A quick web search could have directed you to a Wiki page; in particular see the external references:-
https://en.wikipedia.org/wiki/Precis...path_indicator
PAPI is a very adaptable and versatile system which can be applied to many situations and uses.
The system can be set up for a range of transition angles - angular difference between individual boxes, which a pilot might relate to the 'tightness' of the combined beams - how easy is it to use. These settings depend on location and chosen aircraft type / operation.
These values will also require adjustment for steeper values of glideslope - consider the vertical distance between transitions as the GS angle increaces.
The system should be harmonised with other approach aids - see extensive previous Pprune discussion. This area has to consider aircraft types, threshold crossing height, and in some instances length of runway.
Thus any attempt to find a simple relationship will depend on knowledge of the specific installation - there will not be a rule of thumb.
A better strategy is to learn about the system, practice using it, and when able experiment with GS deviations, including speed and height deviations; noting that transitions become progressively tighter with decreasing height - as related to range. i.e. because of the nature of angular systems the geometric relation will change according to the distance from the origin.