This work visualizes the surface swept by a vortex filament evolving from a square loop under the vortex filament equation, which models the self-induced motion of vortices in an ideal, inviscid fluid such as smoke rings or bubble vortices. While these flows usually produce smooth motion, the equation admits well-defined evolution even for polygonal vortex filaments with corners. These evolve periodically and generate trajectories with multifractal properties. The rendered surface reveals the geometry of this motion, exposing layered, Romanesco-like patterns that emerge from a single local rule. How much of this intricate geometry can be captured in real experiments with vortex rings remains an open and exciting question.
https://gallery.bridgesmathart.org/exhibitions/2026-jmm-art-exhibition/jiri-minarcik
