It has not been easy to distinguish between tornadic and nontornadic mesocyclones based on such single parameters such as maximum rotational speed, maximum vertical vorticity, or radius of maximum tangential speed. Past studies trying to use these single parameters to estimate a mesocyclone’s tornadic potential turns out to be inclusive. Inspired by rapid spreading of fractal geometry into numerous areas of physics, a unique method to look at some simple parameters such as maximum vertical vorticity of a mesocyclone in the fractal geometry perspective is investigated using ELDORA data from VORTEX 95. It is found that there is a linear relationship between Log (L) and Log (VORT) for various L, where L is the horizontal resolution and VORT is the maximum vertical vorticity of the mesocyclone obtained under this particular space resolution. The linear vorticity curve suggests that the vorticity obtained using different space resolution resembles the power law demonstrated by a fractal structure. The slope of the vorticity line bears a characteristic that is unique to this particular mesocyclone. The Log (VORT) / Log (L) curve was produced for the tornadic Garden City and nontornadic Hays mesocyclone for L ranging from 0.3 km to 9.6 km. It is found that vorticity line of the tornadic mesocyclone has a steeper slope compared with that of the nontornadic mesocyclone. It is speculated that the slope of the vorticity line might be an indicator of a mesocyclone’s tornadic potential although more case studies definitely will be needed to validate this claim.