Hi Alan,
There are already some methods to characterise these differences, such
as 'hub-centre', 'hub-periphery', the existence of a 'central-core'
and so on, even if all of them are 'small-worlds' or, 'scale-free' and
so on.
The problem is to transform graphs to maps. The 'segment graph' has
the same problem.
I believe a proper model must either generate 'city blocks' or street
networks, and then create the graph.
Best Regards,
Lucas Figueiredo
On 05/09/07, Alan Penn <[log in to unmask]> wrote:
> Nice idea Sheep, but isn't it exactly the axial map, rather than the graph
> which you would want to grow? Let me be specific. It is easy to make a
> deformed wheel core axial map, edge to centre integration pattern and back
> out in several directions etc. It is then possible to take exactly that
> graph - the set of line connectivities - and 'lift' the central lines out
> and put them on the periphery (maintaining the axial connections, but not
> the order of those along the line) The result is an axial map with
> peripheral integration and internal segregation - as a 'type' the antithesis
> of the deformed wheel core, and so substantially different in social,
> economic etc terms. Note that these two have the same graph but different
> maps (not just sheet of rubber topology maintaining transformations). The
> question is, how much value is there in the axial graph growing approach the
> real interest is in the axial map?
>
> Of course, segmental representations, because they are planar, and using
> angularity to achieve the same results as axial, do not have this
> limitation. My own preference then would be to grow segmental angular
> graphs...
>
> Alan
> >
> > On 5 Sep 2007, at 01:35, Roy Wagner wrote:
> >
> > > Further, generating an axial graph doesn't automatically translate
> > > into generating an axial map.
> >
> > Well I think that would be an advantage not a disadvantage. Consider
> > you want to build a shop in a growing city like Milton Keynes or
> > Atlanta. You want to buy ground cheap on the edge of the city and
> > invest for the future urban growth. You don't really care how the
> > city will be laid out in the future only how it will affect the
> > integration patterns of your existing street ( and so your likely
> > future foot fall and so profits).
> >
> > Assuming it was possible to find some kind of parameter set for the
> > historic growth of the city you could then use some generative
> > algorithm to create the graph BUT NOT the axial map. You could then
> > process integration and get a an idea of how one 'future' played out.
> > Doing this a few thousand times you might get a Montecarlo sampling
> > of the 'future' and have a distribution of values. For example you
> > might see that as the city grows your location generally becomes more
> > segregated and hence is a poor choice for a passing trade type of shop.
> >
> > Now if it was possible to grow a graph so that it was configured like
> > an axial map (low clustering coefficient + what ever else is
> > necessary) the lack of an axial map is an advantage. One graph can
> > represent hundreds or thousands* of axial maps. Hence each grown
> > graph with a few thousands sample growths would give a much greater
> > magnitude of possible axial growth patterns than growing the axial
> > map alone.
> >
> > You could imagine watching the axial map surrounded by a point cloud
> > and watch the 'future' versions of London evolve. You could only see
> > the integration colours to the already built sections but the rest of
> > the alternatives would be out there invisibly surrounding the city.
> >
> > that's the vision,
> >
> > naturally this all depends on the ability to get a 'true' or at least
> > 'accurate' way to grow the graph. Of which grow like Barabasi style
> > algorithm might have been a starting point, if it were not for the
> > strangeness of axial maps.
> >
> > sheep
> >
> >
> > *how many graphs I'm not sure more than one.
> >
> >
> > ------------------ cut out and keep
> > ---------------------------------------------------
> > + S.N.C. Dalton Lecturer Maths & Computing. n.dalton(AT) open.ac.uk
> > + phone 07908 64 9005 OU Extension 53153.
> > + http://www.mcs.open.ac.uk/People/n.dalton
> > ------------------------------------------------------------------------
> > ---------------------
>
--
Lucas Figueiredo
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