FRACTAL DIMENSIONS OF DIFFERENT WRITING SYSTEMS AND THEIR POSSIBLE IMPLICATIONS

Resumo

The fractal dimension is an indicator of structural complexity. It represents a ratio of the change in the details of a pattern to the change in the scale used for measuring it. In this study, fractal analysis was applied to different writing systems. Each script investigated was considered as a distinct image and its fractal dimension value was estimated by using the box-counting method. Firstly, the presence of characteristic fractal dimensions for Greek, Latin and Cyrillic was established by using different types of fonts to show the validity of such an investigation. Then, possible relationships were sought for between different writing systems by considering their fractal dimensions. It was observed that some scripts with known close relations indeed exhibited relatively close fractal natures in the range of mesh size used in the calculations. Latin and Cyrillic known to be derived from Greek exhibited fractal dimension values rather close to and slightly higher than that of Greek. This might imply the increase in complexity of a writing system as other scripts are developed from it. Arabic and Hebrew, Devanagari and Thai, Armenian and Georgian exhibited quite similar fractal natures to each other, supporting available knowledge/speculations on their kinship. The Korean script, which is known to be developed uniquely, was investigated for obtaining some clues about its possible inspirations. The fractal dimension of the Korean writing system Hangul was determined to be close to those of Devanagari and especially Thai scripts, when the Far East scripts were taken into consideration. On the other hand, the fractal natures of the Old Turkic and Japanese scripts seemed to be less similar to the Korean script. As shown in this study, fractal analysis may be utilized as a helping tool, together with other techniques, in determining the origins and/or relatives of various unknown scripts, or alternately to show that they are irrelevant. Additional information, such as regional and historical relationships between different writing systems may reinforce the implications obtained from investigations carried out by fractal analysis.