We propose a new concept “ambiguous tiling”, which is the combination of tiling art and ambiguous cylinders. Tiling art is an artistic pattern consisting of copies of one or a few kinds of tiles which cover the whole 2D plane without gaps or overlaps. Escher's regular-division artworks are typical examples. There is a strong condition for figures to be used as the tiles for tiling. On the other hand, ambiguous cylinders are 3D solid objects that give two quite different appearances when they are seen from two specific viewpoints. There is also another strong condition for a pair of figures to be satisfied to realize the ambiguous cylinder. In this paper we find figures that satisfy both of the conditions and so we can create 3D objects which give two different tiling patterns when we see them from two specific viewpoints. We first give a necessary and sufficient condition for a pair of tiling patterns to be created as the ambiguous cylinder. This condition is theoretically correct but not practically useful. So we next consider special type of tiling for which we can design the ambiguous tiling relatively easily.

我们提出了一个新概念“模糊拼贴”，该概念是拼贴艺术和模糊圆柱的结合。平铺艺术是一种艺术图案，由一种或几种瓷砖的副本组成，这些瓷砖覆盖整个2D平面而没有间隙或重叠。埃舍尔的常规画作就是典型的例子。将人物用作瓷砖的条件很强。另一方面，模棱两可的圆柱是3D实体，当从两个特定的角度看时，它们会给出两种截然不同的外观。实现一对模糊圆柱体还需要满足一对人物的另一个强大条件。在本文中，我们找到了同时满足这两个条件的图形，因此我们可以创建3D对象，当从两个特定的角度来看它们时，它们会提供两种不同的平铺模式。我们首先给出一个必要的充分条件，以便将一对拼贴图案创建为歧义圆柱体。此条件在理论上是正确的，但实际上没有用。因此，我们接下来考虑一种特殊类型的平铺，对于这种平铺，我们可以相对容易地设计模糊平铺。