Shape

66 I What Makes It Visual?
calculating. The dimension i of basic elements makes a difference—what happens as
rules are tried depends on the value of i, and whether it’s zero or not.)
Evans’s grammar contains rules like this one
Three lines fi Triangle
that defines triangles in the ordinary way as polygons with three sides. In order to
show how the rule works, I first have to give the embedding relation, and then tell
what options there are to satisfy it. For Evans, embedding is identity among constituents.
This is the same for points. The rule applies to a shape when all of its constituents
(points) are also in the shape. Moreover, the constituents in the rule may be transformed
as a whole arrangement—they can be moved around, reflected, or scaled—to
determine the right correspondence with constituents in the shape.
Evans uses this shape
as an example. The shape has a finite set of constituents. It’s twenty-four line segments,
each one defined separately by its endpoints—first there are the four sides of
the large square and their halves
then the two diagonals of the square and their halves
and finally the horizontal and the vertical and their halves
And Evans’s rule—the one for three lines—applies without a hitch to pick out the sixteen
triangular parts of the shape. There are eight small triangles, four medium ones,
and four large ones