Shape

358 III Using It to Design
that works in the same way with answers from four to six. But now, the erasing rules in
my schema apply to give definite results—polygons are numerically distinct. And now,
these rules apply to shapes in rules. This is important. Shapes are shapes wherever they
are—it doesn’t matter whether they’re in rules or not. Either way, they’re exactly as
they’re given, without finer divisions. Divisions are determined as I calculate.
Once k is defined, it’s easy to say what rules do. First, there’s an m n grid of
walls that’s described by the coordinate pair ðm; nÞ, where m is the number of rectangles
in a row and n is the number of rectangles in a column. (This counts columns before
rows. It’s interesting how things can get switched or turned around in shapes and
words alike.) These values are set in the inverted T used to produce the grid. If I try a
rule like this
to add a rectangle vertically, my description rule is
ðm; nÞ fi ðm; n
kÞ
where k ¼ 1. And in the corresponding way, if I apply a rule to add rectangles
horizontally
then my description rule is
ðm; nÞ fi ðm
k; nÞ
and k ¼
2. So, in the Villa Foscari with the inverted T