Shape

270 II Seeing How It Works
square fi four triangles
The rule is still context free, but it doesn’t work. It applies once to the square
and then can’t be applied again to the shape
Now there are four triangles and no squares. I can patch this up by dividing triangles
and squares into three sides and four sides apiece. After all, this is the way they’re normally
defined. It’s what Evans did in part I, and it gives me a new way of describing the
rule
square with four sides fi four triangles with three sides apiece
But if this is the case, then the rule must be context sensitive. Four lines are in the left
side of the rule and twelve lines are in the right side. And it’s easy to see that the increase
in complexity pays off when I calculate in this way
where the long sides of four triangles become the four sides of a square. This is convincing
proof that the rule is context sensitive—or is it? There’s still a lot more to
worry about. The rule doesn’t work in the longer series
It has to apply to the outside square in the second step. Under the description of the
rule I’m using now, each side of the outside square is divided in two. The outside
square is four lines at the start, and then eight lines one step later after adding triangles.
I can try another rule that changes how squares are described, maybe one with
the description
eight lines fi four lines