Hagerstrand model on diffusion of innovation
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Hagerstrand traces the diffusion process by imitating it with numbers. Such imitation, leading to prediction or forecasting of the pattern of diffusion, is called a simulation of diffusion. To follow the mechanics of this strategy, it is necessary only to understand the concepts of ordering the non-negative integers and of partitioning these numbers into disjoint sets.
The figure on the left shows the spatial distribution of the number of individuals accepting a particular innovation after one year of observation (Hägerstrand, p. 380). The figure on the right shows a map of the same region and of the pattern of acceptors after two years--based on actual evidence. Notice that the pattern at a later time shows both spatial expansion and spatial infill (more concentrated use and greater density per unit of land area). These two latter concepts are enduring ones that appear over and over again in spatial analysis---as well as in planning at municipal and other levels.
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