Shape

247 Spatial Relations and Rules
that contains four squares.
Decomposing shapes to define spatial relations for rules can be very useful. I can
begin with shapes I like, and try to find rules to produce them and new shapes of the
same kind. It’s the beginning of stylistic analysis and a way to handle stylistic change.
Or I can use these rules with whatever I’m doing to follow up an interesting motif or
salient feature (part) in a way that’s copying it and more. And it’s especially nice that
decomposing shapes is really calculating, too—for example, with identities defined in
the schema
x fi x
or with erasing rules from the schema
x fi
But even better, there are telling decompositions no matter how I calculate. That’s one
of the things I showed in part I with rules from the schema
x fi tðxÞ
and stars and superstars.
Right now, though, the inverse schema
A þ B fi x
is loaded with unexpected possibilities. Certainly, the cross
can be divided neatly into squares—either four of five of them—to define three distinct
spatial relations