Characterization of Cultural Traits by Means of Fractal Analysis

Archaeology, as a science, dares to explain how extinct societies functioned. As in all sciences, knowledge is built through the classification of data. In this case, data appear as fragments of objects that human groups have left behind. Traditionally, archaeological classification systems use stylistic criteria to assign the belonging of fragments to a territory, to a moment in time, and to a culture. The underlying idea is that changes in the characteristics of objects respond to changes in cultural processes. Despite a long tradition in the analysis of archaeological material, there is still a significant subjective component in which the classification criteria should be. If the archaeologist uses one that is too broad, then fragments with very diverse characteristics can be included in the same group. Conversely, if the criterion is too narrow, fragments that are very similar to each other, but not identical, will not be considered of the same type. Conclusions that depend on the size of the tool used in the analysis do not seem to be very sound. Therefore, the limits of traditional archaeological analysis have been reached. New perspectives are required to move forward. In this chapter, it is proposed that social vestiges acquire fractal properties by the repeated iteration of culturally transmitted rules embedded in their production processes. Complex patterns emerge in a variety of cultural manifestations, but are all related to the way in which cultural practices of different groups occupy space: practices related to, for example, tool elaboration, symbolic representation or the choice of the geographic location where they settle. Fractal properties are the reflection of these cultural practices and the metrics that synthesizes the properties of each of the cultural manifestations is its fractal dimension. The fractal signature is built as a distinctive set of fractal dimensions of cultural traits of a social group. This is intended with the construction of the Xajay culture's "fractal signature." Xajay civilization flourished to the south of the northern border of Mesoamerica from around 350 AD until its collapse in 900 AD.