  The diversity and density of urban functions have been known to affect urban
vibrancy positively, but the relation between the two has not been empirically
examined; if high density is associated with low diversity in an area, its
vibrancy may not increase. To obtain a better understanding of the metabolism
of cities and directions for urban planning interventions, this paper offers
empirical evidence on the association between the diversity and density of
urban functions in the Tokyo Metropolitan Area, using a robust density index
that was determined via a Monte Carlo simulation. By conducting association
analyses, it was found that highly dense station areas tended to display low
diversity at multiple scales. Further investigation indicated that this
negative correlation was owing to different spatial characteristics of
functions and complementary functioning among highly accessible station areas.
This paper argues for considering both diversity and density in urban planning
to make station areas vibrant and resilient.
