Tortoise: An Algorithmic Fractal Torus Connecting Hopf Geometry, Global Symbols, Myths and Altered-State Visions

Tortoise is an animated algorithmic artwork by Fabin Rasheed built from two oppositely rotated Hopf fibre bundles repeatedly nested at their intersections to create a fractal torus with a “wheels within wheels” appearance. Inspired by “turtles all the way down” and Kurma, Vishnu’s tortoise avatar, the project includes an interactive visualiser that varies the artwork’s parameters to produce visual matches with 37 scientific concepts, sacred geometries, religious symbols, architectural forms and visionary art. Rasheed stresses that these are pattern matches rather than proven historical, scientific or metaphysical connections, with the scientific interpretations especially speculative. A later phenomenological layer uses ControlNet and Stable Diffusion to render different beings, objects, natural forms and environments over the same geometric blueprint, exploring how shared underlying structures might produce diverse altered-state experiences.