The first figure depicts an isospectral flow through closed finite type spacecurves in R3 of spectral genus 2. The curve returns to a translation of itself. This is an example of a vortex filament flow. The spacecurves are spherical by with changing sphere radius.
The second image depicts an isoperiodic flow through elastic torus knots in R3 of spectral genus 1, from a 2-wrapped circle to a 3-wrapped circle. In contrast to isospectral flows, the spectral curve changes during isoperiodic flow. Both flows preserve the closing of the spacecurves.