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Minimal Complexities is an architectural design research focused on the form-finding and fabrication of minimal surface structures. Computationally generated, the surfaces use an algorithmic process inspired by principles of self-organisation found in nature, while conforming to various construction and digital fabrication parameters. Modularity and efficiency are improved through the repetition of identical components which creates intricately complex surfaces with only a few types of component, with applications in architecture, product and fashion design.