Shape

335 Chinese Lattice Designs—Seeing What You Do
Let’s try the ice-ray lattice
It’s one of my favorites—in this case because what I see looks hard to do, but isn’t. I
need four kinds of rules like these
perhaps from the schema x fi divðxÞ to divide triangles, quadrilaterals in alternative
ways, and pentagons. Then it’s one more case of parametric variation using general
transformations t g. Dye summarizes the process nicely—
In the case of the ice-ray pattern [the artisan] divides the whole area into large and equal light
spots, and then subdivides until he reaches the size desired; he seldom uses dividers in this
work.
Or I might think of my rules in another way in terms of a fractal-like schema
x fi xA þ xAA
where one polygon x is replaced by the sum of two, xA and xAA. Whatever I do, it’s the
same—visually, there’s the series of shapes in figure 4. Maybe the series is excessive
and even a little indulgent—I like to draw—but it seems to me that it’s worth seeing
once for ice-rays that rules work throughout; and after all, I’m only showing half of