“The Leading Provider of Science Images and Footage.” Science Photo Library. N.p., n.d. Web. 26 Nov. 2012. <http://www.sciencephoto.com/>.

An analysis of overlapping and shifting skin cell conditions in biological systems demonstrates how inherent geometries in biological skin cells or “scutes” allows the best possible surface pattern in order for skin to be shed and a underlying layer to be exposed for further growth. Studying tiling pattern logic in natural skin systems provided a larger understanding of how scales come together to assemble flexible vaulting and skin systems that could adapt to varying conditions.

Skin Studies

11

MODELING,MATERIAL STUDIES

3

12

Source(s):

“Home Geometric Toy Tile Magic-5.” Home Geometric Toy Tile Magic-5. N.p., n.d. Web. 25 Nov. 2012. <http://www1.ttcn.ne.jp/~a-nishi/tile/z_tile_m5.html>.

+=

https://vimeo.com/20004747#

Examples were studied that show how a series of geometries could be expanded and contracted through a mechanism that is allowed by their pat-tern. These systematic approaches would sug-gest a logic to open and close; however, these models only promote a two dimensions of expan-sion and contraction. These were simply studied to see how a packing pattern logic could be used to open and close a geometry.

Contraction

Components

Digital

Precedent Studies

Mechanical

Expansion

+

+

13

Source(s):

“Grasshopper - Generative Modeling for Rhino.” Grasshopper - Generative Modeling for Rhino. N.p., n.d. Web. 26 Nov. 2012. <http://www.grasshopper3d.com/>.

Utilizing a definition that implements a series of vector poitns in Rhinocerous, sliders were utilized to adjust the scale and step size of the geometry. These parameters allowed for the initial geometry to be adjusted to the desired size while the f(x) and f(y) function propoagate further geometries outward from the center.

Experimenting with Definitions in Rhinocerous / Grasshopper

11

14

Experimenting with Definitions in Rhinocerous / Grasshopper

Source(s):


Analyzing the pattern logic used in the muqarnas til-ing as well as the biological studies, a composition of the research resulted in a geometry with a central at-tractor point whereby the geometrical logic would be harnessed from. The “scales” in the installation would presumably be capable of sliding past one another, and the initial geometric pattern developed by a fibo-nacci series would make this possible.

12

15

angleofrotation

In a spiral staircase, there is a primary system that the steps align with while a secondary system acts as a series of points that the steps are arrayed out to that form a consistency between all the steps; the mechanism by which the in-stallation would operate, would function similarily in how the scales overlap

Run / Scale Length

Riser / Scale Thickness

Step / Scale Width

16

Source(s):

Oster, Gerry, and Yasunori Nishijima. Moiré Patterns,. San Francisco: W.H. Freeman, 1963. Print.

A series of overlapping transparent scales would enable a filtered light effect and playing with trans-parency through thickness and porosity of material

Moiré Effect

Phsyical study conducted to achieve the moiré ef-fect found in overlapping grids done with varying colored cells. Cells could shift, overlap, and rotate in order to distort the appearance of the surface.

variating cells/scales

connection points

Variating Cells / Scales

Connection Points

17

Variating Cells / Scales

Connection Points

Chuck Hoberman

With a background in design and engineering, Chuck Hoberman is known for several installations that allow a set geometry to be able to perform several actions and adapt to circumstances when forces are applied. He is widely known for the Hoberman sphere, an object that a group of the students in the studio examined in order to com-prehend how similar performance could be dupli-cated in a pattern or material logic. The exper-iments conducted in studio thereafter were used to determine a pattern logic that would facilitate similar flexibility and allow for an object that could be rapidly installed and generate a space.

Hoberman Sphere

Chuck Hoberman. New York: Museum of Modern Art, 1994. Print. 18

Three Formal Studies

Studies were conducting using the golden spiral generated by the fibonacci series that created a pat-tern that could be extruded and extended in order to translate from a strictly 2D pattern to a 3D form. This pattern would provide a much more flexible sys-tem that could be rearranged according to its de-sired use; furthermore, it would allow the lattice to be stacked and packed away when no longer needed.

