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Table 1 Hypothesis and space measurement

From: The mathematics of spatial transparency and mystery: using syntactical data to visualise and analyse the properties of the Yuyuan Garden

Hypothesis Interpretation Mathematical properties Result
The sense of mystery in the TCPG is a by-product of structural permeability rather than visual accessibility. The network of paths in the TCPG is very difficult to navigate and understand, but the spaces that can be seen from the paths are more intelligible. 1) Intelligibility: being the Pearson correlation between integration and the connectivity values of all vertices in the plan graph.
2) Control: the degree by which a space controls access to its neighbours.
If the hypothesis is true, then:
1) path-related intelligibility measures will be lower than vision related intelligibility.
2) path-related control measures will be lower than vision-related control.
The visual sense of mystery in the TCPG is heightened by the complexity of its spaces. Spaces in the TCPG have both high levels of visual mystery and of visual complexity. 1) Isovist occlusivity: the total length of all occluded edges in a view-shed.
2) Isovist jaggedness: the ratio of Perimeter2 to Area in a view-shed.
If the hypothesis is true, then:
There will be a positive correlation between spatial integration (i) and both occlusivity (O) and jaggedness (J) results.
The sense of phenomenal transparency in the TCPG is a by-product of the visual pull and directionality experienced in major spaces. The sense of transparency experienced in large spaces is caused by spatial irregularity, meaning that the eye is drawn to look deeper into the environment. 1) Isovist area: the area of isovist polygon.
2) Drift magnitude: the distance from observation point to centre of mass of isovist polygon.
If the hypothesis is true then:
Drift magnitude will increase in line with isovist area.