Yang Tao

This article, based on the conceptual experiments and the evidence-based studies on the historic districts of London and Beijing as well as the London Docklands, argued that a city should not be treated a spatial network divided into a series of differently intensified and well-defined sub-grids or communities, or an analogy of an organ composed by a group of cells; but it should be considered as a continuous network in which differently intensified areas vary with scale with an aim of optimising the accessibility among streets across scales.

Recent syntax studies showed that street is a place for social community in which different ways of connecting streets promote the different degrees of social integration. When we treat cities from a point of view of different scales of connectivity, we will observe different dimensions of urban spaces with their functional activities. The configurational relationship of spaces perhaps enhances the classification or consolidation of socio economic activities. However,the classification of the socio economic activities can be realized through the extent to which those spaces are connected. In this way, the spatial connectivity has become an interface between the patterning of physical spaces and the distribution of socio economic activities.The change rate of density can be treated as a tool for classification.

Empirical studies demonstrated the kind of periodic structures in which warm coloured patches,referring to higher rate of change of street density, are mixed up with cold coloured patches,showing lower rate of change of street density.In fact, this implied that more intensified areas repetitively appear to become the neighbours of less intensified areas, and meanwhile more delicate configurations emerge from each area.The warm coloured patches were identified as peaks in which the summits correspond to the most metrically integrated spaces with smaller blocks. Those spaces are surrounded by larger blocks. This phenomenon is called the centre-to-edge motif. The cold coloured patches were picked out by troughs in which the bottoms relate to the most metrically segregated spaces with larger blocks. Those spaces are encircled by relatively smaller blocks. This is called as the edge-to-centre motif. Both motifs appear side by side, which also reflects the kind of periodicity. In essence, such periodicity results from the change rate of street density.

This leads to the conception of dimensionality.A linear space is considered as one-dimensional space, and a plate treated as two-dimensional space. The equally intensified grid should have a dimension of two, which approximates a two-dimensional place on the earth. The empirical studies demonstrated that the street segments selected from the warm patches have the exponents less than 2; but those chosen from the cold patches have the exponents higher than 2. To a large extent, it can be suggested that the centreto-edge motif is a sub-grid with the dimension less than 2; but the edge-to-centre motif is a sub-grid with the dimension higher than 2. This in fact shows the fluctuation of dimensionality found within urban networks. It can be called as the dimensional distortion of the urban grid,which can be applied to reveal the complexity of cities.

In theory, the city adopts the centre-to-edge motif, which produces the minimum of mean metric distance at the level of the whole city.However, at the levels of medium and/or small scales, the motifs of the centre-to-edge and the edge-to-centre emerge simultaneously in order to optimise the mean metric distance across those non-global scales. This article argued that urban network intensified at different scales in fact aims to make a balance among the different scaled integrations and to optimise the different scaled accessibility among various streets and/or areas. In this way, different intensified areas with different geometric layouts accommodate various functional activities taking place at different scales. As a result, the periodicity of patchwork patterns is generated by geometric transformations operated at the non-global scales.

In this sense, the optimization of connectivity among all the streets across scales results in a non-equally intensified urban network, but demonstrating the scenario in which street segment density changes with the variation of scales, or the variation of the scope from which we perceive the city. This can be an analogy of the dynamic fluctuation of trough-peak patterns.Therefore, the partition of the urban network is produced by the change rate of street segment density.

Different functional patches or social communities essentially correspond to the variation of connectivity of spaces observed at different scales. Through this variation, some kinds of functions are mixed up and meanwhile some of them start to dominate some locations and even rejecting the invasion of other functions.

Street segment density, in itself, is the local effect, but the change rate of street segment density demonstrates the extent to which those streets are connected to each other. The latter is the basic geometry supporting multi-scaled vitality in cities. For the sake of practice, not only should we focus on small blocks and high density of the street network, but also take advantage of change rate of block size and street density as well as mixed uses and functional integration or segregation. In such way, we can generate more diverse and organic complexity of cities, in which small and middle-sized blocks, big compounds, commercial pedestrian streets, high speed expressway and other urban elements and meanwhile all those urban forms can be used to accommodate different activities satisfying diverse needs for human beings.