## Parametric Coral Growth – Final Project by J. Barnthouse, Q. Chen, W. Lin, Rodríguez Carrillo Alan

**Parametric Coral Growth**

[Barnthouse, Q. Chen, W. Lin A. Rodriguez Carrillo Alan]

Prof. Achim Menges

Tutor: Ehsan Baharlou

The 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 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 biological fractal structures found in nature, including tree structures, human anatomy, fruits and plants. Further, corals were studied and 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 structure 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 buildings like columns.

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 system would represent the coral.

From there, we wanted to see how we could manipulate 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 surface, as coral would likely grow on the surface of a rock when the two objects.

Further, we introduced an attractor point growth pattern 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.

Fractal Patterns

The 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 nature. Was also wanted geometrically interpret the behavior of certain organic structures from fractal geometry.

Natural Growth

As 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 conclusion.

Computation

The more complex to see nature path is to study and understand their behavior and try to imitate from scientific and numerical human theories. The interpretation of environmental and geometric parameters that were studied previously gave us the starting point to generate a study based on visual programming parameters. Thus, each element that influenced our design interepreto with geometric and numerical parameters employing the use of software. Through the use of Rhino, 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.

Through anenome loops, pipe connection, brep exclusion 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 3dsMAX + VRay. A Series of Animation slides were also rendered from a semilar process. 3D printing served as the best medium to fabricate the final iteration of our project. Parameters were set such that the final project would be physically stable.

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 pattern 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 fabrication. The final model clearly shows the design intent, and alludes to how the design could be used in a real-world setting.

A 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 branching and controlled subdivision from studies of organic and plant systems such as the lungs, the human central 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 expanded exponentially and, if a branch has one line, then after 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 geometry of 3D structure from a checkpoint that was used for this purpose. This checkpoint was modified from physical 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 configuration 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 satisfactorily mimic a natural system, besides being able to control your character through mathematical parameters and numerical.

Realization

When working with 3D editing programs and 3D graphics, 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 final product should be formed such that it could be realized with the use of 3-D printing. with that, we created a number of design iterations that could be phyically help together once fabricated.

Technical Development

Architecture and design, concerned with control over rhythm, and with such fractal concepts as the progression 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 express a complex understanding of nature. Rapid prototyping tools and 3D printers have made posible 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 inspiration is combined with mathematics in order to move beyond the superficial inspiration and realize structurally designs. Mathematics offer rules which guide designers to understand the complexity of natural shapes.

The irregular non-Euclidean geometry of natural tres have been now possible to explain through mathematics 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).

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