The ‘global’ Space Syntax-type measures, Mean Metric Depth, Mean Visual Depth, Mean Angular Depth and Integration (HH) are all calculated using a novel ‘mean aggregate isovist cascade’ analysis algorithm (McElhinney, 2024). The algorithm, with some relation to a ‘jump flood fill’ algorithm (Rong & Tan, 2006), propagates an information cascade from a single origin point to all other points in the subject plan. It does so by starting from a single isovist in space, seeding new isovists from its occlusive edges, and recursively expanding until all space is covered. At each step in the cascade, the visual depth, the metric depth, and the angular bearing of each point ‘seen’ is assessed. The outcome is recorded at the point in question, and also affects the information that is passed on to the next level of the cascade. One complete isovist cascade, covering all points in the plan, can thus be viewed as a field of relative ‘to location’ point depth values (i.e. Visual, Metric or Angular) and provides a single ‘global cycle’.

Above: Cycles of visibility flooding in Hans Hollein’s Monchengladbach Museum

With the conclusion of each new isovist cascade, the values recorded are concatenated with all past values to provide means. A new origin is then stochastically selected and a new isovist cascade initiated. As the cycles iterate, the mean values produced refine, rapidly producing high definition global mean depth fields.