M.C.에셔의 심메트리 형식과 프랙탈 특성

The solidity and stability of symmetrical forms and structures are strongly appealing in graphic design. It plays a strong role in our aesthetic appreciation. Because of this, from ancient times until the present, symmetry has caught the interest of people from many different fields. Escher made in depth investigations into the mathematical principles of symmetry and introduced the concepts he found into his work. Escher’s investigations into symmetry and the systematic order of planes allowed him to increase the possibilities for its practical application in education and artistic creations. The following conclusions arose out of Escher’s inquiries. First, what we have to understand is that the symmetry in a form informs the shape in all aspects and will change if one moves and observes the shape from another viewpoint. Second, to understand the seventeen concepts of symmetry, one must understand not only art and creativity, but also the fundamental principles of basic form. Third, from the foundations of geometric figures, Escher presented six standard figures. These six figures are the smallest units that comprise the systematic order of planes, making up unit cell that play an important role in the creation and analysis of design patterns. Fourth, the form of expression and tessellation’s formal qualities are equal in the systematic order of planes. The systematic order of planes also blurs the difference between the background and the figure, while at all times maintaining the unique features of visual illusion. Fifth, the harmony between symmetry and fractals is made apparent when one compares all the sections of a form to each other as well as sections to the whole. Sixth, even before the appearance of fractal theory, Escher had, through the help of symmetry and fractals, opened up room for the exploration and recognition of non-Euclidean geometry.