Tessellation
October 2019The formation of an urban landscape like the Kathmandu Valley consists of two contrary processes. The first one, described in prio, is the morphology of the landscape through erosion processes (see blog "Erosion") mainly driven by water. The second one is the emergence of urban and biological structures that grow according to a systemic interconnection between various social, economic and ecologic parameters on multiple scales. These two contrary processes (Growth vs. Erosion) occur at different scales and also in a different time frame but like any other network they have an important influence on the systemic interconnections of the overall system.
In the following experiment computational Design techniques were used as a speculative approach to develop growth patterns. Using algorithms in the design process allows me to use simple principles that can create complex results which closely correspond to growth patterns found in nature.
“The successful survival of the “real-time world city” requires participation and exchange at the various social levels and material scales; a code that incorporates participation must be able to grow as the network grows, it cannot be defined a priori in a controlled or predetermined environment. “Urban algorithms” co-evolve within their milieu, the articulation of their structure increases in relation to the complexity and diversity of the urban network they serve. “Urban algorithms” are the necessary coding logics for the self-organizing city.”
Poletto/Pasquero, Systemic Architecture, p. 20
The following approach for an growth algorithm is based on the idea of 3d-tesselation. Repeating branching systems similar to the growth of a tree or a coral can be generated using simple building elements. The figures below illustrate how this looping algorithm can create a complex geometry by adding a V-shaped branch on top of itself and iterating this process multiple times. This process can be applied to an infinite variety of building elements and thus create endless amounts of output geometries.
The catalogue above shows how a deformation of the starting geometry influences the output geometry after 8 iterations of tessellation.
Using a simple plane as a starting geometry limits the tessellation algorithm to one direction. Using a V-shaped branch results in a morphology which closely corresponds to growth patterns of certain coals and various plant species.
Tesselating a branch on a cube as a base geometry let's the tessellation process take place on all 6 faces of the cube. Deformations to the base cube additionaly influence the output geometry.
These 3D-Tessellations describe a growing process which does not react to any external parameters. For a more elaborated representation of human and non-human growth patterns we have to conceive the growing urban environment as an adaptive system with constant feedback loops, rather than a deterministic system because of the constantly changing external parameters. Most patterns found in nature are created through the interaction between two or more materials with external forces (Water, Wind, Gravity etc.) driving the process.