Variance (Tv) expresses the mean of the square of deviation between all radial lengths and average radial length of an isovist (Benedikt, 1979). In visibility graph terminology, it represents the point second moment for a location. Variance indicates both the complexity and eccentricity of an isovist. It takes other measures, studied simultaneously, to sort out which. For example, low Drift and high Variance will indicate complexity but not eccentricity (i.e. non centered-ness in one’s isovist).
To determine Variance, the Isovist_App first calculates the difference between the current radial length and the average radial length. The resulting value is squared, before being recorded as a mean over successive radial iterations for every point ‘V’ in plan. The final sum outcome is subsequently square rooted, producing a relative value between 0 and infinity.
In notation form the calculation for Variance is expressed as:
Where ‘Li’ is radial length, ‘Qv’ the average radial length from V; and ‘n’ the total number of radials sampled.