After formulating an access map, the spatial system represented may be described in terms of its
Figure 2.12. “Interface Map” of a Town in the Var Region of France. Hillier and Hanson (1984: 100). Reprinted with the permission of Cambridge University Press.
Figure 2.13. Combined Convex and Access Diagram of Palenque Palace Phase 1. Palenque Palace modified after Greene Robertson (1985b: fig. 1).
“syntactic relations,” or more specifically in accordance with mathematical principals of “symmetry-asymmetry” and “distributedness-nondistributedness” (see Hillier and Hanson 1984: 93). A space or system of spaces is characterised as distributed if there is more than one route of access between spatial units that include passing through intervening space to get to the target space. Conversely, a space or system of spaces is categorised as nondistributed when there are fewer or no more than one route to a given space (Hillier and Hanson 1984:108). Distributed and nondistributed relationships
Between spatial units function as indicators of how well a system of spaces is integrated (Blanton 1994: 32). Highly nondistributed access maps will often appear treelike (“dendritric”) in shape, as they tend to comprise fewer connections (i. e., pathway options) between spatial units. In contrast, an access map comprising the same number of spaces, but with a greater number of connections, will often appear flatter in shape and comprise fewer permeation levels. A system that displays a high number of spaces but relatively few levels of depth would be described as a highly distributed. The flatter appearance of the diagram is a consequence of the increased number of route options increasing accessibility through the system. Justified access maps totaling a relatively high number of permeation levels would be described as deep and suggestive of a more restricted spatial system. In a deep system, persons must pass through a greater number of spaces to gain access to the target space. In the most restricted of systems, only one space controls access to the next. Distributed systems will usually form diamonds or rings on access maps (Hillier and Hanson 1984:94,148; Bavin 1996: 159).
A unit of space within the system of spaces is defined as symmetrical if it has a large number of similar relationships with other spaces in the system, an indication that, on average, fewer boundaries have to be traversed to access that space (Grahame 1997: 148-149). Conversely, a unit of space within a system of spaces is defined as highly asymmetrical if it has a low number of similar relationships with other spaces within the system. In line with Grahame (1995: 74-75), this concept is best described by example. In Figure 2.15, two spatial configurations are represented, each comprising the same number of spaces (nodes) and boundaries (edges). In Example 1, the spatial arrangement would be described as highly symmetrical, as the relations of a, b, c, and d are equivalent with respect to their level of accessibility from other spaces in the system. More specifically, in Example 1, one would have to cross no more than two boundaries, starting from any point in
Figure 2.15. Example of “Symmetric" tionships between “Nodes.”
Figure 2.14. Access Diagrams of Examples of Andrews’s (1975) Building Group Archetypes.
The system, to access any other space within the spatial assembly. If we randomly take position a as our destination, the number of boundaries that need to be crossed to reach this space, starting from all other positions, is as follows: from b to a, two boundaries; from c to a, two boundaries; from d to a, two boundaries; from e to a, one boundary. In contrast to Example 1, the spatial configuration of Example 2 would be best described as asymmetrical, as the spatial relationships among a, b, c, d, and e vary distinctly. For example, the relationship between b and a is different than the relationship between e and a. Whereas access from b to a would be achieved by crossing one boundary, three additional boundaries would have to be traversed to access a from e, including passing through b. Consequently, this difference defines the spatial configuration as asymmetric. Spaces seen to have asymmetric relations “always involve some notion of depth, since we must pass through. . . [intervening spaces] to go
And “Asymmetric” Rela-from one space to another” (Hillier and Hanson 1984: 94).
In Figure 2.16 are some simple examples of justified access maps as offered by Hillier and Hanson (1984) indicating depth relationships between nodes as well as patterns of symmetry, asymmetry, distributedness, and nondistributedness (Hillier and Hanson 1984: 148149). In these examples, symmetric relationships between spaces will be apparent if neither space a nor b controls access to the other, for example, where a is to b as b is to a with respect to c. Alternatively, spaces a and b will be considered to have asymmetric relationships if a is not to b as b is to a, or, more specifically, if one of these spaces (a or b) controls access to the other from a third space, designated c (Hillier and Hanson 1984: 148-149; see also Foster 1989a: 43 and Bavin 1996: 160).
(1) a and b are in an asymmetric and nondistributed relationship with respect to c
(2) a and b are in a symmetric and nondistributed relationship with respect to c
(3) a and b are in a symmetric and distributed relationship with respect to c
(4) a and b are in a symmetric relationship with respect to c, but d is asymmetric to both with respect to c
(5) d is in a nondistributed and asymmetric relationship to a and b, which still remain symmetric to each other with respect to d (or to c).
Figure 2.16. “Justified” Access Maps Showing Symmetric-Asymmetric and Distributed-Nondistributed Relationships. Hillier and Hanson (1984: 94). Reprinted with the permission of Cambridge University Press.
World History
