In the simulations described herein, we seed a micellar assembly with a random composition, and follow the growth-split dynamics driven by the entry and exit of lipid monomers. Upon reaching a prescribed maximal size, the assembly fissions, and one randomly selected progeny initiates the next growth generation. Typically, upon examining subsequent growth-split generations, the composition of a fully-grown assembly bears only small resemblance to that of the previous generation. However, in some cases the system reaches a privileged compositional state, termed composome , in which a high compositional similarity is seen for 3 or more generations. This is illustrated in a principal component analysis of the time-dependent assembly compositional vector (Figure ). In this example, the system is seen roaming through long compositional distances along 8 generations, until it reaches a composome, in which the system lingers for 11 generations with minor compositional changes. Such behavior is shown in kinetic details in Figure . The observed compositional invariance along time is an epitome of assembly reproduction, whereby compositional information is faithfully bequeathed across growth and fission generations .