  To understand the formation of stars from clouds of molecular gas, one
essentially needs to know two things: What gas collapses, and how long it takes
to do so. We address these questions by embedding pseudo-Lagrangian tracer
particles in three simulations of self-gravitating turbulence. We identify
prestellar cores at the end of the collapse, and use the tracer particles to
rewind the simulations to identify the preimage gas for each core at the
beginning of each simulation. This is the first of a series of papers, wherein
we present the technique and examine the first question: What gas collapses?
For the preimage gas at the t=0, we examine a number of quantities; the
probability distribution function (PDF) for several quantities, the structure
function for velocity, several length scales, the volume filling fraction, the
overlap between different preimages, and fractal dimension of the preimage gas.
Analytic descriptions are found for the PDFs of density and velocity for the
preimage gas. We find that the preimage of a core is large and sparse, and we
show that gas for one core comes from many turbulent density fluctuations and a
few velocity fluctuations. We find that binary systems have preimages that
overlap in a fractal manner. Finally, we use the density distribution to derive
a novel prediction of the star formation rate.
