Shape

333 Chinese Lattice Designs—Seeing What You Do
This raises an important issue. I began with a corpus of shapes—designs in a given
style—and specified rules in my schemas to define the corpus and to produce other
designs of the same sort, and nothing else. There’s even an easy kind of stylistic change
where I add rules to divide squares with new motifs. In many ways, this is all very convincing.
I can recognize what’s in the style—do my rules generate it?—and I can produce
novel instances of the style that haven’t been seen before. I can go from known
to new, and I can say exactly what’s happening in terms of the rules I try. And that’s
the problem. When I look at the lattice just above—or the one with the H motif, for
that matter—I don’t automatically see the checkerboard or how its squares are divided.
In other rule-based systems in which shapes are represented in terms of symbols (vocabulary
and syntax), this is just something to get used to—learning the ‘‘right’’ way
to see according to given rules. There’s no ambiguity. Nonetheless, I have a creative
way to handle any discrepancies between the rules I apply to produce designs and
what designs look like. This is what I set out to do at the beginning of this book with
embedding and transformations, and the effort pays off handsomely when I calculate
with shapes and rules. That’s why the mathematics was worth doing and getting right
in the first place. Now calculating seems almost too easy, and it may be something of
an anticlimax. I simply augment my rules with identities defined in the schema
x fi x
to pick out any other parts I see—according to Dye, ‘‘octagons’’
‘‘octagon-squares’’