Minimal surfaces have been gradually translated from mathematics to architectural design research due to their fascinating geometric and spatial properties. Tensile structures are just an example of their application in architecture known since the early 1960s. The present research relates to the problem of generating minimal surface geometries computationally using self-organizing particle spring systems and optimizing them for digital fabrication. The algorithm is iterative and it has a different approach than a standard computational method, such as dynamic relaxation, because it does not start with a pre-defined topology and it consists of simultaneous processes that control the geometryis tessellation. The method is tested on triply periodic minimal surfaces and focused on several fabrication techniques such as a tensegrity modular system composed of interlocked rings (Figure 1).