Shape

271 Classifying Rules with Parts
or a rule that applies recursively to fuse the segments in any division of a line
two lines fi one line
Either way, a general rewriting system is defined. Alternatively, I can represent the rule
in two ways, so that squares have either four sides or sides described by their eight
halves. And notice further that if I have reason to put four triangles in the right side
of the rule, then its different versions are of different kinds—one is context sensitive
(four lines go to four triangles) and then the other isn’t (eight lines go to four triangles).
What the rule is depends on how it’s described. Maybe the rule is context free,
maybe it’s context sensitive, and maybe it’s in a general rewriting system.
I can calculate with the rule
to get the shape
but I have no way of deciding how complex this is before I begin. Just looking at the
rule isn’t enough. I have to examine things anew every time I apply it, and determine
how different descriptions of shapes interact. There are simply too many ways of calculating
and too many different descriptions for this to be of any practical value.
In the introduction, I warned that the analogy
shape grammar : designs < generative grammar : sentences
shouldn’t be taken too far. And my discussion of the Chomsky hierarchy shows why
in fairly rigorous terms. It provides a very useful taxonomy for generative grammars,
but it doesn’t work for shapes made up of lines, etc. Perhaps this is the fatal
flaw in visual calculating—‘‘Wouldn’t it be wonderful if we could classify shape grammars
the way Chomsky classifies generative grammars.’’ Complexity is measured by
counting symbols (units), and this is fine for shapes containing points and other
things that are zero dimensional, for example, sets with members. They have definite