Measuring Indian coastline using optimum scale: a case study

Measuring the length or perimeter of zig-zag features, for example, a cloud, a coastline, or a fern using a fixed scale, is always erroneous. Also, it is intuitive that if we reduce the size of the measuring scale, length/perimeter estimate of such zig-zag objects gets bigger and more accurate. Thus, length or perimeter of such objects are considered scale dependent, and hence, it is not a fixed number, rather than that, it depends on the scale used to measure it. Such objects are also called ‘fractal’ which do not have linear geometry. We have developed a new method based on fractal theory to freeze an optimum measuring scale for the measurement of such objects so that a definite length/perimeter of zig-zag objects can be determined. As a case study, we have demonstrated use of this new methodology to measure the length of mainland Indian coast, which comes to about 7567 km. The advantage of this methodology is that it can be applied to any fractal object.