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In this paper, the author uses fractal dimension to measure the tortuosity of two-dimensional trajectory - Using Complexity Measures of Movement for Automatically Detecting Movement Types of Unknown GPS Trajectories

Here are some links about fractal dimension: (1) An introduction to fractals (2) Fractal dimension

How do I calculate the fractal dimension of below trajectory? enter image description here

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    I think the ideas in the paper are not likely to be applicable to a path with 6 steps. Rather, you need a process which (potentially) generates infinitely many steps. – 2017-01-04
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    If you have a *very* long path, it's not too hard to estimate the so-called [box-counting dimension](https://en.wikipedia.org/wiki/Minkowski%E2%80%93Bouligand_dimension) of the path. This is really just an estimate, though, to the fractal dimension that is expected to be generated by the process. – 2017-01-04
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    I've gone through the link but still not sure how the calculation goes. – 2017-01-04

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