The Impact of Spatial Parameters on Spatial Structuring

How is the spatial structure of a city organised at different scales, varying from connecting one street with its neighbouring streets to aggregating all the streets into a well‐structured city as a whole? In order to approach this question, this paper seeks to investigate the sequence of the streets encountered at a series of consecutive radii, from the point of view of any an individual street as a root space, termed as the embeddedness trajectory in this paper. If we clarify such embeddedness trajectory on which each individual street is progressively interconnected with all other streets with regards to its distance to them, this will enable us to better understand the spatial structuring of the whole city, because a collection of the embeddedness trajectories of all the streets of the city can illustrate the entire configuration of the city. Based on the axial and segment representations of the empirical cases, it examines the mathematical relation between node count at the radius of k (NC_Rk), measuring the accumulated number of the new streets encountered up to the radius of k, and radius (Rk). The two‐parameter Weibull relation seems to approximate the variation of node count with an increase of radius, which is expressed by the formula of NC_Rk ~ f(Rk; a, b), where ‘a’ is the scale parameter and ‘b’ is the shape parameter. Then, a strong linear correlation is found between the parameter of ‘a’ and mean topological depth (or mean metric depth) at the infinite radius, which suggests that as for each street, the number of the encountered streets up to a constricted radius is influenced by the mean topological/metric depth from that street to all other streets in the system. And meanwhile, the parameter of ‘b’ is correlated with the average embeddedness pace, meaning the average change rate of node count across all the radii. Thus, as for each street, its embeddedness trajectory is in general impacted on by the parameters of mean depth Rn and the embeddedness pace. From the above analyses, it suggests two things: first, the spatial structuring of a city is influenced by two spatial parameters: the average distance from all streets to all other streets and the average change rate of node count from the local to the global; second, the spatial structuring of all the parts of a city at the local and medium scales are constricted by the emergence of the whole structure – arising from the local structuring ‐ of the city at the global scale (measured by the infinite radius), which supports Hillier’s theory of the emergence of urban structure (Hillier, 1996, 2001)