The geometry of the H I of several members of the M81 group: The H I is fractal

We use the box-counting method on single H I contours and the perimeter-area method on families of contours to show that the projected H I distributions of seven members of the M81 group are fractal. All seven have fractal dimensions that cover a small range, 1.5 greater than or equal to D greater than or equal to 1.2. This is nearly the same dimension as that of CO clouds in the Milky Way and suggests that the ISM may have a fractal dimension that stays within a limited range at all scales. Reliable determination of fractal dimension requires that observations be made with high angular and frequency resolution. If theorems of projection of opaque fractals apply to H I, then the dimension of the deprojected H I distributions may be 1.5 greater than or equal to D greater than or equal to 1.2 as well. Fractal structures have much more surface area than smooth structures, allowing heating, cooling, and material exchange to proceed much more rapidly.