*4.5. The Fractal Dimension*

Very often such local parameters as its length or width of the opening are insufficient to describe the complexity of the cracking pattern. Thus, in recent years there has been a growing interest in using the concept of fractal dimension for this purpose. The use of fractal geometry to characterize the cracking pattern has many advantages compared to the use of Euclidean geometry. In order to use this dimension, it is necessary to assume that the structure created by the cracking pattern is in fact a fractal, i.e., it has certain characteristics such as [103,104]:


Looking at these assumptions, it is not difficult to resist the impression that the cracking pattern visible on the surface of cement composites fully meets these assumptions. In such a case, in the fractal geometry, it is the fractal dimension that determines how densely a fractal fills the metric space it is in. In the studies on the cracking patterns described so far, the fractal dimension is used as a stand-alone parameter, but often also serves as a component of an extensive index for evaluating the degree of material degradation [105].
