Shape

340 III Using It to Design
but occasionally they repeat in some delightful ways
With shapes and rules, it’s easy to add new motifs and to take advantage of what they
do. It requires nothing more than a drawing to show what I want to see and do. That’s
how rules are defined. And that’s all I need to calculate.
Earlier on, near the beginning of this part, I said that the same schemas worked
in different contexts to produce different results. The schema x fi divðxÞ that I’ve been
using to divide regions in ice-rays is a perfect example of this. I’ve already shown that
the schema is good for other kinds of lattice designs and, as an inverse, for Klee’s palmleaf
umbrella. But more conspicuously, it works in various algebras for painting and
architecture. The painter Georges Vantongerloo did a large number of designs like this
one
in which he starts with a pinwheel division and then makes orthogonal cuts. No
one would ever call it an ice-ray, but it really is. And then the Portuguese architect
Alvaro Siza relies on the same idea in designs for floor plans in his ongoing housing
project at Malagueira—about twelve hundred units to date that repeat at least thirtyfive
plans. Here’s one design that’s produced with a biaxial cut followed by three
more divisions