Beniamin Kostrubiec


Division of the shortest dendrite according to maximum intra-group likelihood

Barbara Jokiel, Beniamin Kostrubiec

Geographia Polonica (1976) vol. 33 2, pp. 191-197 | Full text

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Barbara Jokiel, Wrocław University
Beniamin Kostrubiec, Wrocław University

Harmonic analysis of urban spatial growth

Piotr Korcelli, Beniamin Kostrubiec

Geographia Polonica (1973) vol. 25, pp. 93-102 | Full text

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Several authors have recently suggested that urban growth can be representedas a wave-like diffusion process (Blumenfeld 1954, Boyce 1966, Morrill1968 and 1970, Korcelli 1969, 1970 and 1972). It may be assumed that this lineof research will also expand in the future. Its relation to other approaches, aswell as some insights it gives into the nature of the spread of urbanization, arediscussed elswhere (Korcelli 1972). This form of analysis, however, beside certainadvantages it offers, brings also some dangers, which can not be overemphasized.Two particular problems may be noted:

The improvement of the concepts has not been supported by an extensivebody of sound, empirical evidence. This, in part, is a consequence of scarcity ofadequate data, especially when large spatial and temporal series should be employed.If it persists, such a gap may eventually prevent further developmentof the theory.

The second problem relates to the methodology itself. While it is usuallytempting to classify a phenomenon under investigation as a part of a broadersystem, one may loose, by doing so, some of its rather essential properties. Thefollowing citation from Beckmann (1970, p. 116) well illustrates the point:"Although it is interesting that the same mathematical equation appears toapply to a particle, heat diffusion, and to human migration, this conclusionshould not be accepted uncritically. After all, we do not seek to reproduce thewell-known equations of mathematical physics but to develop models that bestreflect economic conditions".

The objections of this paper are, therefore, twofold. First, we attempt tofind some statistical evidence, however limited, for the aforementioned conceptsof urban growth. The method applied is believed to be consistent with the theorytested. Second, we want to trace, on the basis of the data employed, some of thespecific features of the urban growth process, as opposed to other spatial diffusionprocesses.


Piotr Korcelli, Institute of Geography and Spatial Organization Polish Academy of Sciences ul. Krakowskie Przedmieście 30, 00-927 Warszawa, Poland
Beniamin Kostrubiec, Wrocław University