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It is known that for any non-zero $M in (-1/4,infty)$, if we roll the conic{(x,y): 4 x^2-y^2/M}=1} on a line in a plane, and then we rotate about thisline the trace of a focus, then we obtain a surface of revolution D(M) withmean curvature 1. If M<=0, D(M) is embedded and it is called unduloid, if M>0,D(M) is not embedded and it is called nodoid. These surfaces are calledDelaunays and they are foliated by circles. The trace of the focus in theconstruction above is called the profile curve of the Delaunay and it istransversal to the circles. Another well known family of constant meancurvature surfaces are the Twizzlers, they are foliated by helices and we cannaturally define a profile curve which is transversal to the helices. To makethe presentation in this abstract easier, we will be only considering Twizzlerswith mean curvature 1. In this paper we will prove that if we roll the profilecurve of a Twizzler on a line in a plane and, simultaneously, we move thepoints in the line at the same speed, so that the rolling motion of the profilecurve looks like if it were placed on a treadmill, then, the trace made by theorigin of the profile curve is one of the closed heart-shaped curvesHS(M,w)={(x,y) : x^2+y^2+y/(1+w^2 x^2)=M} for some M>-1/4 and w>0. Using thisdynamical interpretation we will prove several properties for Twizzlers

A dynamical interpretation of the profile curve of cmc Twizzlers surfaces