Tiling the plane

   

Is it possible to tile an infinite plane with an single seki?
Yes, provided there are no corners. I don't think its possible with corners because you would form two eyes with the corner group.
Generator for tiling a plane with no edges.

[Diagram]


Generator for tiling a plane with one edge (horizontal)

[Diagram]


Attempt at a generator for tiling a plane with at most two parallel edges. Fail.

[Diagram]


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