_zur form (_on form) is a collaborative mixed-reality installation by Florian Grond, Thomas Kienzl and Gabriele Engelhardt. In it, mathematical formulas are transformed into 3D forms and are presented as sculptures together with a tangible mixed reality installation. The project also features photographs of the support forms, the negative casts that emerge out of the form production process.

_zur form makes a contemporary contribution to the well-established tradition of representing mathematical functions as 3D forms, which dates back to 19th-century Germany. The early forms inspired a number of artists in the 19th and 20th centuries, and also became the point of departure for the conception of our project.

In German, the word "begreifen" (to understand) literally means to grasp an idea, as with a hand. The transformation of formulas into forms also emphasizes the original meaning of the word "information," which is "bringing into form." Thus, by making tangible objects out of abstract mathematical concepts, the sculptures and their representations underline both the material and physiological aspects that pertain to the construction and accessibility of knowledge.

The represented forms emerged out of Florian Grond's research into the stability of chaotic attractors, which are solutions to nonlinear differential equations. Grond developed algorithms that accentuate the curious topological properties of chaotic attractors.

Thomas Kienzl developed a tangible mixed reality interface (MRI) for the project. The MRI allows for a tactile manipulation of the mathematical objects in virtual space.

Gabriele Engelhardt's photographic work focuses on various sculptural elements. With her photographs of the negative casts of these forms, Engelhardt extends the tradition of using mathematical functions as model objects in the history of photography.

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