Parametric Coral growth

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Course Name: Associative and Algorithmic DesignCourse Number: 22790

Term/Year: Winter Term 2014/15Examination Number: 22791

Examiner Number: 02442Prof. Achim Menges

Tutors: Ehsan BaharlouInstitute: Institute for Computational Design

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Coral GrowthParametric Patterns in Nature

John BarnthouseQueenie Chen

Weiyi LinAlan Rodriguez Carrillo

AbstractThe object of this final design presentation was to explore natural patterns of growth and how physical attriubutes could affect those pattens. The coral species served as an inspiration for our design methodoloy. Further, we look at instances in nature such as sunlight, geology, and physics to explore how standard patterns could be manipulated through multiple processes.

Institute for Computational DesignInstitut für Computerbasiertes EntwerfenUniversität Stuttgart Institute for Computational Design

Institut für Computerbasiertes EntwerfenUniversität Stuttgart

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Coral GrowthParametric Patterns in Nature

Course Name: Associative and Algorithmic DesignCourse Number: 22790

Term/Year: Winter 2014/15Examination Number: 22791

Examiner Number: 02442Prof. Achim Menges

Tutors: Eshan Baharlou

Institute: Institute for Computational Design

John BarnthouseQueenie Chen

Alan Rodriguez CarrilloWeiyi Lin

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Contents

Chapter 01: Project Overview_____Page 05

Chapter 02: Design Investigation_____Page 09

Chapter 03: Biological Precedents_____Page 13

Chapter 04: Mathematic Approach_____Page 17

Chapter 05: Design Concept_____Page 21

Chapter 06: Computational Process_____Page 25

Chapter 07: Fabrication_____Page 33

Chapter 08: Use in Design_____Page 37

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Chapter 01

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PROJECT OVERVIEWThe initial design goal was to investigate a fractal growth pattern , with design parameters to simulate natural growth pattern. We worked with the idea of growth on an adjacent object and the power of the sun. Through the use of Rhino, Grasshopper, Anenome, and Kanga-roo we thought to achieve a parametric form that could be manipulated with our set parameters. We also create a number of design iterations in order to physically help the fabrication with 3d-priting.

During the initial stages of design, we looked at examp-les of biological fractal structures found in nature, inclu-ding tree structures, human anatomy, fruits and plants. Further, corals were studied and ultimately inspire the project.A mathematic process needed to first be determined in order to generate a parametric form. We started with 2D random, 2D branching and ultimately, a 3d branching

structure best fit the needs of the project.

Parametric fractal forms can be found in industrial de-sign, such as a coat hanger or a lamp cover using the 3d branching system. Growth pattern system can also be used in structural components of buildings like co-lumns.

Through anenome loops, pipe connection, brep exclu-sion and projection we developed the 3d coral fractal pattern. Further, we set the attractor point(sun) and use kangaroo to pack sphere.The final design was able to be baked in Rhino and rendered using 3dsMAZX+VRay. A Series of Animation slides were also rendered from a semilar process. 3D printing served as the best me-dium to fabricate the final iteration of our project. Pa-rameters were set such that the final project would be physically stable.

FIGURE 01: Exampe of coral structure. (Source: AnimalsWorld.de) FIGURE 02: Speical growth patterns can be found in differnet coral types. Brain coral is one example (Source: Scott Kinmartin)

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Chapter 02

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DESIGN INVESTIGATION

FRACTAL PATTERNSThe initial design goal was to investigate a fractual growth pattern, with design parameters that could be manipulated to generate specific forms. These growth patterns range from simple structures to complex na-ture. Was also wanted geometrically interpret the be-havior of certain organic structures from fractal geom-etry.

NATURAL GROWTHAs the form began to grow, we hoped in simulate natural growth patterns, such as attraction towards the sun or gravitational pull of large objects. Ultimately we worked with the idea of growth on an adjacent object and the power of the sun and different environmental aspects that could influence the growth form and formal conclu-sion.

COMPUTATIONThe more complex to see nature path is to study and understand their behavior and try to imitate from sci-entific and numerical human theories. The interpreta-tion of environmental and geometric parameters that were studied previously gave us the starting point to generate a study based on visual programming param-eters. Thus, each element that influenced our design interepreto with geometric and numerical parameters employing the use of software. Through the use of Rhi-no, Grasshopper, Anenome, and Kangaroo we sought to achieve a parametric form. the final result could then be manipulated based on our set parameters. The final images and representation was made with 3ds max + VRay engine.

