Aiming at the increasing research demand of the resonance properties of semantic waves in quantitative analysis of English corpus, this paper constructs a three-dimensional integrated fractal model of semantic waves, and extends the transformation of semantic waves in system functional linguistics to the lexical grammar level. The in-depth analysis provides objective and explicit analysis and identification criteria for the study of semantic waves in the legalized code theory. Through the experimental method, the type resonance characteristics between different types of semantic waves in English popular science discourses are investigated. The experimental results show that the frequency of peaks and troughs varies from 2 to 153 based on different characters, and the construction of different types of semantic waves presents the legalized communication process of knowledge popularization, embodies the social education essence of popular science practice, and is the basis of popular science discourse. The legal representation of persuasive and informative discourse features in the process of knowledge construction provides a reference standard.