Any discussion in the initial stages of a GIS project has an episode where people argue about what should be the exact scale at which to carry out the analysis. The paper by Danielle J. Marceau gives a great overview of the various ways in which space and scale is conceived and how scales affect the results of analysis. However, many things in nature do repeat themselves very regularly with scale. An entire field of mathematics called Fractals deals with things that are self-similar at different scales. So, a set of formulas can define them very precisely and those formulas are all that is needed to reproduce it at any scale.
So, is it accurate to say that many things in geography appear entirely different at different scales? Or does it change gradually with scale? If so, probably we can view these things as a continuous function of scale. Then it is possible that we will come up with equations that explain this gradual change. All we would require then will be an equation to describe the process at a particular scale, and another equation to describe how the process changes with scale, and we would be able to reconstruct how the object or phenomenon will look at any required scale.
– Dipto Sarkar
Tags: Scale
I found fractals to be a very interesting way of thinking of the scale problem. wonder how much research goes into it!