This system largely focused on the idea of extruding the existing spi-ral pattern that could perhaps be stacked as a primary system, while it would be suspended by a sec-ondary system using rope or wire.

This study was performed in order to understand how two of the same spirals could be connected from end to end in order to continue the form of this golden spiral while simply ag-gregating one unit continuously. In addition, it proposed the idea of surr-rounding and engulfing the user with-in the space.

+

Lastly, this study was a summation of the previous studies in that we utilized a spiraling set of diamonds that would allow not only for a more defined geometry, but give the spiraling legs a more crystalline for-mation, providing space to play with transparency and opaqueness of the material.

19

Further studies were conducted in order es-tablish more efficient connections between the units. Tape and rubber bands were utilized for the connections between the cells. This meth-odology of connections allowed the sequence of cells to snap back; therefore, the usage of rubber bands is prevalent in future studies in or-der to achieve this same effect. 20

Folding Lines

Process

Connection Points

Individual Unit Assembly

21

This study model was constructed to demonstrate how connection points could allow a fairly rigid cell to snap back and forth when applying pressure to areas where four separate cells meet. This would allow operability for the apertures in the vault and allow a varying surface condition.

Bent Scheme B

Bent Scheme A

22

This study was conducted to determine whether a simplified set of triangles could be generated the golden spiral and still assembled to create a vaulted dome. The golden sprial pattern was overlaid with a series of vectors connecting interlock-ing points, which is where the connection points would be established to hold the units together. Unfortunately, the usage of simple rubber band connections was not sufficient in holding the structure together, and it required a rigid wire at the base and top in order to retain its form, so ultimately it became more a study of flexible and rigid connection points in the unit aggregation.

Source(s):

Jean, Roger V. Phyllotaxis: A Systemic Study of Plant Pattern Morphogenesis. Cambridge [England: Cambridge UP, 1994. Print.Cambridge UP, 1994. Print. index.html>.

ABCA B C

23

Considering that the research focused largely on pyramid, conical forms, and the research focused on an operable unit that was capable of being installed on a site and being adaptable, a study model was built to determine the variability a subdivided cube could provide. It was ideal that the user of the deployable tiles could bring this object to the site and install it according to the desired use in mind. In this study, the corners were the points of operabilty and pyramid cells could be turned on an axis from that point. In addition, the rubber band connections allow a recoiling behavior in the object so that one could open up the object, but its inherent behavior would force it to snap back into the cube form.

Pyramid

Components

Contracted

Deployed24

Cube - Enclosed

Cube - Unrolled 25

Additional study models were built to see if a vaulting system could be constructed using solely pentagons and triangular shaped cells, and they were successful in creating arches that would span above the user; however, they were no more operable than a static muqarnas dome; therefore, further studies would have to be applied in ordert obtain a unit aggre-gate that would allow an operable tesselation of similar units.

Pentagon - Triangle Connections

Pentagon - Pentagon Connections

26

FINAL DESIGN 4

27

Building off the previous subdivided cube study, this was a culmination of the previous investiga-tions and the resultant was essentially a dodeca-hedron that would allow a immense operability while utilizing little volume prior to installaiton in the space. Considering that the installation would provide little time to set the proposed object in the space, the goal was to generate a vaulting mech-anism that could be introduced rapidly, and have the connection points provide considerable oper-ability.

The dodecahedron is made up of several pentago-nal crystals, while two of them are divided into five smaller triangular edged crystals. The rationality behind the subdivision of these two points is to cre-ate a female connection for additional dodecahe-drons to mount onto the object and allow the object to not be just solitary vault, but a larger aggregate that could span larger spaces.

