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Designers, students and educators of design use graphs and diagrams to illustrate the process of product analysis and synthesis. The available visual aids in the toolbox of designers are extremely limited. This article introduces a new pictorial representation tool that helps designers encode the process of composing and classifying the forms of generated designs. The proposed tool is based on a cross-cultural reproduction of finite state automata from the field of formal languages to represent the form derivation process in architectural design. Exercises on some applications of the new tool are constructed to illustrate an incremental process of form generation in design. The proposed tool implementation as suggested by the exercises can be used to train students to think logically and analytically about the design process. However, within the scope of this article, the tool is not tested in real design studio settings. The tool is developed to form a basis for further transformations from mathematical formalisms into computerized models that may be used to automatically derive, analyse and recognize stylistic features of formal compositions, and may be further developed into an E-learning design program.