Fractal which was named by Mandelbrot in 1975 and its theory have been taken notice of many fields of scholarship, namely mathematics, physics, geography, architecture, art, philosophy and so on. If we approach Fractal on the basis of the designing cogitation, it can be used not only as one of materials to take a crease thinking in design, also as a due of the methods to assess the design problem with a new point of view. Based on above background, in this study, it was studied on the graphic artist, Morits Collelius Escher who has been well known as the great artist of illusion," and on the attributes of Fractal which were contained in his various workulcorner As a reset, the four attributes, namey ′fractal dimension′, ′self-similarity, ′recursiveness′and ′infinity were founded in his works. Also, it was founded that Escher had employed the attributes of Fractal in his almost works for "the representation of the condition of unified-duality," that is to say, for the union of two different dimensions. After this, it is expected that this study shoed be extended to the development of the principle of Fractal-Design on the basis of ′Fractal which can be defined as the phenomenon of repetitious pattern between chaos and order and′the formative beauty of Fractal′.