afford while they are still struggling to survive and 
succeed, Some activities never succeed, but gradually 
wither away and die, leaving their premises free for 
occupation by another generation. Others succeed, and 
if successful most activities grow. In the process of 
growth they need more space, and begin to move around 
among the stock of structures in the city acquiring more 
space each time, balancing out location and rent against 
the kind of premises or accomodation they need. Because 
each move is made to acquire more space, more 
investment is required each time. Therefore the stay in 
each successive piece of accomodation becomes longer, 
as the activity sinks more and more funds into its 
accomodation. At the same time the activity, because of 
its growing resources, is able to devote more effort to 
acquiring information about available accomodation over 
a wide and wider area, Moves, in addition to taking 
place at longer intervals, may be made over increasing 
distances. Finally, the most successful activities grow 
sufficiently large to build their own accomodation, 
where they settle down for a very long time indeed. A 
new phase begins as these successful activities continue 
to grow and experience problems in arranging their 
dependent activities in a satisfactory manner. Such an 
outline is very crude, and does not deal with many 
special cases of the growth of activities. For example, 
the pattern of size and growth in professional offices 
may be entirely different. But for the majority of 
commercial offices, which are not tied to industrial 
plants, the general pattern has some meaning. 
If the general hypothesis is correct, then old and 
converted accomodation should contain a predominance 
of small, young activities. These would have a history 
of moves confined to their local area, although their 
latest move would be over the longest distance; they 
would also be planning to spend longer in their present 
accomodation than in any place previously, On the 
other hand new accomodation should contain a wider 
mixture of longer scale activities, all of them successful 
and growing, many of them having moved some distance 
from their previous location. 
We can thus begin to frame the kind of questions we 
should ask about the process. Who builds offices? Who 
occupies them? Why has office space grown at 
particular speeds? Why is it located in particular areas 
of the city? How have social control and intervention 
affected the development of offices? How do office 
firms make decisions about their accomodation? These 
and other questions form the basis for our study. 
A Plan of Work 
We have tried to combine the rigorous analysis and 
development typical of American work with the interest 
in policy and controls which is so strong in Britain. We 
have constructed some models of office growth and 
development and have surrounded them with 
complementary studies of different facets of the city 
which have affected the process. We have adopted this 
approach because it seems unlikely that at the present 
time of writing, models alone can provide a full 
understanding of urban patterns. The time will surely 
come when mathematics can handle the problems of 
urban growth in all their complexity, but just now 
certain facets remain outside their scope. The 
behavioural aspects of urban life are beginning to 
ARCH + 1(1968) H.4 
receive attention from model builders, but their 
development has been slower than the more mechanical 
treatment afforded by transportation models and so on. 
Thus a study of those who occupy office space, their 
behaviour, decisions and the preferences and choices 
which influence their reasons for occupying a 
particular building has been necessary. Similarly we 
have investigated the providers of offices for it is their 
decision which governs the final pattern of office 
growth in the city. And these are joined by an analysis 
of the patterns of policy and control within which each 
set of "actors" operates, 
A detailed account of our research programme is given 
elsewhere (1), and it would take too long to go into all 
our work in a short paper such as this, I propose there - 
fore to touch upon the modelling aspects of our study, 
leaving aside more descriptive anecdotal work, which 
made such a valuable contribution to the final report, 
I do this because model building may be less familiar 
than other aspects of our work and may be of more 
general interest than those parts which apply 
specifically to London. 
Alternative Approaches to the Office Model 
Our objective in constructing models of office 
development was, first to understand and explain the 
patterns of office growth in London since the war, and 
second to discover whether there were any ’rules’ for 
this kind of development which might be useful for 
predicting future patterns. We concentrated upon the 
amount of office floor space at different locations and 
the rate of change of office space in the city. We did 
not consider office employment or rents. Our basic 
spatial units of observation were a series of 500 metre 
square cells, stretched across the whole of the urban 
area. This unit was largely dictated by the pattern of 
existing land use information. Our time unit was one 
year. 
Both models started with two very simple hypotheses. The 
first stated that "like breeds like"; that is to say, a cell 
with a large amount of floor office space already in it 
is more likely to attract further increments of office 
space than a cell which has less initial space. The 
second hypothesis suggested a distance decay factor, so 
that the attraction of a particular cell for office 
development, falls off as some function of distance. 
Clearly both hypotheses could be upset by such things 
as zoning constraints, but they did provide a starting 
point. 
Our first model was essentially an exercise in the 
analysis of time series, leading to a quasi-Markov 
process, Markov processes have been neglected in 
location analysis but they possess some interesting 
properties. The essence of the approach is that the 
future behaviour of the process, is independent of the 
past, providing that the present state is given. 
Suppose we have a series of consecutive trials, n= 0,1, 
2, ..., the outcome of the n-th trial is represented by a 
random variable such as Xn. We can assume that this is 
discreet and takes one of the values j =.1,2, ... The 
actual set of outcomes at any trial is a system of events 
Ei,i= 1,2, ... These are called states of the 
system and they may be finite or infinite in 
Sy