Here we define measures of urban diversity, density and segregation using new data and software systems based on GIS. These allow us to visualize the meaning of the multifunctional city. We define various indices which show how diversity and density manifest themselves spatially. We argue that multifunctionalism is a relative concept, dependent upon the spatial and temporal scale that we use to think about the mixing and concentration of urban land uses. We present three examples using spatially smoothed indicators of diversity: for a world city - London, for a highly controlled polycentric urban region - Randstad Holland, and for a much more diffusely populated semi-urban region - Venice-Padua-Teviso. We conclude by demonstrating that urban diversity varies as people engage in different activities associated with different land uses throughout the day, as well as through the vertical, third dimension of the city.
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