With data for small system collectivity getting ever more precise and diverse, and new experiments such as the EIC promise data with unprecedented geometric control, Monte Carlo generators face the requirement of a space-time picture of the initial state, to complement the more traditional momentum-space one.
In this seminar I will present how the Muller dipole model has been used to that effect, previously in the DIPSY event generator, and is now being used in PYTHIA as well. Since all parameters of the model can be fitted to inclusive quantities, it offers a solid starting point for such efforts. Furthermore, since the model calculates projectile and target Fock states event-by-event, color fluctuations of the nucleon-nucleon, or γ*-nucleon, cross-section comes about as a by-product.
Finally, once there is an initial space-time structure, a mechanism is needed to transport initial state anisotropies to the final state. Over the past years we have developed a model based on interacting strings, with exactly this aim. I will discuss recent developments, with a focus on response to initial state geometry, and similarities to hydro.