The aim of the study is to identify the innovative methods of artistic cognition characteristic of poets in the postmodern era. The scientific novelty of the study lies in the fact that the author identifies such methods of artistic cognition as artistic fractal, chaotic thinking, cognition through linguistic structure and interaction with the reader, the functioning of which is considered based on the American language poetry of the late 20th century. The specific characteristics of the postmodern poets’ creative thinking, expressed in a special language of lyrical texts, are determined. As a result, it has been found that the chaotic nature of modern creative thinking is realized by such linguistic means as paradox, oxymoron, paronomasia, an extended metaphor, a semantic flow, a line break, etc. One of the forms of the chaotic nature as a method of artistic cognition are fractals, represented at the structural level as complex graphic systems. Cognition through linguistic structure is realized both at the lexical (paronomasia, metaphor, oxymoron, paradox) and the grammatical (a line break, violation of grammatical norms, use of graphic symbols and drawings) level. Interaction with the reader is carried out in the course of solving logical riddles represented by paradoxes.