Shape

339 Chinese Lattice Designs—Seeing What You Do
is good for a half-turn p. Then the compound schema
x þ pðxÞ fi divðxÞþpðdivðxÞÞ
gives rules for any polygon x, even if it looks a little complicated. Still, there’s no reason
to worry. I can recast what the schema does in a two stage process in which the
schema x fi divðxÞ is applied first to x and next to pðxÞ. This guarantees that divðxÞ
and pðdivðxÞÞ are both in the design as long as divðpðxÞÞ ¼ pðdivðxÞÞ. Or equivalently,
there’s the schema
x þ pðxÞ fi divðxÞþdivðpðxÞÞ
But in fact, x fi divðxÞ alone may really be enough—simply let
x þ pðxÞ fi divðx þ pðxÞÞ
I can always divide more than polygons. Schemas and the rules they define work with
remarkable ease.
Of course, there are other ways to change ice-rays that are of equal interest. Just
as checkerboard lattice designs contain different motifs, ice-rays can be divided in alternative
ways. In particular, there are axial motifs with three to six arms
Usually, these devices are used once centrally to start