Mean aggregate isovist cascade analysis; a temporal approach to spatial analysis
McElhinney, Sam (2024) Mean aggregate isovist cascade analysis; a temporal approach to spatial analysis. In: Space Syntax Symposium 14. Gruppo editoriale Tab S.r.l., Rome, pp. 1949-1976. ISBN 9791256690329
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Our paper distinguishes between two types of graph structures; 'sparse' and 'dense.' Sparse graphs, such as axial line graphs of cities, can succinctly summate vast spatial networks. In contrast, dense graphs, such as Visibility Graph Analysis (VGA) of architectural spaces, bring nodal redundancy and scalar challenges. As the spatial detail of a VGA grid increases, the computational cost of measures such as integration grows exponentially. We posit that Turner's development of VGA (2001) overlooked qualities of isovists that resolve such issues.
As units of spatial perception, isovists bind inter-visibility relations within their geometry, and encode potential further connectivities through their occlusive edges. We use these insights to generate 'isovist cascades' of visibility relations across architectural plans in real-time; starting from a single isovist in space, seeding new isovists from its occlusive edges, and expanding until all space is covered. We demonstrate how propagation of isovist cascades from stochastically evenly distributed locations, and their subsequent concatenation, produce high definition fields of mean visual depth and integration.
Our approach allows significant gains in computation speed and detail over VGA. Additionally, the temporal resolution of isovist cascade analysis (ICA) facilitates three observations that may offer insights to the cognitive understanding of space. Firstly, the minimum stochastic seed total to establish a mathematically stable field, (our 'sufficient set'), is low, being circa 15 - 50 for all plans. Such findings have implications for cognitive spatial mapping, indicating that surprisingly few orientation points may be necessary for effective navigation.
Secondly, after factoring a logarithmic reduction of field change over time, our case study plans show consistent residual variations, each with distinct amplitude and range, or ‘spatial wobble’. We evidence how such values might describe topological qualities of spatial systems in a dimensionless manner; providing a single coefficient metric and a broader prototype relational matrix that classifies spatial systems from the multiaxial to the mono-cursive and from entropic to self-similar.
Finally, we discuss a paradox wherein apparently ‘complex’ spatial configurations can exhibit ‘spatial wobble’ factors lower than 'simple' examples. Elaborate spatial systems often contain distinct or recognisable structures that, in turn, afford development of landmark knowledge. Conversely, ‘simple’ systems often have indistinct and or unexpectedly entropic sub-features, and so afford disorientation. It appears our method reflects such cognitive easements and challenges, suggesting a novel metric for the ease of development of ‘sufficient’ or functional spatial cognition.
Proceedings of 14th International Space Syntax Symposium, Nicosia, Cyprus, 24-28 June 2024.
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