We present analyses of the spatial distributions of stars in the young ( 1 – 3 Myr ) star-forming regions IC 348 and NGC 1333 in the Perseus Giant Molecular Cloud .
We quantify the spatial structure using the \mathcal { Q } -parameter and find that both IC 348 and NGC 1333 are smooth and centrally concentrated with \mathcal { Q } -parameters of 0.98 and 0.89 respectively .
Neither region exhibits mass segregation ( \Lambda _ { MSR } = 1.1 ^ { +0.2 } _ { -0.3 } for IC 348 and \Lambda _ { MSR } = 1.2 ^ { +0.4 } _ { -0.3 } for NGC 1333 , where \Lambda _ { MSR } \sim 1 corresponds to no mass segregation ) , nor do the most massive stars reside in areas of enhanced stellar surface density compared to the average surface density , according to the \Sigma _ { LDR } method .

We then constrain the dynamical histories and hence initial conditions of both regions by comparing the observed values to N -body simulations at appropriate ages .
Stars in both regions likely formed with sub-virial velocities which contributed to merging of substructure and the formation of smooth clusters .
The initial stellar densities were no higher than \rho \sim 100 - 500 M _ { \odot } pc ^ { -3 } for IC 348 and \rho \sim 500 - 2000 M _ { \odot } pc ^ { -3 } for NGC 1333 .
These initial densities , in particular that of NGC 1333 , are high enough to facilitate dynamical interactions which would likely affect \sim 10 per cent of protoplanetary discs and binary stars .