Just as computer screens allow us to represent 3-dimensional objects in a 2-dimensional image, the AlloSphere allow us to represent 4-dimensional objects in a 3-dimensional image. This image shows a section of the Hopf fibration, the visualizations of a hypersphere in four-dimensional space. "This photo was taken during a talk about the mathematics of the sphere in four-dimensional space conducted in the AlloSphere, which can be used to render real-time visualizations of four dimensional shapes, a capability currently being exploited by a joint effort of the Media Arts and Technology department and the Mathematics department. The surface of the four dimensional ball is three-dimensional (much as the surface of a normal ball is 2-dimensional), and admits a perspectively correct projection into ordinary three-dimensional space. This particular function was discovered in the 1930's and lies at the foundation of much beautiful mathematics, so was an obvious first choice of mathematical object to try and explore using the AlloSphere.