Variance in the distribution of the winding angle, plotted here as a function of distance along the curve for the four experimental systems and numerical model, all of which exhibit the same logarithmic scaling with a slope of 6/7 (dashed line). The inset shows the distribution of winding angles for a fixed distance along the contour, which is closely approximated by a Gaussian (dashed line). Both findings are consistent with that predicted for conformally invariant curves, which exhibit the same fractal dimension that we obtained for our data in a . The dashed lines correspond to a slope of 6/7 and a standard Gaussian distribution. The inset also shows that the winding angles are obtained for segments of contours with lengths of 64 (filled symbols) and 512 (empty symbols), and measured relative to the average angle of the contour. Here we show the mean (symbol) and s.d. (error bar) from n > 85 separate measurements of the flow field for each dataset ( Methods ).
