Abstract
The purpose of this study is to describe analytically how some kind of urban activities are distributed in cities based on the interaction which is determined by the distance between two points in the city. In order to obtain such a distribution, employing the threshold value regarded as the limit distance/time to which the influence from the arbitrary point in the region can be reached, we define the adjacency function of which value is either 1 or 0. By using the adjacency function, we make the formulation as it can be applied to the several practical cases including the continuous urban space. As a result, we show that the concentration and dispersion occurs by the ratio of the size of city to the threshold, and that the activity distribution is proportional to the area of the region reachable within the threshold in the particular case.
