Kontinuum combines the mathematical iterations 3 to 11 of the Sierpinski curve into a flowing form that develops towards a dense top surface. This gradual densification enhances both structural integrity and visual complexity. The resulting shape is efficient, slightly flexible and durable, making it suitable as both a stool and a small side table.
Our main goal was to design a 3D-printable stool that is both strong and efficient to print, ideally on consumer-grade printers. We had to rethink the fundamentals of printing large objects to keep production times and costs down.
Subdividing the seating surface reduces the need for thick top layers while maintaining strength. Fractal patterns, particularly the Sierpinski curve, are ideal for this. Its closed perimeter and symmetrical nature make it particularly well suited to 3D printing, allowing an efficient, strong design with minimal use of material.
The result is a naturally flowing shape that gradually transitions through different iterations of the curve. At the base, an early generation forms four distinct legs, while towards the top a later generation creates the seating surface, all printed in one continuous extrusion, making Kontinuum a fusion of mathematics, natural aesthetics and technology.
The Sierpinski curve is a recursively defined fractal curve that evolves by subdividing a 2D space and connecting these subdivided areas with a continuous line. With each iteration, the curve becomes more intricate, filling more of the space and creating a denser structure.
Kontinuum's parametric design allows for extensive customisation. Using a Grasshopper script, users can make adjustments to height, shape and other parameters, affecting both aesthetics and functionality. This gives customers the unique opportunity to create a personalised, bespoke piece of furniture that is only possible with additive manufacturing.
The manufacturing process is fully optimised for FFF (Fused Filament Fabrication). The parametric structure allows precise control of the slopes, ensuring that no overhangs exceed 30-40 degrees. In addition, the aforementioned closed contour of the stool and the use of relatively thick and wide extrusions allow it to be printed in a continuous loop, making the printing process both reliable and clean.
To reinforce the structure, especially in the most flexible central area, an internal cross-shaped support has been added. Each side of the cross extends into the centre on different layers, ensuring a strong connection in both the X-Y and Z directions. This structure was designed to be printed seamlessly in vase mode, resulting in an exceptionally rigid and durable joint.
Michel Bauer
Kontinuum is 3D printed using highly recyclable PETG, a durable and impact resistant material widely used in additive manufacturing. PETG offers an ideal balance of strength and flexibility, making it work well with the natural resilience of the Sierpinski curve.
A core goal of this project was to fully utilize the efficiency of 3D printing and to showcase what is possible with local, on-demand production and sustainable material use. By using additive manufacturing, each stool is produced with minimal material waste and without the need for large-scale industrial tooling, thus highlighting the potential of 3D printing as a sustainable alternative in modern furniture design.
This project was developed together with Michel Bauer as an Applied Research Project during his internship.
