I am currently testing various models of on-lattice (square lattice in two dimensions) cluster growth for anisotropy. I end up with a cluster, the boundary of which, in case of a truly isotropic model, should look like a circle. In anisotropic cases the cluster boundary will deviate from the circular shape.

I've been told that the Legendre polynomials can be used in order to determine the anisotropy of a cluster, but I'm not exactly sure of how I can use these Legendre polynomials in order to say something about the isotropy of otherwise of the clusters.

I gather that one can write the angular functional dependency of the cluster boundary in terms of a Legendre series due to the orthogonal nature of the Legendre polynomials, but once I've calculated the coefficients of the series I'm not sure how to interpret them in terms of anisotropy of the cluster or even if this is the correct thing to do doing.

Any hints, tips or further reading would be appreciated.

Thanks for your time and help.


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