A

B

C

D

Components

A

B

28

Once we had the foundation for the object we began material studies in order to de-termine the potential of playing with trans-parency and irridescence of the material utilized on the final implementation. Studies performed with 3M irridescent adhesive film applied to the plexi would create a intrigu-ing crystalline mass, and would illustrate a curious field effect when implemetned at full scale. The user would be able to inhabit the space, and the variation between outside and inside would compell the inhabitants of the space to explore the interior and exterior of the inverted installation.

The investigative study would suggest that we had developed some sort of inverted muqarnas vaulting mechanism, that was not only compact when necesesary, but ul-timately, an expansive vaulting scheme that could ultimately provide shelter, while the openings in the pentagonal shaped crystalls would distort and refract light into the space.

1

Process of Assembly

2

3

4

5

29

Individual Unit from Proposed Installation

30

31

Initial design proposed at a larger scale that would adequate for human inhabitation and utilization. This scheme suggest-ed a logic that would allow people to inhabit the spaces carved out by the vaults and domes.

Building Types / Unit Assemblages

32

In addition, a secondary scheme was developed that would encourage the developed inverted muqarnas components to stack and arch over over spaces. The initial intended use case was sculptural components that would work alongside the dome scheme; however, it yielded very little interactivity for the user.


33

Assembly Methodologies: Cluster

Unit Aggregates

Units Assembled

34

Assembly Methodolgies: Tier

Fourth Tier

Third Tier

Second Tier

First Tier

First Tier

Second Tier

Third Tier

35

Edge Details

21 3 4 5 6 7

1 Pressure Plate Anchor2 Tempered Double Pane Glazing with embedded 3M Radiant film3 Silicon Strip Sealant4 Rotating Steel Hinge5 Inner Aluminum Extrusion 6 Outer Clamp Extrusion 7 Magnetic Locking Notch

36

For the purposes of the physical installaitno we would install in Lower Rosendin we considered either CNC milling or la-sercutting grooves and joints as part of the fabrication components that would allow these units to share edge to edge connections. Some of the early studies like the interwoven had effective results; therefore, they were utilized in the final installation.

Installation Model Interlocking Joint Connections

StaticEdges

RotationalJoints

InterlockingJoints

37

This simple diagrams explains the process when two edge conditions meet and how the adaptive hinges allow latches on to interlock.

Full Scale Interlocking Joint Connections

1

2

3

38

The joints allow for considerable operability since they feature a rotational aspect to

Joint Flexibility

39


Tower A594 Edge Connections / 297 of Units / 1782 Faces 40


Tower B565 Edge Connections / 113 of Units / 678 of Faces 41


Tower C1188 Edge Connections / 594 Units / 7128 of Faces 42


Tower D460 Edge Connections / 230 Units / 1380 Faces 43


Vault A164 Edge Connections / 82 Units / 492 Faces 44


Vault B112 Edge Connections / 56 Units / 336 of Faces

45


Vault C450 Edge Connections / 150 Units / 900 of Faces

46


Vault D92 Edge Connections / 46 Units / 276 Faces

47


Building Skin A248 Edge Connections / 124 Units / 744 of Faces

48


Building Skin B160 Edge Connections / 80 Units / 480 of Faces

49


Building Skin C292 Edge Connections / 146 Units / 876 Faces

50


Building Skin D234 Edge Connections / 117 of Units / 702 Faces 51


Dome A104 Edge Connections / 52 Units / 312 Faces 52


Dome B130 Edge Connections / 65 Units / 390 Faces

53


Half Dome84 Connections / 42 Units / 252 Faces

54


Dome C42 Edge Connections / 21 of Units / 126 of Faces

55

The realized design would suggest areas for the users to occupy as well as interact with one another. The idea was that these units would allow for temporary installation to be used for varying purposes, and then when the object was no longer needed it could be disassembled and removed from the site.

