The pentgagonal subdivision rule --- gzipped ps file, pdf file --- This is a simple but beautiful example. It was studied in depth in the Bowers-Stephenson paper A "regular" pentagonal tiling of the plane.

The twisted pentgagonal subdivision rule --- gzipped ps file, pdf file --- This is a simple example with a single tile type. It has rotational symmetry but not dihedral symmetry. The lack of dihedral symmetry makes it more challenging to show that this example is conformal.

The Lattes subdivision rule and related examples --- gzipped ps file, pdf file --- The Lattes subdivision rule is a simple example in which the two tile types are quadrilaterals and each is subdivided into four quadrilaterals. One can make more complicated examples from this one by "blowing up" edges. We learned about this technique from Kevin Pilgrim.

Examples with a single hexagonal tile type and an edge pairing --- gzipped ps file, pdf file --- We consider here several examples with a single hexagonal tile type and an edge pairing. Since the Teichmueller space of the subdivision complex is 1-dimensional, these are good test examples for conformality.

An examples from the Cannonfest, June 2003 --- gzipped ps file, pdf file --- This is another example of the hexagonal subdivision rules considered above. It has a Thurston obstruction.