The regular plane division of mosaic graphics is called mosaic, and mosaic graphics are the arrangement of closed graphics, with no overlap and no gaps. Generally speaking, the basic unit of mosaic pattern is polygon or similar conventional shape, such as square tiles commonly used on the floor. However, escher is fascinated by every kind of mosaic, whether it is regular or irregular; Moreover, he is particularly interested in a shape he calls morphs, in which the graphics change and influence each other, sometimes breaking through the freedom of the plane. His interest began at 1936, when he traveled to Spain and saw the patterns of tiles used locally in Alhambra. He spent a few days sketching these tiles, and later declared that they were "the richest source of inspiration I have ever met". In 1957, he wrote an article about mosaic graphics, in which he commented: "In the field of mathematics, regular plane division has been studied theoretically ... Does this mean that it is just a strict mathematical problem? In my opinion, no. Mathematicians have opened the door to a vast field, but they have never entered it themselves. By nature, they are more interested in the way they open the door than in the garden behind it. "

Whether this is fair to mathematicians or not, one thing is true-they point out that among all regular polygons, only triangles, squares and regular hexagons can be used for mosaic. However, many other irregular polygons can also form mosaics after tiling. For example, many mosaics use irregular five-pointed star shapes. Escher used these basic patterns in his mosaics. He used reflection, smooth reflection, transformation and rotation in geometry to obtain more diverse patterns. He also carefully twisted these basic patterns into animals, birds and other shapes. These changes have to be symmetrical three times, four times or even six times to get the mosaic pattern. This effect is both amazing and beautiful.