Stochastic self-propagating star formation models describe galactic structure through local triggering and feedback but are commonly formulated using discrete spatial cells and time steps. We extend the spatio-temporal log-Gaussian Cox-Hawkes framework to obtain the Spatio-Temporal Self-Propagating Log-Gaussian Cox-Hawkes Process, a continuous point process model for the locations and times of star-forming events. The model combines spontaneous formation, correlated environmental effects, outwardly propagating excitation, local inhibition, differential rotation, and saturation. An observation layer transforms the conditional event intensity into idealised maps of instantaneous star-forming arm emissivity and recent young stellar surface brightness. For the selected parameter setting, the displayed realisation exhibits transient flocculent spiral-like patterns without any deterministic spiral geometry being imposed. The Monte Carlo experiment finds similar event production with and without rotation, whereas the stationary-front case produces fewer events. The displayed maps further suggest that differential rotation contributes to the winding and spatial arrangement of activity. The proposed framework provides a basis for future statistical inference from spatially and temporally resolved observations of star formation.

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