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connect with other isovist viewpoints and the good correlation between connectivity and maximum radial length demonstrates this.

There is an even better correlation between connec- tivity and mean radial length, with an r-squared value of 0.801. Mean radial length is a good indica- tor of the location of road junctions. At junctions, the isovists that are generated are particularly spiky, with ‘fingers’ of visibility that stretch down every street leading from that junction. The ‘spikier’ the isovist, the more likely it is to be well connected, for exactly the same reason that a long line of sight will be well connected. As well as correlating highly with connectivity, mean radial length also has a signifi- cant correlation with mean depth and total depth. Although this relationship is not as strong as the relationship between the mean radial length of the isovist radials and isovist connectivity, it is still a good correlation. This suggests that when analysing urban areas using visibility graphs, junctions are more likely to represent integrated rather than segre- gated locations. The r-squared for this relationship is 0.657.

The standard deviation of radial lengths is another measure of the spikiness of an isovist and can result in higher than average values at locations such as road junctions in urban areas. Although the rela- tionship between radial length standard deviation and mean depth is good, (r-squared of 0.596) it is not as good as the relationship between mean radial length and mean depth.

Maximum radial length correlates well with connec- tivity, so it is no surprise that it should also correlate fairly well with mean depth and total depth. This correlation is not as good as the correlation with

connectivity (an r-squared of 0.459 compared to 0.733). The reason for this is that if a particularly long line of sight radiates from an isovist viewpoint, then it is probable that this isovist will connect with a number of other isovist viewpoints. If an isovist is well connected it is likely to be integrated too, but this is not a surety, which explains why the relation- ship between maximum radial length and mean depth is not as good as the relationship between maximum radial length and connectivity. Another strong relationship that exists between mean depth and one of the geometric measures of an isovist, but one that essentially owes this correla- tion to connectivity, is the relationship between area and integration. The r-squared correlation coeffi- cient for the relationship between area and integra- tion is 0.587. Because area is such a good approxi- mation to connectivity, then the relationship between connectivity and mean depth is conse- quently a significant one. The r-squared of the cor- relation between connectivity and mean depth is 0.603.

The relationship between geometric measures of iso- vists and syntactic measures of isovists, as demon- strated above, is highly significant. The geometric properties of isovist are measures of the single isovist in which an obser ver stands. These are local proper- ties and can be instantly apprehended by someone standing in the space. A person standing in a land- scape can look around and immediately perceive the size of the space they are occupying, the shape of the space, whether or not it is an open space evenly distributed about their standing point or they are situated to one edge of it or perhaps it is a particu- larly ‘spiky’ space, allowing glimpses of other spaces past occluding surfaces. All of this information can

be judged by a person who is visually surveying their environment. The syntactic measures, in con- trast with geometric measures are not properties of an individual isovist considered in isolation but are properties of that isovist’s relation to all other iso- vists in the system. The syntax measures of the iso- vists refer to the overall structure of the world, be it a building or an urban area. The fact that there is a strong correlation between certain geometric meas- ures of isovists and syntactic measures implies the potential to make global inferences from purely local information. This means that a person can pause in an environment and make a judgement about their position within the whole system based on visual information of the space that they are occupying. It also implies that when wayfinding, a subject may be strategic about the direction they choose to take (whether or not this is a conscious decision). This conjecture is supported in the next section of this chapter where the geometric and syn- tactic properties of isovists at pause point locations are compared to the distribution of isovist measures throughout the world.

Isovist Analysis of Worlds

Each of the seven worlds in the following section has been analysed using the application OmniVista. The presentation of the results of the analysis is fol- lowed by a discussion of the distribution of isovist results as calculated for each measure and for each world.

Since, in the previous chapter, it was suggested that people were pausing in the vicinity of road junc- tions, this hunch can now be tested using isovist data. If the complete set of all possible isovists is held to be a ‘population’, in the statistical sense,

then this population can be compared to the ‘sam- ple’ of isovist properties calculated for each of the pause point locations (as described in Chapter 7). There are many statistical methods for comparing a sample (from a population) to the population itself to determine how representative that sample is of the whole population. The two6_{methods used in this} chapter are the central limit theorem and the z-test. The z-test relies upon the population being approxi- mately normal (either one-tailed or two-tailed) whereas the central limit theorem can be applied to a completely random population.

The central limit theorem states that for any sample population drawn from a population (which need not be normally distributed) then as long as the sample size is relatively large (n>10) then the distri- bution of the sample will be approximately normal. The larger the size of the sample the better the approximation. The sample size of pause points used in this section of the chapter is very large, using this definition. If the population is not normally distrib- uted, then the sample will only ever approximate a normal distribution whose mean will be the same as the population mean. The value of z using the cen- tral limit theorem is shown below.

Where µ is the mean of the population, is the standard deviation and is the mean of the sample. The z-test is a statistical method for comparing a sample against a population to determine how likely it is that the sample was drawn from that particular population. The test relies on knowing the values

z=

x −

x

Equation 8.9 Formula for Calculating z