Shape

356 III Using It to Design
(2) Furthermore, if there are more squares, then there are four more triangles, where
triangles are defined in the identity
These description rules apply in conjunction with the rule
to say what happens as I continue to draw lines in a certain way—I get additional
squares and triangles. Symbolically, I might summarize this with the rules
(1A) number of squares fi number of squares þ 1
(2A) number of triangles fi number of triangles þ 4
Then, for the series of shapes
there’s the corresponding series of descriptions
from step 0 1 2 3
number of squares 1 2 2 3
number of triangles 0 4 4 8
I’m calculating in parallel to produce shapes and the descriptions that go with them.
And notice that I can even distinguish descriptions that are the same, if I count the
steps in which they’re produced. To start, there’s a zero for bookkeeping, and then,
the description rule
step fi step þ 1
There’s a lot going on to tell me what I’m doing. The mechanics for all of it is
straightforward enough, and extends neatly to many other things. For example, I can
record the transformations I use to apply rules and define my topologies to show how
rules pick out parts of shapes. Then there’s more than mere mechanics that concludes
with dry numbers. Well, the mechanics still isn’t much—that’s the way I like it when I