  The conventional mathematical methods are based on characteristic length,
while urban form has no characteristic length in many aspects. Urban area is a
measure of scale dependence, which indicates the scale-free distribution of
urban patterns. Thus, the urban description based on characteristic lengths
should be replaced by urban characterization based on scaling. Fractal geometry
is one powerful tool for scaling analysis of cities. Fractal parameters can be
defined by entropy and correlation functions. However, how to understand city
fractals is still a pending question. By means of logic deduction and ideas
from fractal theory, this paper is devoted to discussing fractals and fractal
dimensions of urban landscape. The main points of this work are as follows.
First, urban form can be treated as pre-fractals rather than real fractals, and
fractal properties of cities are only valid within certain scaling ranges.
Second, the topological dimension of city fractals based on urban area is 0,
thus the minimum fractal dimension value of fractal cities is equal to or
greater than 0. Third, fractal dimension of urban form is used to substitute
urban area, and it is better to define city fractals in a 2-dimensional
embedding space, thus the maximum fractal dimension value of urban form is 2. A
conclusion can be reached that urban form can be explored as fractals within
certain ranges of scales and fractal geometry can be applied to the spatial
analysis of the scale-free aspects of urban morphology.
