Gandhi, Haneet
(2014)
Covering the plane with repeated patterns- part II.
At Right Angles, 3 (2).
pp. 5-9.
ISSN 2582-1873
Abstract
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.
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