The main objective of this paper is to demonstrate that the developed exploratory data analysis algorithm can be applied to the processing of pattern systems, data sets, and their cladistic modelling. Pattern systems are specific representations of symbolic communication, consisting of symbols and the syntactic rules that govern their use. Among the pattern systems, the authors focus specifically on those exhibiting temporal evolution, particularly historical scripts. The cladistic method presented has been applied to selected varieties of Arabic and Aramaic scripts. The cladistic models were created by the maximum parsimony and the maximum likelihood methods; three indexes evaluated the obtained cladograms, namely length, consistency index, and retention index. To find the most parsimonious tree and optimize the initial brute-force searching, the branch and bound and heuristic searching optimization methods were applied. The results that have been getting from different methods were plotted on cladograms.