Fractal Estimation Using Extended Triangularisation and Box Counting Algorithm for any Geo-Referenced Point Data in GIS

Abstract

Fractal dimension is often used as a measure of how fast length, area, or volume increases or decreases with increase or decrease in scale, or as a measure of complexity of a system. In this paper, input depends only on the Geo-referenced point data where the point event has occurred. An Extended Triangularisation Algorithm is developed to cover the area of point data as a polygon and its perimeter is calculated. Box Counting Algorithm is applied on those point data to calculate the Fractal values, which in turn work as an input to Prediction Plot Linear Model, to show that fractal value increases or decreases as perimeter of Polygon increases or decreases. To validate this model, Crime data was used and its results were analyzed. It provides information to police officials about the intensity of crime, area of patrolling and deputation of police in the sensitivity area. This model could be applied for any Geo-referenced point data such as cancer data, hypertension data and so on.