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MINIMAL SURFACES AS SELF-ORGANISING SYSTEMS 2009

Minimal Surfaces as Self-Organising Systems is a research project  developed around the design problem of minimal surface structures. The outcome is an alternative algorithmic method for generating minimal surface geometries as well as several applications in building them from modular components. The alternative characteristic of the study comes from the different approach of the project, as opposed to the existing ones in the field. This uses the principle of simulation of virtual soap films in order to generate minimal surfaces, while optimizing them for a modular fabrication system. The main difference in this approach comes from the bottom-up algorithmic strategy of not starting with a predefined topology, as in the case of existing methods such as the dynamic relaxation for example, but simulating an iterative growth process, optimized to reach a state of tensional equilibrium of the system.

This method aims to define a computational framework for developing the design and fabrication of triply periodic minimal surfaces, by using a particle-spring system. The form-finding strategy is based on the properties of infinitely periodic minimal surfaces. The problem is reduced to creating the basic surface region within the faces of the kaleidoscopic cell, a basic tetrahedral geometry. After reflection this region forms a triply periodic minimal surface. Schwarz’s P Surface was chosen as a case study by which this methodology was tested. This surface’s kaleidoscopic cell is a tri-rectangular tetrahedron which represents the 48th part of a cube. While the algorithm is performing a self-organizing process of the particles to define the geometry of the surface, the springs are controlled by a custom Delaunay triangulation function in order to obtain an efficient topology. Standard sizes for fabrication components can be determined as the lengths of the springs are programmed to reach a pre-set dimension. The project is developed in Processing 1.0.6.

The architectural problem which launched the investigations of this research was essential in structuring a dual process methodology; this involves the form-finding algorithm running simultaneously with the modular dynamic tessellation of the surface. Using the particle-spring system as a framework for the simulation process, the potential of the proposed method could open new directions in the computational design field, by having the ability to involve more parameters in the generative design process. Together with achieving minimal surface properties and an optimal modular tessellation, the system could be programmed to reach a multiple objective optimisation character which could include spatial, social or structural parameters.

The algorithm is materialized through a concept derived from the principle behind the state of equilibrium of natural organisms – in strict correlation with the conservation of energy. Each iteration is programmed to update the relationships between the components of the system, reapply the defined rules and minimize the energy, in our case the tensional energy, in order to achieve a state of equilibrium. From a cellular point of view, if we were to consider the particles as cells or molecules and the springs as the forces between them, the proposed system reaches an emergent quality of self-organization similar to one found in nature.

Many thanks to: Sean Hanna, Alasdair Turner, Ruairi Glynn.  Bartlett, UCL.

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