About the animated GIF

This animation was produced using Mathematica 3.0, together with Ulead GIF Animator (to assemble 67 individual GIF files into an animated GIF file). The animation illustrates a mathematical construction described in Straightening soliton curves -- see Recent papers for a downloadable version of the paper. In this particular example, the initial curve is a planar elastic curve (described explicitly in terms of elliptic integrals). Going forwards (or backwards) in time, the curve lifts out of the plane, unravels, and approaches a straight line (for ease of viewing, the animation has been looped). More subtle is the time evolution of twist in the binormal ribbon displayed in the animation; the latter exhibits apparent interconversions of twist and writhe, in the sense of the Calugareanu-White Theorem. (As in some of the famous applications of the theorem in molecular biology, pioneered by Vinograd and Fuller, there is not actually a smooth closed framed curve, so the use of the theorem is not entirely straightforward.)

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