in islamic culture, geometry is everywhere. you can find it in mosques,madrasas, palaces and private homes. this tradition began in the 8th century ceduring the early history of islam, when craftsman took preexisting motifsfrom roman and persian cultures and developed them into new formsof visual expression. this period of history was a golden ageof islamic culture, during which many achievements of previous civilizations were preserved and further developed, resulting in fundamental advancementsin scientific study and mathematics.
accompanying this was an increasinglysophisticated use of abstraction and complex geometry in islamic art, from intricate floral motifsadorning carpets and textiles, to patterns of tilework that seemedto repeat infinitely, inspiring wonder and contemplation of eternal order. despite the remarkable complexityof these designs, they can be created with just a compass to draw circles and a ruler to make lines within them, and from these simple tools emerges a kaleidoscope multiplicity of patterns.
so how does that work? well, everything starts with a circle. the first major decision is how will you divide it up? most patterns split the circleinto four, five or six equal sections. and each division gives riseto distinctive patterns. there's an easy way to determinewhether any pattern is based on fourfold, fivefold, or sixfold symmetry. most contain stars surroundedby petal shapes.
counting the number of rays on a starburst, or the number of petals around it, tells us what category the pattern falls into. a star with six rays,or surrounded by six petals, belongs in the sixfold category. one with eight petals is partof the fourfold category, and so on. there's another secret ingredientin these designs: an underlying grid. invisible, but essential to every pattern,
the grid helps determine the scaleof the composition before work begins, keeps the pattern accurate, and facilitates the invention of incredible new patterns. let's look at an example of how theseelements come together. we'll start with a circle within a square,and divide it into eight equal parts. we can then draw a pairof criss-crossing lines and overlay them with another two. these lines are called construction lines, and by choosing a set of their segments,
we'll form the basis of our repeating pattern. many different designs are possiblefrom the same construction lines just by picking different segments. and the full pattern finally emerges when we create a grid with manyrepetitions of this one tile in a process called tessellation. by choosing a different set of construction lines, we might have created this pattern, or this one.
the possibilities are virtually endless. we can follow the same stepsto create sixfold patterns by drawing construction linesover a circle divided into six parts, and then tessellating it,we can make something like this. here's another sixfold patternthat has appeared across the centuries and all over the islamic world, including marrakesh, agra, konyaand the alhambra. fourfold patterns fit in a square grid,and sixfold patterns in a hexagonal grid. fivefold patterns, however,are more challenging to tessellate
because pentagons don't neatly fill a surface, so instead of just creating a pattern in a pentagon, other shapes have to be addedto make something that is repeatable, resulting in patterns that may seemconfoundingly complex, but are still relatively simple to create. also, tessellation is not constrainedto simple geometric shapes, as m.c. escher's work demonstrates. and while the islamic geometric design tradition doesn't tend to employ elements like fish and faces,
it does sometimes make use of multiple shapes to craft complex patterns. this more than 1,000-year-old traditionhas wielded basic geometry to produce works that are intricate,decorative and pleasing to the eye. and these craftsman prove just howmuch is possible with some artistic intuition, creativity,dedication and a great compass and ruler.