Self-Similar Fractal Drawings Inspired by M. C. Escher’s Print Square Limit
Self-Similar Fractal Drawings Inspired by M. C. Escher’s Print Square Limit
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DOI：
10.1145/3456298
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Peichang Ouyang;K. Chung;Alain Nicolas;K. Gdawiec
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文献类型：
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作者：
Peichang Ouyang;K. Chung;Alain Nicolas;K. Gdawiec
分形拼贴是一种很少被探索的具有自相似性且其边界为分形的相似多边形拼贴。荷兰平面艺术家M. C. Escher以类似等腰直角三角形的平铺为基础，创作了一幅巧妙的“正方形限制”版画，其中鱼在接近平铺边界时，尺寸均匀缩小。在这篇文章中，我们提出了四个家庭的f-tilings，并提出了一个易于实现的方法来实现类似的埃舍尔图。通过对f-瓦局部星形结构的系统研究，我们首先列举了风筝形或飞镖形原瓦所允许的4个f-瓦族。然后，我们建立了一种快速分割算法来可视化f-tilings。为了便于在报告的f-tilings上创建类似埃舍尔的绘图，我们接下来分别引入正方形、风筝和飞镖之间的一对一映射。这种处理允许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埃舍尔的图库。因此，本文中建立的方法能够生成各种奇异的埃舍尔式绘画。
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.