{'fraction_non_alphanumeric': 0.019448946515397084, 'fraction_numerical': 0.0, 'mean_word_length': 5.0, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Rhythmic generation of trees and languages

This work builds on the notion of breadth-first signature of infinite trees and (prefix-closed) languages introduced by the authors in a previous work. We focus here on periodic signatures, a case coming from the study of ra-tional base numeration systems; the language of integer representations in base p q has a purely periodic signature whose period is derived from the Christoffel word of slope p q . Conversely, we characterise languages whose signature are purely periodic as representations of integers in such number systems with non-canonical alphabets of digits.