## Monday, October 3, 2011

### Girih Seven

The images below are my first examples of a girih tile system based on the heptagon. Girih tiles have interior angles that are multiples of π/5. In the examples shown here I've applied the girih concept to tiles with angles that are multiples of π/7. Like girih tiles these have interior decoration (strapwork) that make a pattern without the tile edges. The midpoints of every tile edge have two lines coming from the edge, always at the same angle.

Girih tiles are equilateral, but I extended the tile set to include scaling tiles, allowing me to repeat the tiles at different scales while maintaining an edge-to-edge tiling. This means I can create girih patterns with variation in density of line. Girih seven continues this system. The tile set includes a heptagon, tetradecagon, elongated hexagon, rhombus, and bow tie. I've added a second rhombus, and I'm experimenting with several scaling tiles, including a trapezoid and five-sided kites.

Girih patterns are all straight lines, but starting with girih extended and now with girih seven I've added arabesque versions. Girih patterns are ideally suited for conversion to arabesque using Bézier curves. Since the patterns cross tile boundaries in straight lines, curves are tangent at the boundaries, creating a continuous flow throughout the pattern.

I've found that it's more difficult to create tilings with girih seven. Girih extended made it easy to develop patterns, without gaps. The girih seven example shown below includes a few small gaps, but I think they hardly detract from the finished designs. In at least one case I broke the rule requiring all pattern lines to meet tile edges at the same angle.

#### 1 comment:

SirEnder said...

FYI: http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/press.html

Girih patterns just got the nobel prize! Sort of... :-)