A fractal tiling ( f -tiling) is a kind of rarely explored tiling by similar polygonal tiles which possesses self-similarity and the boundary of which is a fractal. Based on a tiling by similar isosceles right triangles, Dutch graphic artist M. C. Escher created an ingenious print Square Limit in which fish are uniformly reduced in size as they approach the boundaries of the tiling. In this article, we present four families of f -tilings and propose an easy-to-implement method to achieve similar Escher-like drawings. By systematically investigating the local star-shaped structure of f -tilings, we first enumerate four families of f -tilings admitted by kite-shaped or dart-shaped prototiles. Then, we establish a fast binning algorithm for visualising f -tilings. To facilitate the creation of Escher-like drawings on the reported f -tilings, we next introduce one-to-one mappings between the square, and kite and dart, respectively. This treatment allows a pre-designed square template to be deformed into all prototiles considered in the article. Finally, we specify some technical implementations and present a gallery of the resulting Escher-like drawings. The method established in this article is thus able to generate a great variety of exotic Escher-like drawings.

中文翻译：

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受 MC Escher 的 Print Square Limit 启发的自相似分形图

分形平铺 (F-tiling) 是一种很少探索的由具有自相似性且边界为分形的相似多边形瓦片组成的瓦片。基于类似等腰直角三角形的拼贴，荷兰图形艺术家 MC Escher 创造了一个巧妙的印刷品平方限制当鱼接近平铺的边界时，它们的大小会均匀减小。在这篇文章中，我们介绍了四个家庭F- 平铺并提出一种易于实现的方法来实现类似的 Escher-like 绘图。通过系统地考察当地的星形结构F-tilings，我们首先列举四个家族F- 风筝形或飞镖形原型所允许的瓷砖。然后，我们建立了一种用于可视化的快速分箱算法F-瓷砖。为了便于在报告上创建类似 Escher 的图纸F-tilings，我们接下来分别介绍正方形、风筝和飞镖之间的一对一映射。这种处理允许将预先设计的方形模板变形为文章中考虑的所有原型。最后，我们指定了一些技术实现，并展示了生成的类似 Escher 的图纸的画廊。因此，本文中建立的方法能够生成各种奇异的 Escher 式绘图。