Defining urban and rural regions by multifractal spectrums of urbanization

The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper is devoted to defining urban and rural regions using ideas from fractals. A basic postulate is that human geographical systems are of self-similar patterns associated with recursive processes. Then multifractal geometry can be employed to describe or define the urban and rural terrain with the level of urbanization. A space-filling index of urban-rural region based on the generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanization. The census data of America and China are adopted to show how to make empirical analyses of urban-rural multifractals. This work is not so much a positive analysis as a normative study, but it proposes a new way of investigating urban and rural regional systems using fractal theory.Comment: 21 pages, 4 figures, 6 table

Using fractal analysis in modeling the dynamics of forest areas and economic impact assessment:Maramureș County, Romania, as a case study

This study uses fractal analysis to quantify the spatial changes of forest resources caused by an increase of deforested areas. The method introduced contributes to the evaluation of forest resources being under significant pressure from anthropogenic activities. The pressure on the forest resources has been analyzed for Maramureș County, one of the most deforested counties in Romania. In order to evaluate this, the deforested areas were calculated for the period of 2001–2014, by using the Global Forest Change 2000–2014 database. The Fractal Fragmentation Index (FFI) and Fixed Grid 2D Lacunarity (FG2DL) were used to quantify the degree of fragmentation and dispersion of the forested areas, and thereby the extent to which a forest area is affected by deforestation. The process of quantifying the pressure on forested areas included the creation of a database for the period of 2000–2014 containing economic activities (turnover) related to woody recourses, important indicators of forest exploitation. Taken together, the results obtained indicate a dramatic increase in deforested areas (over 19,122 ha in total for the period of analysis), in Maramureș County

The solutions to uncertainty problem of urban fractal dimension calculation

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.Comment: 27 pages, 3 figures, 8 table

Examining the satellite-detected urban land use spatial patterns using multidimensional fractal dimension indices

2013-2014 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Assessment of textural differentiations in forest resources in Romania using fractal analysis

Deforestation and forest degradation have several negative effects on the environment including a loss of species habitats, disturbance of the water cycle and reduced ability to retain CO2, with consequences for global warming. We investigated the evolution of forest resources from development regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis. We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested and compact organization) in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters). Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby enabling quantification of the uniformity, fragmentation, heterogeneity and homogeneity of forests

Land Cover Change in the Andes of Southern Ecuador — Patterns and Drivers

In the megadiverse tropical mountain forest in the Andes of southern Ecuador, a global biodiversity hotspot, the use of fire to clear land for cattle ranching is leading to the invasion of an aggressive weed, the bracken fern, which is threatening diversity and the provisioning of ecosystem services. To find sustainable land use options adapted to the local situation, a profound knowledge of the long-term spatiotemporal patterns of land cover change and its drivers is necessary, but hitherto lacking. The complex topography and the high cloud frequency make the use of remote sensing in this area a challenge. To deal with these conditions, we pursued specific pre-processing steps before classifying five Landsat scenes from 1975 to 2001. Then, we quantified land cover changes and habitat fragmentation, and we investigated landscape changes in relation to key spatial elements (altitude, slope, and distance from roads). Good classification results were obtained with overall accuracies ranging from 94.5% to 98.5% and Kappa statistics between 0.75 and 0.98. Forest was strongly fragmented due to the rapid expansion of the arable frontier and the even more rapid invasion by bracken. Unexpectedly, more bracken-infested areas were converted to pastures than vice versa, a practice that could alleviate pressure on forests if promoted. Road proximity was the most important spatial element determining forest loss, while for bracken the altitudinal range conditioned the degree of invasion in deforested areas. The annual deforestation rate changed notably between periods: ~1.5% from 1975 to 1987, ~0.8% from 1987 to 2000, and finally a very high rate of ~7.5% between 2000 and 2001. We explained these inconstant rates through some specific interrelated local and national political and socioeconomic drivers, namely land use policies, credit and tenure incentives, demography, and in particular, a severe national economic and bank crisis

Remote Sensing-Based Fractal Analysis and Scale Dependence Associated with Forest Fragmentation in an Amazon Tri-National Frontier

Abstract: In the Amazon, the development and paving of roads connects regions and peoples, and over time can form dense and recursive networks, which often serve as nodes for continued development. These developed areas exhibit robust fractal structures that could potentially link their spatial patterns with deforestation processes. Fractal dimension is commonly used to describe the growth trajectory of such fractal structures and their spatial-filling capacities. Focusing on a tri-national frontier region, we applied a box-counting method to calculate the fractal dimension of the developed areas in the Peruvian state of Madre de Dios, Acre in Brazil, and the department of Pando in Bolivia, from 1986 through 2010. The results indicate that development has expanded in all three regions with declining forest cover over time, but with different patterns and rates in each country. Such differences were summarized within a proposed framework to indicate deforestation progress/level, which can be used to understand and regulate deforestation and its evolution in time. In addition, the role and influence of scale was also assessed, and we found local fractal dimensions are not invariant at different spatial scales and thus concluded such scale-dependent features of fragmentation patterns are here mainly shaped by the road paving