Accessibility Gradients · Images showing high (red) to low (blue) accessibility areas in Berlin, pre and post unification (left, right) · Mike Batty (2003)
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Land-use Gradients · Residential land-use gradients in San Francisco. Gradients in cream represent residential parcels of decreasing density · San Francisco Planning Department (2010)
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Paths may not only be identifiable and continuous, but have directional quality as well… this can be done by gradients, a regular change in some quality which is cumulative in one direction. Most frequently sensed were topographic gradients…

- Kevin Lynch, Image of the City (1960)

A morphogenetic perspective on urbanism should include a theory of gradients. In cellular reaction-diffusion systems, a gradient is a concentration differential caused by the diffusion of a reactant through space and time. Whilst physical gradients (pressure, thermal), along with their counterpart, Motility, form the basis for movement in such systems, chemical gradients induce cellular differentiation in the form of gene expression. In urban terms, we can say that both flows (movement) and differentiation (expressivity) can be induced by gradients.

Urban gradients exist as differentials that take diverse forms. Demographic, topographic, accessibility & economic gradients are all simultaneously present in urban space, inducing flows of information, vehicles, individuals and goods, as well as the expression of land-uses. Gradients are directional and continuous phenomena, and can’t accurately be captured by network models. A continuous representation of space, rather than a topological one, is required to deal with gradients in urban modeling.

Gradients are not contiguous through an urban assemblage. They can be ruptured by infrastructure, topography and policy boundaries, countered and splintered by other conflicting gradients produced by diverse activators and inhibitors.

See Also: Morphogenesis, Shapefile, Assemblage, Motility, Boundary