My goal for patterns is to have an interesting and symmetric way of making neighbourhoods for tiling. These 30-gons turn out to have a fair number of choices on how they can relate to their neighbours. Essentially, coming up with easy to follow rules for describing the pattern is a way of completely understanding the pattern. These rules embody what I like about patterns: access to the infinite.
My rule I choose to explore here, has to do with having the internal structures back-to-back. I'll label the structures: loops and arrows. The loops refer to the three positive-space structures composed of six pentagons and 5 triangles. The arrows refer to the three negative space structures (white space) that are pointy and all touch the center of each 30-gon.
To see my rule in affect, imagine the pattern without the pink-centred 30-gons. All the purle-centred 30-gons are connected with back-to-back arrow structures. Paths that follow these arrow structures form a hexagonal grid with the purple centres being at the vertices. A similar story occurs for the loops structures but there is a hitch--there are two types of purple-centred 30-gons: ones to the right of a pink-centred 30-gon and ones to the left. If we ignore all the purple-centred 30-gons on the right, we end up with similar hexagonal grid formed by paths following the loops.
Seeing the above structures makes my rule seem complete. However, pairing the pink-centred 30-gons with the purple-centred 30-gons on the right leaves us with only back-to-back pairs of loops with arrows. Still I am fairly content with this patterns symmetry and it's overall appeal.
I have included this blurred patch that can be used as a background.
