picture of Coral House

Coral House

Differential Growth for Architectural Expression



The Coral House is an exploration into differential growth algorithms for architecture. The growth logic is inspired by the biological growth principals of coral pollips. Our team of computational designers partnered with Biology students from the University of Tubingen to realize this interdisciplanary biomimetic design. This project involved investigating a biological specimen and isolating its key structural principals, then abstracting these principals into computational and architectural design.

smooth texture

We isolated four key differential growth patterns found in biology: repulsion, deferring growth rate, different cell types, and constant surface-volume ratio. Repulsion is the characteristic that prevents cells from intersecting each other. As the global structure grows, the cells need to spread apart in a non-linear fashion to avoid each other. Secondly, biological growth is governed by deferring growth rate. This is where cells will grow at different rates in relationship to their proximity to each other.

pyramid texture

Thirdly, the cell growth rate is related to the cell's position within the global structure. Lastly, biological specimens tend to grow with the constraint of a constant surface to volume ratio. Mathematically, volume grows faster than surface area. As such, biology will form increasingly intricate shapes to make sufficient surface for nutrient absorption in relationship to its size. From these 4 basic rules, we can approximate the growth of many biological specimen.

trapezoid texture


growth animation

Computational Approach

The next step was translating these biological principles into a computational expression. The easiest way to achieve our desired geometry was through the medium of mesh. The logic of a mesh ensures that we will have the final outcome of a good watertight surface for ultimately 3d printing.
The mesh faces expand until they reach a threshold size. At which point, the mesh face is split into two mesh faces. The splitting is done is such a fashion to produce only triangular mesh faces. This avoids problems of non-planar mesh faces that occur with square mesh. The splitting continues recursively, exponentially growing the surface geometric complexity and surface area.



1. For the repulsion of cells, this is abstracted into the repulsion of vertices. The code is scripted in such a way that the vertices push each other away if they become too close to each other. Instead of the vertices checking their distance against every other vertex, we construct an rTree to limit the checking to the vertices’ local neighborhood. In this fashion, we identify vertices that are too close to each other, and construct a new vector that ensures they will not collide.

Secondly, the mesh vertices need a logic of different growth rates in relationship to each other. On the local level, the vertices move apart from one another. Once they achieve a certain distance, the mesh face will divide. On the global level, the vertices rate of movement changes based on their proximity to the center of the structure. They move at a faster rate if they are further from the origin of growth.

Lastly, the code needs to approximate the same surface to volume ratio. We achieve this by having vertex movement stop closer to the center, such that we could maintain valleys in the morphology.

implimentation diagram
Implimentation of Vertices Position



As a proof of the quality of our mesh, we 3d printed the Coral prototype. This proves that our Rhino mesh is indeed watertight, and a good mesh without any non-manifold edges or self-conflicting faces. Thus, we are not just producing an artistic digital model, but something that is actually fabricatable, and perhaps constructable at a larger scale

3d printed coral ring



The coral growth algorithm is then used in an architectural design scenario to examine the practicallity of this type of design generator. The integration of typical architectural elements, such as fenestrations, presents a challenge for such a radically curvilinear geometry. It should be noted however, that the algorithm can undergo as many iterations of differential growth as the designer desires. Thus, the algorithm can be stopped earlier such that the geometry is more practical for a building.

This geometry can has great utility for architecture. The introduction of curvilinear morphology allows the facade to perform in passive cooling. The dramatic undulations allow the building to shade itself from the sun, while still providing large surface area for radiant heat to escape. This facade would thus function similar to a cactus, performing well in hot arid environments.

Coral Haus Wiremesh
coral haus iterations