Shape

296 II Seeing How It Works
And, certainly, this isn’t the end of it either. But the idea of using transformations and
identities to classify parts seems well enough established. It gives a nice taxonomy for
parts and their uses. Rules let me generate shapes and tell a lot about them. In fact, I
like to think that whatever I describe—with transformations, with parts and topologies,
or in some other way—is the result of calculating. Otherwise, what is there to
talk about? Without something to see, there’s nothing to say.
Calculating and Continuity
I’m going to try another rule—it’s the very first one I used in the introduction—to
show how the third scenario works. The rule
rotates an equilateral triangle about its center, so that the center point is permanently
fixed. The rule is applied eight times to define the shapes in this series