An approach to structure in architectural and urban design. 3. Illustrative examples

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Abstract
This paper, the third of a sequence, provides illustrations of the theoretical concepts which have been introduced in the previous two papers. Each example points to the need for a hierarchical collection of sets X, X‘, X“, …, where for example X’ is a cover of X. At any one level, say the N-level, a structural backcloth S(N) is obtained, together with some relevant pattern {π}. Changes {δπ} in these patterns correspond to structural t-forces, and these are experienced by the specific structures defined by the data. The first example is essentially architectural and is based on simple data collected for the village of Lavenham (West Suffolk, England). An interpretation of the Q-analysis is offered at both N and (N- 1)-levels. The second example is based on data collected for a study area in Southend-on-Sea (Essex, England). These data are relevant both to commerce and to public amenities, and the Q-analysis provides a means of studying the changes produced over the period of time, 1910–1972, at the N-level. This enables the appreciation of the relative nature of the static backcloth S(N) over a time period and the interpretation of changes in S(N) in terms of structural t-forces which are manifest during this time. Specific graded patterns are produced that are related to car parking and its effect on the intuitive experience of the town structure. The third example is based on a published community study in the University of Essex (Atkin, 1974c). In this case a span of five hierarchical levels is used, and the examples are taken from the backcloths S(N), S(N- 1), and S(N+ 1). These include an analysis of housing accommodation [together with an illustration of the algebraic pattern generator Θ(K)], catering facilities, and the political structure of the university committees. The most striking feature of this study is the discovery of q-holes in the structure, and their roles as q-objects for traffic. In the case of the committees of the community, a new and disturbing light is thrown on the well-intentioned efforts to make the university more democratic and suggests that, without a deep analysis of the structure, these efforts can easily result in the generation of noise as a substitute for genuine participation.

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