Wednesday, February 2, 2011

More Asymmetry

The two diagrams below continue the work with asymmetrical girh tile diagrams that I described in my last post. In these two, I returned to symmetry for the overall shapes, but shuffled the tiles within. I developed these with edge-to-edge tilings, having no gaps. It may be possible to fill the plane using patches from the complete diagram. The first, which has an overall decagon shape, can be divided into tile patches of three elongated hexagons and one bow tie, each with girih tile angles. These three patches, with all the tiles that subdivide them, might be used to fill the plane, though I haven't proven that they could. I'm not convinced that the patches could be repeated to fill the plane if I assume that tiles must be edge-to-edge. The second diagram can be divided into a single central pentagon, and five rhombi. Rhombus patches could be added to fill the plane. That in short is the geometry of these two diagrams.

I'm not nearly as interested in the geometry as the density of line and changing scale of motifs. The geometry sets up the diagram, but the self-similar tile sets, and asymmetrical arrangement of tiles gives me the result I'm after. These then are about discovering how to create highly irregular, unpredictable line drawings from a scaling tile set. These drawings defy the math art penchant for symmetry, quantification, and categorization. I prefer the discovery process over object manufacturing.

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