Tortoise: An Algorithmic Fractal Torus Linking Hopf Geometry, Sacred Symbols, Myths and Altered-State Visual Experience

Tortoise is an animated algorithmic artwork by Fabin Rasheed built by overlaying two oppositely rotated Hopf fibre bundles and recursively repeating the resulting structure into a fractal torus. Its nested geometry produces a “wheels within wheels” appearance, with particles moving along fibres and tori evolving across the surface. An interactive visualiser varies the artwork’s parameters to create visual matches with 37 scientific concepts, sacred-geometric forms, religious symbols, architectural patterns and visionary-art references, including black holes, wormholes, the Sri Yantra, Kurma, Ezekiel’s Wheel and rose windows. The work presents these as visual correspondences rather than proven derivations, especially where scientific claims are concerned. A further phenomenological layer uses AI image-generation systems to place psychedelic, natural, architectural and physical imagery over the same geometric blueprint, exploring how different people may experience varied beings and forms while responding to a shared underlying structure.