The Solutions to Uncertainty Problem of Urban Fractal Dimension Calculation
نویسنده
چکیده
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 value 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.
منابع مشابه
The Application of fractal dimension and morphometric properties of drainage networks in the analysis of formation sensibility in arid areas (Case Study, Yazd-Ardakan Basin)
Introduction: Many natural phenomena have many variables that make it difficult to find relationships between them using common mathematical methods. This problem, along with the impossibility of measuring all elements of nature, has led to a major evolution in the way of understanding and explaining phenomena. In this way, one can use the fractal geometry with the theory that many natural phen...
متن کاملComparison Density and Fractal Dimension of Drainage Networks in Different Scales and Precision Different (Case Study: Ilam Watersheds)
Every phenomena in the nature, despite the complexity of the subject, has certain rules and regulations. River pattern and behavior as one of the most complex natural phenomena to this is not an exception. Depending on geomorphologic, climatic, topographic and erosive conditions, the waterways exhibit different patterns and behaviors. One of the parameters which can be achieved using the comple...
متن کاملFractal-wavelet-fusion-based re-ranking of joint roughness coefficients
Nowadays, Barton’s Joint Roughness Coefficients (JRC) are widely used as the index for roughness and as a challenging fracture property. When JRC ranking is the goal, deriving JRC from different fractal/wavelet procedures can be conflicting. Complexity increases when various rankings outcome from different calculation methods. Therefore, using Barton’s JRC, we cannot make a decision based on th...
متن کاملExamining and calculation of non-classical in the solutions to the true elastic cable under concentrated loads in nanofilm
Due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. In this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on Gurtin-Murdoch continuum model to consider surface stre...
متن کاملExamining and calculation of non-classical in the solutions to the true elastic cable under concentrated loads in nanofilm
Due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. In this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on Gurtin-Murdoch continuum model to consider surface stre...
متن کامل