  In this letter we propose for the first time to map the heavy-ion collisions
at ultra-relativistic energies, similar to the maps of the cosmic microwave
background radiation, using fluctuations of energy density and temperature in
small phase space bins. We study the evolution of fluctuations at each stage of
the collision using an event-by-event hydrodynamic framework. We demonstrate
the feasibility of making fluctuation maps from experimental data and its
usefulness in extracting considerable information regarding the early stages of
the collision and its evolution.
