The rules of the random walks in Japanese and English were defined as shown in Fig 1A and 1B, respectively, although other configurations could not be excluded. Axis rotation should not have changed properties such as the fractal dimension or periodicity. In our rule, the initial position of the text was always (0, 0) in the (x, y) coordinates. In Japanese, when i-th vowel was “a” (i.e., “a,” “ka,” “sa,” “ta,” “na,” “ha,” “ma,”“ya,” “la,” or “wa”), then the i-th position increased by one in the y coordinate [i.e., (xi, yi) = (xi-1, yi-1+1)]. When the i-th vowel was “i” (i.e., “i,” “ki,” “si,” “ti,” “ni,” “hi,” “mi,” or “ri,”), then (xi, yi) = (xi-1+1, yi-1). When the i-th vowel was “e” (i.e., “e,” “ke,” “se,” “te,” “ne,” “he,” “me,” or “re”), then (xi, yi) = (xi-1−1, yi-1). When the i-th vowel was “o” (i.e., “o,” “ko,” “so,” “to,” “no,” “ho,” “mo,” “yo,” or “ro”), then (xi, yi) = (xi-1, yi-1−1). On the other hand, when the i-th vowel was “u” (i.e., “u,” “ku,” “su,” “tu,” “nu,” “hu,” “mu,” “yu,” or “ru”), then it remained in the same position [i.e., (xi, yi) = (xi-1, yi-1)]. We ignored punctuation characters and space for analysis. All Kanji (Chinese characters) were converted to Kana (Japanese syllabaries), and then above rules were applied.

Since vowels in English are more complicated than those of Japanese, just for comparison, we selected five characters, i.e. when i-th character was “e”, then the i-th position increased by one in the y coordinate [i.e., (xi, yi) = (xi-1, yi-1+1)]. When the i-th character was “o”, then (xi, yi) = (xi-1+1, yi-1). When the i-th charcater was “a”, then (xi, yi) = (xi-1−1, yi-1). When the i-th vowel was “r”, then (xi, yi) = (xi-1, yi-1−1). On the other hand, when the i-th character was “i”, then it remained in the same position [i.e., (xi, yi) = (xi-1, yi-1)]. We ignored punctuation characters and spaces for analysis. Also the analyses were case-insensitive. Although there are many ways for selection of characters in English, and the rule described above is just conventional, but generality is not lost in view of fractal analyses and Fourier transformation.

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