ABSTRACT OF THE THESIS
The Study of Cellular Nets
by BARRY N. BOOTS
Thesis director: Professor Arthur Getis
The study is an examination of the geometric characteristics of two-dimensional cellular networks. Special emphasis is placed on those cellular networks which occur in socio-economic fields. The few existing studies are
examined briefly; their inadequacies, particularly in regard to their basic assumptions, are enunciated. This examination reveals that with the exception of studies of networks created in respect to regular lattices, there is a disregard of geometric characteristics. It is indicated how such a lack of consideration for geometric characteristics has contributed to much of the confusion apparent in existing studies. The advantages,which it is proposed will accrue from gaining a more precise knowledge of geometric characteristics are enumerated.
Using logical division, a typology of cellular networks is established. The differentiating criteria used involve aspects of the behaviour of the network and features related to the evolution of the network. Within cellular networks in socio-economic phenomena, a division is recognized: networks in which the individual cells are created with respect to a set of nuclei, and networks in which the establishment of individual cells is uninfluenced by nuclei. Both classes are further divisible into networks in which all the individual cells are either created simultaneously, or are established at different times. Abstract models representing the random cases of three different classes of this typology and considered to be of particular relevance to geographic research are introduced. Using these models, cellular net patterns
are produced by means of both manual and computer-generated simulation procedures. Moment measures, frequency distributions, and correlation and regression analyses are used to examine the patterns which result from the operation of the random models. The nature of the relations between the geometric characteristics are determined for the three different classes. Each class is shown to possess its own distinct geometric structure.
It is illustrated how certain properties of these geometric characteristics, especially those summarized by moment measures and correlation coefficients, may be selected for use as independent measures by which to
evaluate and compare real world cellular net patterns. Several real world patterns are examined in this manner. Such examinations reveal the limitations of the basic random models and indicate that they can be considered
as specific cases of a more general model. A structure is proposed for this general model which incorporates varying conditions of both individual cell growth and overall network evolution simultaneously. The probable nature of the general model is discussed and a means for its calibration is advanced.