The idea of difference factor was to try to measure the degree of
difference between the integration values of, say, a everyday living room,
a guest reception room and a kitchen in the context of the whole house
which of course was made up up many more spaces.. We needed some index of
the degree to which main functions were spatially differentiated, since in
some cases the differences seemed to be small and in others large, and this
seems to be an important feature of the house. If you have a large number
of spaces, then of course the spread of values, can be indexed by measures
like standard deviation, but this won't work for just three, or even a
small number of spaces, especially as in some cases, one space was much
more integrated or segregated than others. Difference factor can of course
be applied to the minimum, maximum and mean integration values of a system
with a large number of spaces (in which case it would often tell a similar
story to standard deviation), and then to selections of the main functional
spaces, and this would enable you to see how much of the overall
differentiation in the system was taken up by functional spaces, as opposed
to, say, the difference between transitions spaces like hallways and
functional spaces. The measure is far from perfect, but in most
circumstances it seems to give a rought indication of what it is intended
to measure.
We used to use entropy based measures on axial maps for exactly the same
reason: to try to measure the degree of difference between one or a few
spaces and others. Again, what we were trying to get at was that in some
cities one or two streets were much more integrated than others, while in
others differences were more marginal. As I recall (it was back in the
eighties) we used to normalise the measure against the hatural number
system, since this maps on to the depths of space from a root in a unlinear
sequence. Eventually the measure fell out of use because it did not give
very interesting results. We need to go back over some of this and try to
reconstruct where we got to. I sense there is something interesting here,
but at the time we never found any results which were interesting enough to
publish. Perhaps its time to look at it again. - Bill
>Hello everyone,
>
>Iíve got some questions about the ëdifference factorí. In my unique
>reference, Hiller and his colleagues proposed it for a system with three
>spaces only.
>
>*Hillier, Bill; Hanson, Julienne e H. Graham. ëIdeas are in Things: An
>Application of the Space Syntax Method to Discovering House Genotypesí.
>Environment and Planning B: Planning and Design 14, 1987, pp 363-385*
>
>This measure is based in the entropy, and its maximum value is ln(k) for
>a system with k lines.
>
>But, why doesnít the minimum value is zero? Or, at last, a value
>generated by the ëlinear graphí ń the maximum asymmetry ?
>
>o ----- o ----- o ----- o ----- o
>
>Iíve modified the formula to n spaces and tested it in some axial maps.
>Iíve got results close to the maximum value for any map Iíve tested.
>
>Anyone has ever used the difference factor for axial maps?
>
>Thanks in advance,
>
>Lucas Figueiredo
>MDU - UFPE - Brasil
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