Thursday, January 6, 2011

Scaling Girih, Seventh Scaling Tile

This drawing from a series of scaling girih tilings was created with a new kite scaling tile. It differs from earlier drawings in the series in that the girih lines and the tile edges for the kite share a common vertex. Traditionally, and in all other tiles in the series, girih lines or strapping have endpoints on the midpoint of tile edges or within the tile. In this case, the girih lines share one vertex with the tile edges.

This scaling tile also lacks a girih line ending on either of the two shorter edges. Consequently, this means that all the girih lines at a common scale connect, but are discontinuous with the lines at other scales. I choose to limit these drawings to only edge-to-edge tilings, so this disconnect is complete and only at the transitions.

The scaling factor for this unique kite is the golden ratio, which is also the scaling factor for the trapezoid scaling tile. Both the trapezoid and kite could be used in the same drawing to transition tiles, and the trapezoid would connect girih lines from one scale to the next.

I have used two other scaling tiles that lack girih lines along the shorter edges. There are no such tiles in traditional girih tilings.

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