# Minimal Path Networks

Minimal path networks denote the shortest connections between sets of nodes.

In the physical world, soap film behaves in a manner which minimizes its surface area given a certain boundary. The edges of multiple minimal surfaces form spatial minimal paths as analyzed by Frei Otto through the Minimal Way Apparatus in 1988.

Recent developments allow us to digitally simulate minimal paths. They can be resolved by energy minimization techniques by computing the equilibrium configuration. This task of combinatorial optimization for finding the shortest connections between points in space is known in mathematics as the "Steiner tree problem.” In the Steiner tree problem, extra intermediate vertices and edges may be added to the graph in order to reduce the length of the spanning tree. Each of the new points must have a degree of three and all the angles between the edges incident to such a point must be equal to 120 degrees. These characteristic features of all minimal path systems make them highly appealing for an architecture of minimal material usage.

The potential architectural applications of minimal paths are not limited to the building scale. We also investigate to which extent minimal paths can be applied in urban planning strategies.

(F. K. Hwang, 1992), (Frei Otto, 2001), (Gass, 1990), (Leach, 2009), (Otto, 2008)

Peter Cachola Schmal, Oliver Elser (2012), The architectural model_Tool,Fetish, Small Utopia

Form Force Mass 5 _ Experiments/Experiments on dependence of form, force and mass.Process of self generation in biology and building. Formfinding and methods of modelling.(Thesis of Siegfried Gaß) (1990)(288 S., 1023 III., DM 68,--)