56

This installation served as a working prototype that would illustrate how these units could be put together and used to com-pose the larger aggregate suggested in the drawings. 3M radiant film was applied to 1/16th inch plexi, and the patterns were laser cut. Zip ties were then used to support the triangular units together. To limit the amount of weight in the units, each unit would have three faces that were open to limit the amount of material weight. The arrived design would allow for rapid installation in varying locations and depending on the desired use case could serve as a adaptable scheme that could be applied anywhere. The investigation conducted in the studio provided a developed understanding of the varying flexibility in a pattern logic while also demonstrating the ephemeral light quality a material can have on a space.

57

Aa

58

CONCLUSION5

59

Through the investigation of Islamic tiling patterns, biological pattern studies, computational and physical modeling, a developed understanding was yielded that demonstrates how a simple pattern assembled using a series of similar units can be assembled to create a larger aggregate. The methods used in ancient Islamic Muqarnas and tiling patterns are reintroduced into these modern systems that are active and operable, while requiring a small footprint for storage of the units themselves. Similar to the Islamic tiling patterns and Muqarnas domes and vaults, a simple geometry allow for a greater aggregate whole, which was reproduced in our final proposal.

The Biological studies served as an additional investigation into understanding how scales are used in skin systems to adapt to change in the specimen’s change in size over time through shedding systems or the overlapping of new scales as old ones decay. This process in dynamic skin systems discussed the idea of overlapping, sliding and shifting, which differentiated from the static system of pattern logic in a Islamic tiling system that resisted any movement.

The physical model studies served to develop an assembly unit that could be aggregated in a large scale system that could easily be packed away and removed from the site, but also efficient in its utilization of connections. The dodeca-hedron provides variability in its inherent geometry while allowing for hundreds of different methods for assembly, and it was the driving force towards the end result. In addition, a focus of the studio was material intelligence and the effect it can have on a space; the 3M radiant film applied to the surface of the acrylic and the material effect it would propose at a larger scale would present an ephemeral light quality about this object and would invite users to interrogate the spaces and volumes.

60

Bibliography

“Ancient Islamic Penrose Tiles | Numbers | Science News.” Ancient Islamic Penrose Tiles | Numbers | Sci-ence News.

Brayer, Marie-Ange. Biothing, Alisa Andrasek. Orléans: HYX, 2009. Print.

Brend, Barbara. Islamic Art. Cambridge, MA: Harvard UP, 1991. Print.

Chuck Hoberman. New York: Museum of Modern Art, 1994. Print.

Dunlap, R. A. The Golden Ratio and Fibonacci Numbers. Singapore: World Scientific, 1997. Print.“Flowers and Fibonacci.” Flowers and Fibonacci. N.p., n.d. Web. 25 Nov. 2012. <http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html>.


“Home Geometric Toy Tile Magic-5.” Home Geometric Toy Tile Magic-5. N.p., n.d. Web. 25 Nov. 2012. <http://www1.ttcn.ne.jp/~a-nishi/tile/z_tile_m5.html>.

“Islamic Textiles.” Islamic Textiles. N.p., n.d. Web. 11 Sept. 2012. <http://www.belovedlinens.net/fabrics/islamicT.html>.

Kheiri, Sattar. Islamic Architecture. London: J. Tiranti, 1923. Print.

Meinecke, Michael. Patterns of Stylistic Changes in Islamic Architecture: Local Traditions versus Migrating Artists. New York: New York UP, 1996. Print.

Miller, Susan Gilson., Mauro Bertagnin, Emily Gottreich, and William Granara. The Architecture and Memory of the Minority Quarter in the Muslim Mediterranean City. Cambridge, MA: Harvard Univ Graduate School of Design, 2010. Print.

Moussavi, Farshid, and Daniel Lopez. The Function of Form. Barcelona: Actar, 2009. Print.

Oster, Gerry, and Yasunori Nishijima. Moiré Patterns,. San Francisco: W.H. Freeman, 1963. Print.


Robinson, Chase F. A Medieval Islamic City Reconsidered: An Interdisciplinary Approach to Samarra. Ox-ford: Oxford UP, 2001. Print.

61

DN

Documents

A402a_Fall 2012