<p>There are two types of expressions in modeling composition in which shapes are arranged from structure based on a mathematical order (hereafter referred to as a mathematical structure) such as a square lattice or a regular polygon. One is a regular expression that excludes arbitrariness and chance, and the other is an irregular expression that deliberately arranges uneven shapes. There is still yet any research, however, that comprehensively captures these as the development of works based on mathematical structures. In this study I aimed at arranging works based on mathematical structures by first organizing the method of introducing irregularity.</p><p>The subject of this research is limited to expressions based on two-dimensional mathematical structures, the most basic approach. The subject of the survey is limited to static expression. The five ways for introducing irregularities that were made apparent from discussions are as follows:</p><p>1) Using natural or unevenly generated materials</p><p>2) Established directly in the medium as a trace of an act that incorporates chance</p><p>3) Making the distribution of labels irregular in the process of labeling, which is done to systematically assign a specific form or action to the smallest unit of a point, line, or plane of structure</p><p>4) Incorporate random elements based on chance or arbitrariness into the operation content assigned to the label.</p><p>5) Transform the structure irregularly</p><p>The results of this research will be the basis for future research that expands the foundation and development of expression by systematizing formative design using mathematical structures.</p>