REALIZATIONWhen working with 3D editing programs and 3D graph-ics, the easiest way was to represent our prototype based on the use of a printer to give us the opportunity to build our design successfully without errors. The fi-nal product should be formed such that it could be real-ized with the use of 3-D printing. with that, we created a number of design iterations that could be phyically help together once fabricated.

FIGURE 03: Exampe of fractal pattern in 3D. (Source: Gregory Bard) FIGURE 04: Plants have a natural tendency to grow towards sunlight. (Source: Jenni Goddard)


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Chapter 03

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BIOLOGICAL PRECEDENTSDuring the initial stages of design, we looked at ex-amples of biological fractal structures found in nature. These included tree structures, human anatomy such as simulating the breathing process of human, as well as the growth of fruits and plants under the external in-fluence such as sun and gravity. Further, corals were studied and inspire the project.

A coral “head” is a colony of myriad genetically identi-cal polyps. Each polyp is a spineless animal typically only a few millimeters in diameter and a few centimeters in length. A set of tentacles surround a central mouth opening. An exoskeleton is excreted near the base. Over many generations, the colony thus creates a large skeleton that is characteristic of the species. Individual heads grow by asexual reproduction of polyps.

FIGURE 05: Exampe of coral growth. (Source: Dave Fleetham) FIGURE 06: Groth pattern found in the human lungs. (Source: B. Sapoval)


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Chapter 04

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MATHEMATIC APPROACHA mathematic process needed to first be determined in order to generate the parametric form. ultimately, a 3-D branching structure best fit the needs of the project.

2-D Random

The first method to try to imitate and represent a growth pattern in nature, was to establish a pattern of growth determined by a standard 2-D who was represented by lines and divisions. The pattern of growth in 2-D enabled us to successfully manage growth in two dimensions of the final order and served as a basis for establishing the final dimensions based on the number of divisions and segments that could have our system.

This system allows us to control from Anemone plugin iterations and divisions from specific control points.

2-D Branching

This system was developed from the concept of branch-ing and controlled subdivision from studies of organic and plant systems such as the lungs, the human cen-tral nervous system and fractals found in the nature of plants and microorganisms.

The development of a system based on ramifiación of division XY / 4 from each of our initial lines and expand-ed exponentially and, if a branch has one line, then af-ter 4 and 16 have branches with three iterations growth 2-D. This rule can be represented by 1=1, 2=4, 3=16, etc, where the unit represents the interaction growth and the numbers 1, 4 and 16 the braching system in 2-D space.

3-D Random

The structures found in nature tends to grow at random, but always tends to follow specific sources such as the sun or moving water energy due to static and dynamic force. Therefore, as well as human and living beings on this planet we are influenced by these energy sources.

The interpretation was performed from the movement of the sun and the way it has this in changing the geom-etry of 3D structure from a checkpoint that was used for this purpose. This checkpoint was modified from physi-cal components such as gravity and wind forces that affect natural systems.

The movement of the sun represented by a checkpoint, gave us the opportunity to have different spatial config-uration structures from physical forces interacting in it.

3-D Branching

By having a static element as it is a rock or a body with inertia 0, we use the 3D branching system in order to control the growth of our geometric body in three-dimensional space, the above was performed following the pattern of growth 2-D logarithmic but applied to 3D space with physical forces encountered in space, such as gravity and compression interpreted and carried out with the Kangaroo plugin.

With a branching system in three dimensional space, the growth pattern and geometric formal outcome of our body, had resulted in a system that could satisfac-torily mimic a natural system, besides being able to control your character through mathematical param-eters and numerical.

FIGURE 07: Exampe of fractal pattern in 3D. (Source: Andrea Rossi) FIGURE 08: Plants have a natural tendency to grow towards sunlight. (Source: Theverymany)


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Chapter 05

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DESIGN CONCEPT

Our design concept dealt with the manipulation of the coral fractal pattern that was initially generated in Grasshopper. The thinking was that the branching sys-tem would represent the coral.

