Fractals, a term coined by their originator Benoît Mandelbrot, in 1983, are objects of any kind whose spatial form is nowhere smooth (i.e., they are “irregular”) and whose irregularity repeats itself geometrically across many scales. The irregularity of form is similar from scale to scale, and the object is said to possess the property of self-similarity; such objects are scale invariant. Many of the methods and techniques of geographic information science assume that spatial variation is smooth and continuous, except perhaps for the abrupt truncations and discrete shifts encountered at boundaries. Yet this is contrary to our experience, which is that much geographic variation in the real world is jagged and apparently irregular. Fractals provide us with one method for formally examining this apparent irregularity.

A ...