The description of pores and fracture structures is a consistently important issue and certainly a difficult problem, especially for shale or tight rocks. However, the exploitation of so-called unconventional energy, such as shale methane and tight-oil, has become more and more dependent on an understanding of the inner structure of these unconventional reservoirs. The inner structure of porous rocks is very difficult to describe quantitatively using normal mathematics, but fractal geometry, which is a powerful mathematical tool for describing irregularly-shaped objects, can be applied to these rocks. To some degree, the cementation index and tortuosity can be used to describe the complexity of these structures. The cementation index can be acquired through electro-lithology experiments, but, until now, tortuosity could not be quantitatively depicted. This research used the well-logging curves of a gas shale formation to reflect the characteristics of the rock formations, and the changes in the curves to indicate the changes of the rock matrix, the pores, the connections among the pores, the permeability, and the fluid type. The curves that are affected most by the rock lithology, such as gamma ray, acoustic logging, and deep resistivity curves, can provide significant information about the micro- or nano-structure of the rocks. If the rock structures have fractal characteristics, the logging curves will also have fractal properties. Based on the definition of a fractal dimension and the Hausdorff dimension, this paper presents a new methodology for calculating the fractal dimensions of logging curves. This paper also reveals the deep meaning of the rock cementation index, m, through the Hausdorff dimension, and provides a new equation to calculate this parameter through the resistivity and porosity of the formation. Although it represents a very important relationship between the saturation of hydrocarbons with pores and resistivity, the Archie formula was not available for shale and tight rock. The major reason for this was an incorrect understanding of the cementation index, and the calculation of saturation used a single m value from the bottom to the top of the well. Unfortunately, this processing method is clearly inappropriate for the intensely heterogeneous material that is shale and tight rock. This paper proposes a method of calculating m through well-logging curves based on a fractal geometry that can change with different lithologies, so that it would have more agreement with in situ scenarios than traditional methods.