Girih patterns start with simple straight-line decorations on the five girih tiles. I've extended the system with scaling polygons to get variation in density of line. In July and August of 2011 I showed examples of Girih Extended at Chambers @ 916. The image below is the first example of another variation on girih patterns. I've converted the geometric, straight-line patterns to arabesque. This is more a working example than a finished design.
It's possible to apply this same technique to just the five girih polygons. The underlying structure of the example includes four of the five. As in my girih extended series I've added an additional rhombus, plus the scaling polygons: a kite and trapezoid. I've been using up to six scaled copies of the extended polygon set within a single design. The scaling polygons allow me to create edge-to-edge tilings or tile patches with considerable variation in scale and density of line. Sometimes I design with inner gaps, and sometimes not. Sometimes the designs are symmetric, sometimes asymmetric. Since my interest is art, not math, I'm not constrained by a requirement to develop tessellations that might fill the plane. The design above could be filled and extended to fill the plane, without gaps or overlaps.
As far as I know this is the first example of girih arabesque. The decoration or strapwork on the polygons has been converted to Bézier curves. At the polygon boundaries the curves meet tangentially, or nearly so. This gives the appearance of continuously flowing lines. There are numerous possible ways to elaborate the curves. In the example I show the curves were easily programmable, and more or less true to the original girih patterns.
It's possible to apply this same technique to just the five girih polygons. The underlying structure of the example includes four of the five. As in my girih extended series I've added an additional rhombus, plus the scaling polygons: a kite and trapezoid. I've been using up to six scaled copies of the extended polygon set within a single design. The scaling polygons allow me to create edge-to-edge tilings or tile patches with considerable variation in scale and density of line. Sometimes I design with inner gaps, and sometimes not. Sometimes the designs are symmetric, sometimes asymmetric. Since my interest is art, not math, I'm not constrained by a requirement to develop tessellations that might fill the plane. The design above could be filled and extended to fill the plane, without gaps or overlaps.
As far as I know this is the first example of girih arabesque. The decoration or strapwork on the polygons has been converted to Bézier curves. At the polygon boundaries the curves meet tangentially, or nearly so. This gives the appearance of continuously flowing lines. There are numerous possible ways to elaborate the curves. In the example I show the curves were easily programmable, and more or less true to the original girih patterns.
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