From there, we wanted to see how we could manipu-late this system beyond simple repition. To achieve this, we introduced a brep “rock” into the project that would ultimately interfere with our growth pattern. The points which fell inside this brep were then projected on its sur-face, as coral would likely grow on the surface of a rock when the two objects met.

Further, we introduced an attractor point growth pat-tern of the endpoint spheres that represented growth towards the sun.

Finally, we worked with Kangaroo physics to have a sphere packing effect that would represent the real-life interaction of the final spheres.

FIGURE 09: Exampe of fractal pattern in 3D. (Source: John Barnthouse) FIGURE 10: Plants have a natural tendency to grow towards sunlight. (Source: Academy of Arts University)


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Chapter 06

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COMPUTATIONAL PROCESS The grasshopper plugin allows you to manipulate not only geometry but physi-cal strength related parameters and complex mathematical implementations. For this sys-tem the random geometric Anemome plugins growth were used for the system of branch-ing and D 2-3 Kangaroo plugin to simulate the physical forces of inertia lacking a living organic computational system. Our first step was to define an origin point in 3D space Rhinoceros 5.0 to be able to deploy our system into a spatial coordinate and control its growth. This procedure was performed with the help of Anemone plugin that allowed us to begin and end a system of

branches in 3D through lines and lines sub-divisions in the components of grasshopper. Later these lines are divided into segments that rotated from the last point as to give rise to a system of circles that were divided into 3 parts and gave the start of the tertiary branch-es of our system. These segments from the subdivisions of the circles make our final itera-tions that lead to initial branch system organ system. The second step was to find the end-points of each of the segments obtained from the circles points in order to obtain the cent-ers of the “A” areas our 3D geometric pattern formed.

Due to the need of an object without inertia and stable in which our organic system could grow, a rock which represents stability and inertia = 0 was placed and a subtraction of points held within the rock in order to prevent internal and external growth only because the system can not grow inward when influences of solar energy. The centers of the end segments of our system are located and 3D branching genera-tion continues spheres intersect each other to give rise to a complex spatial form which can be controlled by dividing numerical parame-ters, scale and rotation through elaborate the grasshopper definition.

An interpretation of the behavior of the sun and its dynamic motion is made from a checkpoint modifying the size and scale within all areas from a “random control” in 3D space. This point simulated the sun not-static and moving gradually influenced by movement the final formal configuration of this system. The last step was to incorporate com-ponents Kangaroo plugin like gravity influenc-es the shape and growth control of our body. The components were added at the end of the random objects represented from the fields and along with the forces described above, gave us the final form system.

FIGURE 11: Exampe of fractal pattern in 3D. (Source: Alan Rodriguez) FIGURE 12: Plants have a natural tendency to grow towards sunlight. (Source: Alan Rodriguez)


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DIAGRAMATIC APPROACHThe design process, as illustrated with the ad-jacent diagrams, was as follows. An initial 3D branching pattern was found that could be used within the Anenome plug-in. This growth pat-tern was then looped to give us multiple brances. sphere packing effect that would represent the real-life interaction of the final spheres. Endpoints were generated from the branching system. Con-nections between the endpoints were found that would serve as a structual connection. A spherical geometry was assigned to each of the individual endpointsThe final sphere geometry was manipu-lated using an attractor point strategy.

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FIGURE XX: Description of Figure. (Source: Alan Rodriguez)

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Chapter 07

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FABRICATIONScript was used to create a scaled physical model of our conceptual idea. 3d printing served as the best me-dium to fabricate the final iteration of our project.

The final design was able to be baked in Rhino. Inter-sections were deleted and all the surfaces were joined to a polysurface. The polysurface is then converted to a mesh. Parameters were set such that the final project would be physically stable and meet the requirements of printing machine. After the printing was finished, the dust on the model was hoovered and the tiny dust was cleaned with a cleaning brush.

FIGURE 13: Exampe of fractal pattern in 3D. (Source: Q. Chen, W. Lin)

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FIGURE 14: Plants have a natural tendency to grow towards sunlight. (Source: Q. Chen, W. Lin)

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Chapter 08

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USE IN DESIGN

Technical Development

Architecture and design, concerned with control over rhythm, and with such fractal concepts as the progres-sion of forms from a distant view down to the intimate details, can benefit from the use of this relatively new mathematical tool. Fractal geometry is a rare example of a technology that reaches into the core of design composition, allowing the architect or designer to ex-press a complex understanding of nature.Rapid prototyping tools and 3D printers have made pos-sible to actualize the intricate digital designs to physical forms easily and quickly.

