## Vega, Luis

The pictures of these section are related to the work I started with F. de la Hoz on 2013 about the Vortex Filament

Equation (also known under the names of Localized Induction Approximation and the Binormal Flow) for a

regular polygon. In this work we performed some numerical experiments establishing a connection with the so-called

Riemann's non differentiable function. After several works with V. Banica we have rigorously proved in

arXiv:2007.07184 that these experiments are correct.

Our results also suggest that if the initial datum is an equilateral triangle for later times the triangle should switch

the axis up and down each half of a period. Also for intermediate times skew polygons with a number of sides that

are multiple of three should be created like for example a skew polygon with six sides.

Below you will find some "domestic" experiments using a smoke cannon done with a card box. And finally some

experiments done in the James Franck Institute of the U. of Chicago (USA) and some numerical simulations done

by F. De La Hoz and S. Kumar.

### Simulations

### Some Vortices

"Vortex 1"

"Vortex 2"

"Vortex 3"

"Vortex 4"

"Vortex 5"

"Vortex 6"

"Vortex 7"

"Vortex 8"

"Vortex 9"

"Vortex 10"

### Vortex Filaments Movies