Shape

26 Introduction: Tell Me All About It
in terms of the rule
that rotates any of its three squares 45 degrees. This is a lot trickier than it looks. The
sides of the small square cut sides of the large squares in half. Nonetheless, squares
aren’t four lines and eight lines apiece
as you might naturally intuit or guess from the way I segmented the shape
It’s difficult to imagine all that’s needed for everything to work out—the squares are
twenty lines and forty lines instead
because of what happens when my rule is used to rotate both of the large squares, and
how rotating the small square factors into this. Lines diffuse in analysis, as different
parts (squares) interact dynamically. Look at my shape fade away (disintegrate) into
finer and finer constituents. What I can draw with eight lines, and represent as sixteen
equal segments to rotate each of its three squares, takes no less than eighty segments of
two incommensurable lengths to describe completely. Every side of a large square corresponds
with the palindrome
ababaababa
p
where b ¼ a
ffiffiffi
2 . The segments a and b in the string are related as the side and the diagonal
of a square—this is too hokey to be wrong. Moreover, substrings are palindromes
at aba and a half. Try these divisions and see how nicely segments align—especially
when both of the large squares are rotated, so that sides match reversed at aba