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Parametric designThe term “parametric design” describes how a given parameter—or data—is able to determine a specific outcome out of the multiplicity provided by a domain. An example of a parameter could be the floor to ceiling height in a tower project. Such parameter could define the overall subdivision of the building mass and generate variation in the final number of floors. Through the use of computer programming or scripting, architects started to engage with procedural definitions, e.g., sequential rulesets that could cascade into one another, determined by the specified parameters. The mathematical and logical relationships that form became the basis of associative geometries that would further characterize the evolution of parametric principles. Parametric design is characterized by tools of interpolation. The gradient becomes a design tool allowing transitions between a multiplicity of design constraints. This is the way in which spline modeling started to impact the world of designers, offering geometric construct with a small number of control points that would result in a mathematically interpolated curve. Spline modeling can be found to be the basis of many software algorithms and tools used to facilitate design. For example, the CatmullClark algorithm integrated into Autodesk Maya software allows the transition from polygonal geometries to intensive plastic topologies. Marching Cubes algorithms allow the generation of geometries and surfaces using any number of isolated inputs, merging discreteness into unified shells. Software FIGURE 2.4 Monolith Interface for voxelbased modeling developed by Andrew Payne. FIGURE 2.5 Graded 3D printed material intensities produced with Monolith developed by Panagiotis Michalatos. such as Monolith, developed by Payne and Michalatos,^{16} provides the infrastructure to think of form as a pixel field of materials—a voxel—that can gradually transition between properties of color, elasticity and opacity, linking directly with the most advanced 3D printing technologies currently available. The Grasshopper plugin for Rhino^{17} constitutes one of the most widely adopted pieces of digital infrastructure for the development of the continuous paradigm, allowing its users to parametrize all the possible variables in a piece of geometry. A parametric definition can be characterized by the “slider”; a digital construct within the parametric repertoire that allows designers to suspend the necessity FIGURE 2.6 3D printed CHAIR by Zaha Hadid and Patrik Schumacher in collaboration with STRATASYS, 3D printed on the Stratasys ObjetlOOO MultiMaterial 3D Printer. Source: Courtesy of Zaha Hadid Architects FIGURE 2.7 The Heydar Aliyev Center in Baku by Zaha Hadid Architects. The design demonstrates Schumacher’s view of parametric articulation, interpolating the building with the landscape. The project portrays the dissolution of tectonics, where details are minimized in favor of the fluidity of form. Source: Courtesy of Zaha Hadid Architects for decision making, allowing decisions to become a variable that exists within a domain. As the slider starts to recur through a parametric model, the model grows in its multiplicity of possible outcomes, defining not a particular solution but a solution space. This solution space defines final form through a complex interplay with clients, budgets and regulations. The commercial adoption of parametric strategies is linked to the ability to digitally simulate large populations of possible designs and testing them with performative criteria. The testing of different parameters, using sliders positioned against a given performative criteria such as structural efficiency, mean that some solutions perform better than others. This process, known as optimization, has been widely adopted by large architecture and engineering practices in the past decades. Architects such as Kostas Terzidis have claimed that in the model of parametric optimization, design becomes a permutation enterprise, where the search for the optimal parameters for a given design problem can yield an objectively better solution.^{18} Such assessment requires us to first accept that there could be an optimal solution to the problem of architecture. The strategy of parametric design could be then understood as practice of model making that declares the boundaries of a problem, variables to be considered and by omission, variables to be excluded. The definition of such a mathematical domain also assumes that an answer to a design problem lives within the domain specified, validating the tools that have been generated for its resolution.The notion of optimization has its own tradition in architecture modeling, as it predates digital technologies. As we will evaluate later, architectengineer Frei Otto since the 1960s developed a framework for modeling form founded in the notion of optimization and selforganization he called “form finding.” 
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