  We use the grid consisting of bits of 3^n to motivate the definition of
2-adic numbers. Specifically, we exhibit diagonal stripes in the bits of
3^(2^n), which turn out to be the first in an infinite sequence of such
structures. Our observations are explained by a 2-adic power series, providing
some regularity among the disorder in the bits of powers of 3. Generally, the
base-p representation of k^(p^n) has these features.
