Shape

321 Tell Me What Schema to Use
define can be shared and used in your own way—it’s copying without repeating the
past. There’s something to learn in the classroom that works in the studio when students
ask, ‘‘What should I draw?’’ Creative design can be taught like language and
mathematics in school, with examples, rules, and practice and the opportunity to experiment
freely. Rules make this possible because they apply to shapes in terms of
embedding and transformations. But I’ll come back to teaching a little later on, after
I’ve presented more evidence to back up my claim that calculating with shapes and
rules is creative.
I’ve been talking about schemas and rules for my designs. I did a lot of them,
but one of the key ideas that worked over and over again in surprising ways
was to add shapes and their transformations. This is minimally expressed in the
schema
x fi x þ tðxÞ
that defines the rule
used for the shapes in the series
And, in fact, this provides for the six designs in figure 1 that keep to what I did with
the schema bðxÞ fi x þ t 0 ðbðxÞÞþþt n ðbðxÞÞ to explore alternative ways of coloring
regions. Whatever I’ve said about counting in the past, permuting colors is sometimes
informative—as long as you know there’s always more to see in another way. And as I
went on, it seemed obvious that with all I could see and do with shapes and rules—my
two examples merely begin to scratch the surface—designing and calculating weren’t
too far apart. But not everyone agreed.
The problem was evident—I was calculating to make designs in my own way. I
could do anything I wanted and call it design. How about producing things that were
designed by others with sensitivity and skill? What about some real examples that had
the stamp of prior approval? Certainly, this wasn’t possible, especially for things that
weren’t as regular and hard-edged as my designs. But, as luck would have it, I didn’t
have to search very far to go on. There were plenty of things to design with shapes
and rules wherever I happened to look. It was surprisingly easy, and there were others
to help who saw this, too. Design was calculating. But in fact I knew that, and I already
had a way to go.