Fractals in urban geography: a theoretical outline and an empirical example

Urban Sprawl and Loss of Agricultural Land in Peri-urban Areas of Lagos

“…Fractals suggest complexities, hierarchies, and selfsimilarities, across scales and time, and they have been helpful for understanding periurbanization processes (Batty-Longley 1994, Tannier-Pumain 2005, ThomasFrankhauser-De Keersmaecker 2007, Lifeng-Fang-Zengxiang-Xiaoli 2015. Fractal analysis describes spatial arrangements of built-up areas as well as their quality.…”

“…Highly fragmented built-up areas representing sprawling patterns have low fractal dimensions, whereas compaction and regularity yield higher figures. Fractal dimensions could range from 1 to 2 for simple geometric objects and from 0 to 2 for urban geometry, similar to Sierpinski carpets (Tannier-Pumain 2005). This study employed a five-year interval multi-temporal analysis; the data used were multi-spectral remote sensing data for the available periods (1984, 1990, 2000, 2006, 2011, and 2015) as shown in Table 1 1980National Population Census 1963, 1991, 2006NPC 1991, 2006 Data on built-up urban areas were extracted from ISODATA classified rasters by coding built-up pixels as black and other land cover types as white.…”

“…However, since the 1990s, studies on urban morphology have focussed on cities' fractal geometry (Batty-Longley 1994, Frankhauser 1994, Terzi-Kaya 2011. Few studies have investigated the morphological processes associated with periurbanization (Tannier-Pumain 2005, Lagarias 2007, Terzi-Kaya 2011. The relevant studies focused on the global North and did not comparatively assess similarities and differences between Northern and Southern countries in the speed, scope, and experience of peri-urbanization (Fragkias et al 2012).…”

Assessment of Textural Differentiations in Forest Resources in Romania Using Fractal Analysis

“…Fractal analysis was conducted because of the ability to provide additional textural information on the effects incurred by deforestation which provides complementary information on forest disturbance as compared to traditional per-pixel forest disturbance analysis. Fractalyse 2.4. software (Research Centre ThéMA, University of Franche-Comté, Besançon, France) was employed for fractal analysis [43,44].…”

“…The box-counting algorithm cannot offer a perfect coverage of a fractal pattern, so the number of occupied boxes is approximative. Hence, the estimation of the box-counting dimension requires a sufficient number of levels of analysis [43] but also the largest possible range of box sizes [46].…”