Shape

384 III Using It to Design
It’s going on, seeing and doing in whatever way you like.
And there are other ways to copy shapes, too. In particular, I can combine
algebras in products and copy across their components. This uses rules in the erasing
schema
x fi
rules in its inverse
fi x
and identities x fi x to calculate in parallel. For example, two new schemas can be
defined—something more to put in my catalogue—that look like this
x; fi ; x
x; fi x; x
where the dash ( ) indicates the empty shape. The first schema has a neat symmetry—
it combines x fi and fi x, so that the component or the part of it that’s copied is
erased. But in the second schema, x fi x and fi x are combined to preserve what’s
copied in its original place without changing anything. A slightly different example is
in part II on pages 287–290. The schema
x; fi ; y
is used to decompose the shape
into squares and triangles in five distinct ways. Simply put, these polygons in x are
copied with the lines or the plane given in y. And this kind of copying is easy to elaborate
in lots of ways—with added transformations, the boundary operator, parametric