With apologies to those designers out there who 
must think we appear to be arguing over the 
number of angles which can sit on the head of a 
pin.

>2) When the same radius, say, radius 3, is applied synchronically, mean
>depth becomes homogeneous across *all nodes* in a system, independently of
>N counted differently within the radius.  Sheep finds this as a universal
>phenomenon. If this is the case, it is clear that RRA values of nodes are
>differentiated not by their mean depth but by their neighbourhood sizes,
>in such a way that RRA ~ 1/log N. So we are in fact saying that a node
>is “more asymmetric” or “segregated” BECAUSE N is small. My question is:
>Is it necessary in the first place to relativise mean depth when it is
>already free from size effects?

Yes Hoon is right I have found this is not a 
homogeneous (universal) phenomenon. I have found 
that there is a very (0.99 almost perfect) 
correction between total depth and number of 
nodes in the system. Hence when you find mean 
depth you get a value which doesn't change ( 
"homogeneous across *all nodes* in a system,").


>  My question is:
>Is it necessary in the first place to relativise mean depth when it is
already free from size effects?

Well there are a number of answers to this.
1) RRA correlates slightly better with observed 
movement than with Total depth or N. (N= number 
of lines encountered) or even a multivarant 
combination of them both. This is in the case of 
4 data sets I have access to so could be 
statistical problem or might be saying something 
else.

2) The strong strong correlation occurs in 
*ALMOST* aLL *topological* axial maps of real 
urban systems. I have a small ( less than 1% of 
all axial maps I have access too) number of maps 
which show weaker (R2= 0.8999 or less ) 
correlations. One is for a US suburb, one is of 
alpha world, one is one map of milton keyens. 
The Milton Keyens map is significant in that it 
highlights on tiny zone with so much integration 
that the rest of the map appears to be totally 
blue.

>3) Randomly generated axial lines ( using Penn 
>style line length distributions) or axial maps 
>which have been randomised typically ( that is 
>orientation and length of an axial line and the 
>average axial density) don't on average posses a 
>strong correlation ( on average ranges between 
>0.7 and 0.9 ). This suggests that the 'universal
phenomenon' is partly but NOT WHOLEY due to the 
use of axial lines. The arrangement of axial 
lines  ( what some people might call the design ) 
appears to be both 'universal' ( appears in 
almost all human settlements known to syntax kind 
) and yet not strictly emerging from the 
materials (axial lines) in question. As an 
analogy its a bit like Chomski deep grammars 
there is a range of configurations which are 
universal to the range of human languages but not 
the range of all possible (alien or machine) 
languages. In general this is not surprising as 
it quite consistent with Bills paper 'A Theoru of 
the City as Object or how spatial laws mediate 
the social construction of urban space' in Urban 
Design. Weather this empirical discovery of this 
near universal consistency constitutes a new 
finding or not is under some debate.

What is does mean is that RRA has not been tested 
outside the realm for which they designed.

4) Building spaces do not always show this 
phenomena - but we hardly use a radius RRA 
version  in a building. Remember this correlation 
is purely a phenomena in the radius cases the 
global (N constant) case does not have this 
correlation(it cannot).

5) Axial angular cases have a weak ( less than 
r=0.9 ) correlation between total angular depth 
and number of items encountered.

6) The topological segmental case has practically 
no correlation between number of items within a 
radius and the total depth encountered. We can 
see this visually as maps of segmental radius 3 
look to have a weak relation with observed 
pedestrian movement. Again Bill and Shinichi's 
solution to this at the moment is to look at the 
depth of the segments belonging to lines which 
are 3 axial lines away.

7) the angular segment case also has practically 
no correlation something we would really need to 
permit doing pedestrian movement on metropolitan 
scale maps.

8) Isovists maps do not show this correlation. 
This makes a radius limited version of an gridded 
or random isovist map difficult to do.

8) Phone email networks ( the graph formed by 
phone conversations between people in an 
organization) do not show this correlation. Again 
it would be nice to have a radius like case which 
says ( of the number of people who know someone 
who knows someone ) who is relatively more 
important ( who is the local conduit of 
information in a team which are part of a larger 
organization).

so
>My question is:
>Is it necessary in the first place to relativise mean depth when it is
already free from size effects?

So think the answer is yes - but not for the 
urban axial case which I am sure you are 
referring to.

sheep
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