Central place theory(CPT) is built with assumptions that traffic condions and demand distribution are uniform. These assumptions are usually not met in the real world. The purpose of this paper is to detect the hexagonal arrangement of hinterlands implied in CPT by transforming the real world into an uniform surface, mainly focusing on demand distrition.
The transformation of the real world into an iso-demand surface is called “map transformation” (Getis, 1963; Rushton, 1972). However, these previous studies have paid no attention to traffic conditions. The idea adopted in this paper is as follows: if boundaries of hinterlands, which are influenced by traffic conditions, were transformed on an iso-demand surface, the resulting areas of hinterlands will meet the above two assumptions. In order to perform this “map transformation”, an area cartogram is used, whose algorithm is developed according to Dugenik et al. (1985).
Public baths are taken as an example of emprical work; their patrons are behaved as if the nearest center hypothesis is confirmed (see Fig. 4), so that boundaries of their hinterlands are easily demarcated using the Thiessen polygons defined around their locations. The study area is the northwestern part of Tokyo City in 1970 where demand and supply of public baths seem to have been well balanced then; CPT assumes that the balance of demand and supply is kept.
Comparing the iso-demand surface (Fig. 7) with the real world (Fig. 3) reveals that variance of areas of hinterlands in the former is much smaller than that in the latter (see Fig. 8). The result of map transformation analysis also suggests that the study area is divided into two districts in terms of goodness-of-fit, which can be differentiated according to the urbanization level in 1970.
The first is the district already developed by 1970-most part of Toshima, Shinjuku, and Nakano Words. The developed district consists of two types of residential areas: residential quarters with detached houses, such as Ochia'i district, and built-up areas with wooden apartments. While in the real world the areas of hinterlands in the former residential areas are much larger than those in the latter, the both areas are nearly equal in the iso-demand surface; there is relatively less demand for public baths in the former residential areas where a lot of high-class houses had been built with a bathroom, and so people were less densely inhabited compared with the latter residential areas. It seems that demand and supply of public baths were belanced in each different type of residential areas.
The second is the developing district, the nortwestern part of the study area. Its hinterland areas are larger than the areas in the developed district, even on the iso-demand surface, which is due to an imbalance of demand and supply.
In sum, this paper has illustrated that hinterlands can be arranged in the manner prescribed by CPT if its all the assumptions are met.
