> One point of clarification on your bailing Lucas out - can you
> expand on : "
> They are not small world graphs ( these require having a high
> cluster factor
> that axial/convex maps cannot)" - can you demonstrate easily that
> axial and
> convex maps CANNOT achieve high cluster factor? Or is this an
> empirical
> statement about real urban systems - that we tend not to find such
> graphs in
> reality?
Watts amd Strpgatz used clustering coefficient of a graph to
determine if a
graph is small world or not.
The only time you get a clustering coefficient bigger than zero is
when 3 or more axial lines
intersect at a junction. Even then your very dependant on the axial
lines all being slightly long and precisely how they intersect to
form lots of mini triangles.
Believe me I programmed in clustering coefficient into webmap@home
and didn't get anything exciting out of it. Basically clustering
coefficient works on the basis that If A knows B and B knows C then
it is likely that C knows A. This is how all the social networking
stuff works.
For an axial map If street A connects to Street B and Street B
connects to Street C then it is highly unlikely that street C
connects to Street A (in fact the reverse is more true).
Same for convex spaces but not for isovist grids.
If you could go out to radius 3 or 4 the case would be different but
this is not how Watts and Storogatz defined it just degree/connectivity.
Notice we are in an interesting twilight world where axial maps are
largely 'scale free' (some highly connected hubs, most are low
connections) but not small world. This is a shame as if they were we
could use the Derek J. de Solla Price generative mechanism and be
able to run the growth of cities into the future.
so short of redefining what you mean by small world axial maps are
not small world and so moderately unique and so abnormal.
sheep
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