Ouroboros, or uroboros, is an ancient symbol depicting a serpent eating its own tail. The symbol appears in various cultures across the globe, and has deep roots in religion, mythology and alchemistry. We study the mythical existence by means of rational mathematical methods, resulting in chaotic motion, conflicts and contradictions. The impossible shape of ouroboros eating its own tail is made possible by elevating to the 4th dimension. We construct the ouroboros on the basis of Klein Bottle, an ideal 4-dimensional topological existence showing self-penetrating formation when projected onto 3D space.
Can supernatrual existence be reduced to scientific knowledge? Does modern technology have reenchantment potentials? Is there a boundary to algorithms and rationality? These are the questions that we put forward to audiences.
The work is done in collaboration with Haomin Xu from Chinese Academy of Fine Arts.
Technical Support, Prototyping, Modeling, Programming
Inside of Ouroboros
Distortion caused by 4D rotation
Outside of Ouroboros
We start from "pinched torus" parameterization of Klein Bottle, which is topologically equivalent to the big belly Klein Bottle shape. It is continuous and non-intersecting in 4D, but projection into 3D causes it to intersect with itself.
According to a mathematical paper Four-Space Visualization of 4D Objects, 4D geometry objects can be projected to 3D space with a certain set of matrix transformations. There is 6 basic kinds of rotation in 4D, that is rotating around axis xy, xz, xw, yz, yw, zw. We use 4D rotation matrices to drive the motion of ouroboros and then use projection matrices for visualization.
Viewing from different 4D rotation angles, the wireframe ouroboros sometimes appears extremely distorted.