Bone microarchitecture is the predictor of bone quality or bone disease. It can only be measured on a bone biopsy, which is invasive and not available for all clinical situations. Texture analysis on radiographs is a common way to investigate bone microarchitecture. But relationships between three-dimension histomorphometric parameters and two-dimension texture parameters are not always well known, with poor results. The aim of this paper is twofold : to study one classical parameter namely the fractal dimension which is easily computed on the 2D binary texture and to explore its relationships with the microarchitecture. We performed several experiments in order to check from ground truth the different possible values and their possible explanations. The results show great variations of the fractal dimension according to the size of the window and its location. These variations can be explained by the number of trabecular and their characteristics inside the window where the fractal dimension is computed. This study also shows a specific interest to work with dual fractal dimension of the bone-spongious tissues. This dual information associated with several radiographic images can give a global idea of the number of trabecular segments and their thickness and constitutes a new histomorphometric parameter.