Scale invariance in the series of Chinese-character lengths

Scale-invariant behaviors have been found in the patterns of written text in phonetic languages, such as in word-length series and word-frequency series. In this study, we examined whether the scale-invariant behaviors exist in the sequential characters of Four Great Chinese Novels. In particular, one Chinese character is featured by its length (the number of its strokes), its frequency (the number of its appearance in a novel) and the number of its interpretations in a dictionary. Then, we obtained character-length series, character-frequency series and interpretation-number series for each novel. For each series of each novel, based on the method of Detrended Fluctuation Analysis, we observed that the scale-invariant behavior, which is characterized by a scaling exponent larger than 0.5, exists at scales larger than a crossover, which is equal to the average paragraph-length, i.e. around 300 characters. Moreover, these scaling exponents are positively correlated between different types of series. Typically, the correlation of scaling exponents is largest between the character-length series and the interpretation-number series. Our findings shed light on the temporal organization of Chinese written texts, and the correlation among the character lengths, the character frequencies and the interpretation numbers.