Application of Fractal Geometry to Lakes

By Shaikh Yusuf H,  Phathan  J M, Maqdoom Farooqui , Khan A R, Behere S H

Abstract

In this paper we are presenting study of characterization of irregular shapes using the concept of fractal dimension. It is demonstrated that the lakes originating as the result of natural process have ramified boundaries and have detailed structure, where as those arising from artificial conditions like human interference do not exhibit ramified boundaries and details of structure. Lonar Lake (India) originating from striking of meteorite is like a circular cup and does not have structural details. Similarly, Kankaria Lake from Ahmedabad in the heart of the city is surrounded by population from all the side and has a circular shape with a small Island in the middle and a passage leading to the Island. Fractal analysis of the lakes studied, using box counting technique, reveals that all the lakes that came into existence as a consequence of competing natural processes are having self similarity and scale invariance over a larger range length scale and exhibit fractal character with higher fractal dimensions. Where as the Lonar Lake and the Kankaria Lake have very limited degree of self similarity over a shorter range of length scale and thus have a smaller fractal dimension. Richardson Plot technique is also known to be a powerful tool in study of structural and textural details of irregular objects, thus few lake boundaries / contours are also analyzed using this technique. It is clearly seen that the natural lakes show more structural complexity as compare to the lakes resulting from human intervention / interference. However at shorter length scale some textural details are seen that represent textural complexity at shorter length scale.   

 

Key Words : Fractal, Fractal dimension, Fractal Geometry, Self-similarity, Richardson plot, Box counting.

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