assume that the center line of the vortex has Hausdorff dimension one, i.e., $D_c=1$, and therefore [@pesin09] $$D
  =
  D_c + D_\Sigma
  =
  1  +  D_\Sigma.$$

We suggest that tornadoes have approximately fractal cross sections based on graphical evidence provided in Figures \[fig:hier-vort\], \[fig:suctionspots\], \[fig:tornado\_fractal\], and \[fig:gene-moore\]. This suggestion is further supported by the existence of subvortices within subvortices (see Figure \[fig:hier-vort\]) as shown in recent videos [@wadena10; @elrenovideo13]. In particular, a multiple vortex distribution in a larger tornado shown in Figure \[fig:wurman\_radar\] exhibits an approximate fractal (box counting) dimension in a range from $1.4$ to $1.7$ computed using pairs of grid sizes $\varepsilon$ and $2\varepsilon$ with $\varepsilon$ fine enough to resolve the subvortices in the radar data; the smallest $\varepsilon$ used in the computations was $250$ m. Other radar images in, for example, [@wurman02; @kosibawurman08] can be analyzed in a similar way.

![A tornado and a vortex sheet roll-up over Lake Wilson, Russell County, KS, May 7, 1993; © Gene Moore. “Some very subtle features make this one of the most interesting tornado photographs ever taken. As the tornado funnel swept across Lake Wilson, what MAY have been the rear flank downdraft wrapped cyclonically around the south side of 