Fractal or Scaling Analysis of Natural Cities Extracted from Open Geographic Data Sources

Abstract: A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are many disciplines that analyze changes in the Earth’s surface, such as urban planning, detection of melting ice, and deforestation management. Moreover, these disciplines can take advantage of remote sensing for research. This study not only uses satellite imaging to analyze urban areas but also uses check-in and points of interest (POI) data. It uses straightforward means to observe an urban environment using the bottom-up approach and measure its complexity using fractal geometry.   Web 2.0, which has many volunteers who share their information on different platforms, was one of the most important tools in this study. We can easily obtain rough data from various platforms such as the Stanford Large Network Dataset Collection (SLNDC), the Earth Observation Group (EOG), and CloudMade. The check-in data in this thesis were downloaded from SLNDC, the POI data were obtained from CloudMade, and the nighttime lights imaging data were collected from EOG. In this study, we used these three types of data to derive natural cities representing city regions using a bottom-up approach. Natural cities were derived from open geographic data without human manipulation. After refining data, we used rough data to derive natural cities. This study used a triangulated irregular network to derive natural cities from check-in and POI data.   In this study, we focus on the four largest US natural cities regions: Chicago, New York, San Francisco, and Los Angeles. The result is that the New York City region is the most complex area in the United States. Box-counting fractal dimension, lacunarity, and ht-index (head/tail breaks index) can be used to explain this. Box-counting fractal dimension is used to represent the New York City region as the most prosperous of the four city regions. Lacunarity indicates the New York City region as the most compact area in the United States. Ht-index shows the New York City region having the highest hierarchy of the four city regions. This conforms to central place theory: higher-level cities have better service than lower-level cities. In addition, ht-index cannot represent hierarchy clearly when data distribution does not fit a long-tail distribution exactly. However, the ht-index is the only method that can analyze the complexity of natural cities without using images.