  We collect experimental evidence for several propositions, including the
following: (1) For each Riemann zero $\rho$ (trivial or nontrivial) and each
zeta fixed point $\psi$ there is a nearly logarithmic spiral $s_{\rho, \psi}$
with center $\psi$ containing $\rho$. (2) $s_{\rho, \psi}$ interpolates a
subset $B_{\rho, \psi}$ of the backward zeta orbit of $\rho$ comprising a set
of zeros of all iterates of zeta. (3) If zeta is viewed as a function on sets,
$\zeta(B_{\rho, \psi}) = B_{\rho, \psi} \cup \{0 \}$. (4) $B_{\rho, \psi}$ has
nearly uniform angular distribution around the center of $s_{\rho, \psi}$. We
will make these statements precise.
