Covering the plane with repeated patterns- part II

I n Part I of this article (reference 1) we had noted how some regular polygons fit with each other to cover the plane without either gaps or overlaps, in arrangements called tilings. During our bus tour around the historic monuments of Delhi (described in the same article), we had seen many patterns based on simple rules, resulting in intricate tilings with great aesthetic appeal. Such patterns have been of interest to humans from ancient times, perhaps dating to the time when we started making shelters and used the logic of fitting rocks and weaving leaves to cover space while minimizing gaps. Over time, such endeavours took on artistic forms. Societies made use of tiles and patterns to emphasize different aspects of their culture. For example, Romans and some Mediterranean people portrayed human figures and natural scenes in their mosaic; the artistic impulse of the Arab artisans showed in their use of shape and colour to build complex geometric designs (as seen in the tiling patterns at Red Fort, Jama Masjid, Qutab Minar and Chandni Chowk; the Alhambra Palace in Granada, Spain, is another rich site of such patterns). Now, in Part II, we look at simple ways by which regular tessellations can be modified to make appealing patterns. We use simple techniques of colouring, shading or modifying a polygon to make interesting designs. The examples taken in this article are basic but lead to many possibilities that the readers can explore