Shape

123 A Second Look at Calculating
And when I connect this series and the previous one via the superstar—it ends
the former and begins the latter—I’m left with what amounts to an extraordinary
transformation
that seems unimaginable in any of the counting and corroborative arithmetic I’ve
done. By calculating with rules that simply move chevrons—they keep their
‘‘shape’’—I can change both a chevron and a triangle into dissimilar ones. It isn’t
normal for things to alter in this way. Still, there it is—not complete in a single rule
that doesn’t show much, but chevron by chevron and piece by piece as in the topologies
in table 2. Neat things happen when shapes fuse and divide. Play around with
rules and see what you get. It’s the best way I know to learn how to calculate using
your eyes. You can start over every time you look.
There’s always more to see and do because superstars are ambiguous when
they’re divided into chevrons and a triangle according to the rules defined in my
schema. And it’s worth reinforcing, so that it isn’t lost in more complicated cases
where seeing may seem harder. Actually, the truth is that I enjoy this kind of stuff
and want to do it again. It’s exciting to see how many ways you can switch what you
see looking at the same thing with the same rules. Visual calculating isn’t just an isolated
trick. Take a look at the nine-pointed superstar
Three chevrons may be picked out in this sequence