  Fractal geometry provides a powerful tool for scale-free spatial analysis of
cities, but the fractal dimension calculation results always depend on methods
and scopes of study area. This phenomenon has been puzzling many researchers.
This paper is devoted to discussing the problem of uncertainty of fractal
dimension estimation and the potential solutions to it. Using regular fractals
as archetypes, we can reveal the causes and effects of the diversity of fractal
dimension estimation results by analogy. The main factors influencing fractal
dimension values of cities include prefractal structure, multi-scaling fractal
patterns, and self-affine fractal growth. The solution to the problem is to
substitute the real fractal dimension values with comparable fractal
dimensions. The main measures are as follows: First, select a proper method for
a special fractal study. Second, define a proper study area for a city
according to a study aim, or define comparable study areas for different
cities. These suggestions may be helpful for the students who takes interest in
or even have already participated in the studies of fractal cities.
