{"id":574,"date":"2025-02-18T12:54:29","date_gmt":"2025-02-18T11:54:29","guid":{"rendered":"https:\/\/artificationofmath.com\/?p=574"},"modified":"2025-02-24T14:44:12","modified_gmt":"2025-02-24T13:44:12","slug":"behangpapier-en-kunst","status":"publish","type":"post","link":"https:\/\/artificationofmath.com\/?p=574","title":{"rendered":"Wallpaper groups and Art"},"content":{"rendered":"\n


When talking about the regularity of patterns in modern art, one often mentions Maurits Cornelis Escher<\/a>. He was born in Leeuwarden on June 17, 1898, and died in Hilversum on March 27, 1972. After studying at the “School voor Bouwkunde, Versierende Kunsten en Kunstambachten<\/a>” in Haarlem, he traveled several times to places like Spain, where he studied Moorish art at the Alhambra<\/a>. Here, he found inspiration for his infinite tessellations<\/a>.<\/p>\n\n\n\n

\"\"
Mosaic copy of an Alhambra tile<\/figcaption><\/figure>\n\n\n\n

Escher used the wallpaper groups<\/a> only as a study of patterns for his further works. Think, for example, of “Sky and Water II,” a woodcut from 1938. Or think of the lithograph “Reptiles” from 1943. In these works, the regularity of the group is used to make a transition from one to the other. In “Sky and Water II,” the woodcut transitions from birds to fish in a gradual transformation.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

In the lithograph “Reptiles,” we have a transition from a flat surface to a spatial one, as the little lizards seem to crawl out of the sheet of paper.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Other Artists<\/h2>\n\n\n\n

There are more artists who use wallpaper groups in their artistic expressions. On the site https:\/\/tiled.art\/en\/artists\/<\/a>, you can find several artists along with their work. Here is an example of Francine Champagne<\/a>:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Often you can see that the tessellations consist of one or more polygons. This is always the case, even if it is difficult to see. In a following blog, we will look at the following two subdivisions: Heesch type and Isohedral type.<\/p>\n\n\n\n

Back to wallpaper groups. If you’re wondering which group a particular pattern belongs to, ask yourself the following question: How many times can you rotate the pattern at most? As we have seen before<\/a>, this can be 1, 2, 3, 4, or 6 times. Call this number n.<\/p>\n\n\n\n