A single filament with a variable core size parameter is used to model how a vortex tube breaks down in the Euler equations. The first singularity is a self‐similar collapse which brings two antiparallel pieces of filament together at a point. This pairing then quickly encompasses a finite fraction of the initial data and the arclength begins to grow faster than exponential. A local model should exist which would allow one to understand the stage of rapid stretching in terms of simpler processes.