A mathematical formulation and computational exploration of Yayoi Kusama’s tentacle artworks

Yayoi Kusama, renowned for her three-dimensional modern artworks, is particularly famous for her tentacle-themed pieces. Each of these works features a room with multiple surfaces, resembling tentacles, where each of these surfaces may be viewed as an incomplete monotonically decreasing sequence (where it has been cut before the convergence). While Kusama's approach is purely artistic, it raises an intriguing mathematical question: Given a surface defined by a monotonically decreasing sequence of j (sufficiently dense) layers, can we predict the surface continuation (by layers) for [Formula: see text], and is a convergence being obtained? We aim to provide a mathematical perspective on abstract art and enable its analysis from a computational perspective. To achieve our purpose, we first made a 3D computer model of each of the tentacles which was created by the designer in the team (for a given 2D image). Second, the computational team received this modeling, sampled it; and formulated a prediction algorithm for a given tentacle. Third and last, each of the tentacle predictions has been sent back to the designer, which smoothly reconstructs each tentacle by the algorithm continuation, locates each continuation in a similar way to the original room in the 2D image and wraps it with the respective texture. In this fashion, the viewer can compare the original artistic artwork of the tentacle room to the mathematical analysis predicted room.