Tackling Complexity with Additive Manufacturing: Wind Musical Instruments as a Case Study

Despite its intuitive allure, complexity is problematic to define, assess, and measure objectively. This counterintuitive realization clashes with the fact that complexity and its evaluation play a relevant, if not vital, role in everyday life and almost every kind of endeavor. Within the broad study of the different types of complexity, topological complexity refers to how intricate shapes and forms are, a highly relevant parameter for design and production. This paper advances a functional approach to define, delimit, and evaluate topological complexity for manufacturing purposes. Based on this assessment, we discuss how additive manufacturing (AM) technologies can be used to deal with the research, design, and production hurdles that topological complexity poses. Finally, experimentation with AM wind musical instruments is presented and discussed as a case study of how this has been achieved in practice.