Idea from Nature

The concept of Biomimicry, considered as the science and philosophy of learning from nature , is a source of design inspiration with different approaches undertaken by designers that refer nature. Often, nature as inspira-tion is combined with mathematics in order to move be-yond the superficial inspiration and realize structurally designs. Mathematics offer rules which guide design-ers to understand the complexity of natural shapes. The irregular non-Euclidean geometry of natural trees have been now possible to explain through mathemat-ics by the concept of complex, non-linear and fractal geometries (Casti, 1989). ‘Fractal׳, coined by Benoit Mandelbrot in the 1970s, can theoretically define the geometry of many natural objects (Mandelbrot, 1982).

FIGURE 15: Exampe of fractal pattern in 3D. (Source: Werner Dieterich)

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FIGURE 16: Plants have a natural tendency to grow towards sunlight. (Source: Luc Valencia)

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References

1 - Marek Kolodziejczyk,Thread Model, Natural – spontaneous Formation of Branches, in: SFB 230, Natural Structures – Principles, Strategies, and Models in Architecture and Nature,Proceedings of the II. International Symposium of the Sonderforschungsbereich 230, Stuttgartr 1991, p.139.

2 - For a pertinent concept of elegance that is related to the visual resolution of complexity see: Patrik Schu-macher, Aguing for Elegance, in: Castle, H., Rahim, A. & Jamelle, H., (eds), Elegance, Architectural Design, January/February 2007, Vol.77, No.1, Wiley – Academy, London.

3 - Grasshopper Primer (http://www.grasshopper3d.com/page/tutorials-1)

4 - Kolarevic, B., 2003. Digital morphogenesis. In: B. Kolarevic, ed. Architecture in the digital age. Design and manufacturing. New York: Taylor & Francis, 12–28.

5 - Leach, N., and Schumacher, P., 2009. Parametricism: A New Global Style for Architecture and Urban Design. Architectural Design, 79 (4), 14–23.

6 - Burry M., 2011, Scripting cultures: Architectural design and programming. John Wiley & Sons

7 - Trummer, P., 2011. Associative Design. From Type to Population. In: A. Menges and S. Ahlquist, eds. Compu-tational Design Thinking. London: John Wiley & Sons, 179–197.

8 - Terzidis, K., 2003. Expressive form. A conceptual approach to computational design. London: Spon.

9 - Alexander, C., 1971. Notes on the synthesis of form. Cambridge, MA: Harvard University Press.

10 - Cross, N., 2001. Can a Machine Design? Design Issues, 17 (4), 44–50. 11 - Coates P.S., 2010, Programming.architecture. Routledge.

12 - DeLanda, M., 2001. Philosophies of design. The case of modeling software. In: J. Salazar, ed. Verb process¬ing. Architecture boogazine. Barcelona?: Actar, 132–142.

13 - Flake G.W., 1998, The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Com-plex Systems, and Adaptation. MIT Press.

14 - Frazer, J., 1995. An evolutionary architecture. London: Architectural Association.

15 - Kolarevic, B., 2003. Digital morphogenesis. In: B. Kolarevic, ed. Architecture in the digital age. Design and manufacturing. New York: Taylor & Francis, 12–28.

16 - Kwinter, S., 1993. Soft Systems. In: B. Boigon, ed. Culture Lab 1. New York: Princeton Architectural Press, 207–228.

17 - Lawson, B., 2006. How designers think. The design process demystified. 4th ed. Amsterdam, London: Archi-tectural.

18 - Leach, N., 2009. Digital Morphogenesis. Architectural Design, 79 (1), 32–37.

19 - Leach, N., and Schumacher, P., 2009. Parametricism: A New Global Style for Architecture and Urban De-sign. Architectural Design, 79 (4), 14–23.

20 - Littlefield, D., 2008. Space craft. Developments in architectural computing. London: RIBA Pub.

21 - Menges, A., 2008. Integral Formation and Materialization. Computational Form and Material Gestalt. In: B. Kolarevic and K.R. Klinger, eds. 2008. New York: Routledge, 195–210.

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22 - Menges A., Ahlquist S., eds., 2011, Computational Design Thinking. John Wiley & Sons, London.

