Visualization: Demetris ShammasFragments from the 3D printed grotto

Design by Algorithm

In computational design, the architect no longer develops form by pen on paper or by mouse in CAD program, but instead defines procedures to generate form. Shifting the design process onto this abstract level has a dramatic impact: Forms can be designed with a complexity and richness that would be impossible to draw by hand. Now these complex forms can be brought out of the computer using additive manufacturing. Bits and bytes can be rendered directly into reality.

The combination of computational design and additive manufacturing can lead to a non-standardized, highly differentiated and spatially complex architecture that is defined at the scale of millimeters. In the Digital Grotesque project, every detail of the architecture is generated through customized algorithms, without any manual intervention. A simple input form is recursively refined and enriched, culminating in a geometric mesh of 260 million individually specified facets. This single process generates many scales of architecture, from the overall form with its broad curvature, to local surface development, down to minute textures.

One Process – Endless Permutations

At a basic level, the algorithm used to generate the Digital Grotesque room functions by gradually refining and enriching a simple input form.The surfaces of a form are divided into smaller surfaces, and these in turn are divided again and again. Changes to one surface propagate down to its children. By altering the division ratios, one can control the geometry of the form.

Using this simple process, one can create astoundingly complex geometries with only a few subdivision steps. By changing the division ratios, one can also generate a surprising variety of forms. The process remains entirely the same; only the division parameters are altered.

The example on the right side show a square at different levels of subdivision as its division ratio is altered. While this example is two-dimensional, the same principle also works for three-dimensional forms.

One Process – Infinite Scales

While computational geometry in architecture is often used to create volumes with smooth, minimal surfaces, in the Digital Grotesque the design goal is the exactly the opposite. A maximal articulation of the surface creates a volumetric depth, where light is reflected in million different directions and the boundaries of the architecture are spatially diffuse.

The single subdivision process produces forms that contain information at multiple scales. The closer one gets to the form, the more features one discovers. Such a hierarchical differentiation can also be found in classic architecture. Yet unlike traditional architectural design processes, here a single process is used both to sculpt the overall form, and to create the minute surface details. This articulation can be used to create features that exceed the threshold of human haptic or visual perception and that would be entirely undrawable using tradional means.

Design development of grotto I

One Process – Both Global and Local

A key quality of the process is that it can produce locally differentiated heterogeneous details that are seamlessly incorporated into an organic whole. This is possible because division ratios can be specified according to the both local and global attributes of the form. Specifically, topological and topographical attributes of each region are mapped to the attributes of the overall landscape.

Although the process is deterministic – as the same combination of rules produces always the same result – it is difficult to foresee the outcome. Small changes in the weighting of parameters can propagate and lead to new and oftentimes surprising results. Thus, while the design is only truly controllable in an iterative trial-and-error process, this unpredictability offers the chance of discovering unexpected results in an open formal range.

The resulting structures maintain an organic connection to the input shape. The generated ornament appears to evolve out of the context rather than being an afterthought. Structure and ornament are fused into a single entity.

Design development grotto II base

Topological ornament of grotto’s center columns

Design development of grotto II column capitals


Customized construction system

Digital Grotesque is the first human-scale immersive space entirely constructed out of 3D printed sandstone. The design consists of two individual halves (Aediculae) that form a volume – the grotto. While on the outside the grotto presents itself as a flat cubical volume, on the inside a complex geometry, consisting of millions of individual facets that awaits the visitor.

The grotto was purely designed and detailed through customized algorithms. It is printed at a resolution of a tenth of a millimeter to dimensions of a 3.2-meter high, 16 square meter large room.

As it is the first architectural high-resolution 3D Print, innovative construction details had to be invented. In order to facilitate the transportation and the assembly of the massive construction, a modular system of individual, prefabricated sandstone bricks with specific details is developed. 3D-Printing as fabrication process allows the planning of three-dimensional details in an unknown consistency and precision, and offer the possibility to develop customized constructions systems.

Printed Bricks

Using currently available technology, the entire room could be printed in just six large elements. The limiting factor for the size of the elements is no longer the printable volume, but the logistics: parts need to be transportable, and they need to be lifted and positioned for assembly. We thus restricted the dimensions of elements so that they would fit onto 120 x 120cm pallets, and could be lifted by 4 people.

The weight of elements was minimized by making them hollow and by using structural analysis tools to reduce their wall thickness to a single centimeter in non-critical areas. An internal structural grid is introduced to increase stability. In the design of the elements, two different load cases were taken into consideration: their orientation in the 3D printer while they are lifted out, and their loads as assembled elements.

Each element has simple printed details for joining pieces together, and details for lifting it. Truncated cones and funnels guarantee a consistent and stable vertical alignment.


The geometry of the grottos consist of 260 million and 1.35 billion individual faces respectively. This large amount of data cannot be adequately processed by existing CAD Software. Customized algorithms were therefore developed to calculate the construction details and to convert the form into printable data.

The articulated mesh is a self-intersecting surface that does not enclose a volume as it is not a differentiable, orientable manifold. In order to extract a volume with a uniquely definied inside and outside from this geometry, a strategy analog to casting is implemented: The folded surface is filled with water. Every part that stays dry in this simulation is counted as the inside of the wall construction. As a result, a clean volume emerges.

To calculate this volumetrization and to insert construction details, the entire mesh is voxelized at resolution of 1mm (0.8mm for grotto 2), leading to 30 billion spatial data points. Such an enormous amount of information cannot be processed as a single entity in the computer: the geometry is loaded only where needed, streamed layer per layer.