aperiodic modularity

Hybrid Danzer System

This is a modular system based on Danzer geometry for the generation of aperiodic as well as periodic space systems. The Danzer System is a further development of two-dimensional surface tessellations into the third dimension. Its tiling consists of four tetrahedrons and their mirrored counterparts, which can be divided into self-similar tiles in the ratio of the golden section. Despite their modularity and self-similarity, they do not show any symmetry of displacement.
Based on this basic geometric principle, a serially producible modular system was generated. The basic shapes of the Danzer tiling could be transformed into point-symmetrical modules, which are both initial geometry and mirrored counterpart by simply rotating them around their pivot point. Instead of the eight tetrahedrons, now only the four point symmetrical modules are needed for geometry generation.
In the following steps, joining methods were developed based on the appropriate handling of the material and the cutting logic of a CNC hot-wire machine. In order to be able to further use the point symmetry of the modules, a positive connecting element was placed on one side of the bodies and the corresponding negative connecting element on the other side, based on the tongue and groove principle.
The modules can be connected to each other but also with themselves. Thus, the initial system was transformed into a hybrid that can be joined both a-periodically and periodically to create complex spatial geometries.