The possibility of everlasting cosmological inflation -- and the resulting unbounded number of causally disconnected post-inflationary regions -- has gained more far-reaching implications since it was uncovered early in the history of inflation theory. This is owing to the growth in acceptance of theory landscapes and anthropic arguments weighing on the origins of cosmological parameters and low-energy particle physics. To what extent does inflation generically produce an eternal "multiverse," without apparent fine-tuning with respect to probability measures over the space of inflationary cosmologies driven by a single, minimally coupled scalar field? We address this and related questions with numerical simulations of inflationary dynamics across populations of randomly generated inflation models, instantiating a few particular simply-defined measures. We go on to explore the toy landscapes sampled from these measures, correlating eternal inflation with observables and characterizing fractal dimension of inflating topological defects.