  We show that the quantum evolution of a spin-1 Bose gas with nearly all
bosons initially in the $F_z = 0$ state has a "quantum carpet" {\em spin-time}
structure with self-similar properties. The system continuously evolves into
"multi-peaked" Schr\"odinger cat like states, returning occasionally to
coherent structures, which leads to large number fluctuations (as seen in
recent experiments). The self similar behavior allows one to reveal the quantum
evolution as a set of peaks in the number probability distribution of a spin
component at times {\em much shorter} than the quantum revival time. We also
show that these features survive small number fluctuations among spin
components up to a few percent.