Burry M., 2011, Scripting cultures: Architectural design and programming. John Wiley & Sons.

23 - Park, K., and Holt, N., 2010. Parametric Design Process of a Complex Building In Practice Using Pro-grammed Code As Master Model. International Journal of Architectural Computing, 8 (3), 359–376.

24 - Terzidis, K., 2003. Expressive form. A conceptual approach to computational design. London: Spon.

25 - Terzidis, K., 2006. Algorithmic architecture. 1st ed. Amsterdam, London: Architectural Press.

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Fig 1: 3dsMax render which shows the attraction pattern of the spheres towards the “sun”.

Fig 3: This closer render clearly shows how Kangaroo physics was used for “sphere packing”.

Fig 5: A final render shows the interruption of the brep “rock” on teh growth system.

Fig 2: 3D printing was used to create the final model.

Fig 4: Pipe connections were used to ensure the final spheres would be held together.

Fig 6: A custom form generated to represent one iteration of the brep “rock:.

ultimately inspired the project. A mathematic process needed to first

be determined in order to generate a parametric form. We started

with 2D random, 2D branching and ultimately, a 3d branching struc-

ture best fit the needs of the project.

Parametric fractal forms can be found in industrial design, such as a

coat hanger or a lamp cover using the 3d branching system. Growth

pattern system can also be used in structural components of buil-

dings like columns.

Through anenome loops, pipe connection, brep exclusion and projec-

tion we developed the 3d coral fractal pattern. Further, we set the at-

tractor point(sun) and use kangaroo to pack sphere.The final design

was able to be baked in Rhino and rendered using 3dsMAZX+VRay.

A Series of Animation slides were also rendered from a semilar pro-

cess. 3D printing served as the best medium to fabricate the final ite-

ration of our project. Parameters were set such that the final project

would be physically stable.

Prof. Achim MengesTutor: Ehsan Baharlou

J. Barnthouse, Q. Chen, W. Lin A. Rodriguez Carrillo

Parametric Coral Groth

Project Overview:

The initial design goal was to investigate a fractal growth pattern ,

with design parameters to simulate natural growth pattern. We wor-

ked with the idea of growth on an adjacent object and the power

of the sun. Through the use of Rhino, Grasshopper, Anenome, and

Kangaroo we sought to achieve a parametric form that could be

manipulated with our set parameters. We also created a series of

geometry within the model in to ensure successful fabrication with

3d-priting.

During the initial stages of design, we looked at examples of bio-

logical fractal structures found in nature, including tree structures,

human anatomy, fruits and plants. Further, corals were studied and

Fig 7: An initial 3D branching pattern was found that could be used within the Anenome plug-in.

Fig 9: Endpoints were generated from the branching system.

Fig 11: A spherical geometry was assigned to each of the individual endpoints.

Fig 8: This growth pattern was then looped to give us multiple branc-es.

Fig 10: Connections between the endpoints were found that would serve as a structual connection.

Fig 12: The final sphere geometry was manipulated using an attrac-tor point strategy.

Project Methodology:

For this project we wanted to generate a final design that was both

beautiful and could be fabricated in real life. We wanted not to simply

copy an existing form, such as coral, but rather use this natural pat-

tern as an inspiration for the project.

We found that exploring a number of corals gave us a variety of ways

to think about growth patterns. Also, how these corals interacted with

their environments played a role in our design process. For example,

we looked at how some coral grew vertically towards the sun, while

others grew in accordance to their surroundings. The idea that these

corals sprung up from the sea floor and would inevitably interact with

other types of geology inspired the idea of introducing a rock into the

project.

As for computation representation, we wanted a design concept that

was based in mathematics, but also had a level of unpredictability to

the final product. To achieve this, we introduced a number of ways to

manipulate the final design in different stages of the growth system.

For example, the number of brances, size of branches, number of

loops, and number of interferences can be controlled within the final

script. Also, the physical aspect of the project, the Kangaroo sphere

packing, can also be adjusted to give a different final result.

When it to came to final production, we wanted to explore the use of

3D printing with our model. For that, we needed to build a structure

that could support itself and could be understood by machine fabrica-

tion. The final model clearly shows the design intent, and alludes to

how the design could be used in a real-world setting.

Documents

Parametric Coral growth