Cite as:
Krieger M H, 1991, "Segmentation and filtering into neighborhoods as processes of percolation and diffusion: stochastic processes (randomness) as the null hypothesis" Environment and Planning A 23(11) 1609 – 1626
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Segmentation and filtering into neighborhoods as processes of percolation and diffusion: stochastic processes (randomness) as the null hypothesis

M H Krieger

Received 6 June 1989; in revised form 16 January 1991

Abstract. A set of models is reviewed in which orderly urban phenomena are accounted for in terms of noise (randomness, stochastic processes): segmentation as a process of runs in random processes (percolation); filtering as a process of random walk and so diffusion, and as a Markov process. In particular, 'continuity' of the spatial price envelope, a truism of real estate, leads to the diffusion equation. No foreordained centers, boundaries, or gravity (or entropy) is needed to obtain clustering in these models. The models are combined in a simulation, implemented in a Lotus 1-2-3 spreadsheet, as well as in a partial differential equation driven by a stochastic source term.

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